SIMULATION of PHYSICAL LAYER IMPAIRMENTS on COMMUNICATION SYSTEM a Thesis Presented to the Faculty of San Diego

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SIMULATION OF PHYSICAL LAYER IMPAIRMENTS ON

COMMUNICATION SYSTEM

______

A Thesis

Presented to the

Faculty of

San Diego State University

______

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

Electrical Engineering

______

Anupama Prasad

Fall 2012

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ABSTRACT OF THE THESIS

Simulation of Physical Layer Impairments on Communication System by Anupama Prasad Master of Science in Electrical Engineering San Diego State University, 2012

A practical software radio system (SDR) typically suffers from a number of impairments in its migration from a baseband signal at the transmitter to its replication at the receiver. This gives rise to error generation and degradation in overall system performance. Analog impairments at the intermediate frequency (IF) can have many of the same issues as radio frequency (RF) signals and they also include modulator and demodulator mismatches between the I and Q-channels. These RF and analog impairments are not conﬁned to SDR systems but may be found in any digital radio system. The fact that the SDR uses such a large portion of digital logic and direct conversion receiver (DSP) introduces additional impairment concerns that may not be found in a traditional radio design. The digital radio receiver’s main function is to extract the variable RF signals in the presence of interferences and transform them into a close replica of the original signal that is the baseband signal. Therefore the main objective of this thesis is to help one understand the impact of measure and visualize implementation impairments related to both the transmitter and the receiver at all stages of a communication system and how they affect the overall accuracy of the system and its effect on the performance. Towards this end a basic communication system was set up with ability to insert and simulate user selectable levels of multiple implementation impairments and software was created to measure and identify the most common impairments in the design and results are presented through constellation plots, eye diagrams and power spectrum.

TABLE OF CONTENTS

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ABSTRACT ...... iv LIST OF TABLES ...... vii LIST OF FIGURES ...... viii LIST OF ABBREVIATIONS ...... x ACKNOWLEDGEMENTS ...... xii CHAPTER 1 INTRODUCTION ...... 1 2 THE COMMUNICATION CHANNEL ...... 3 3 COMMUNICATION SYSTEM ARCHITECTURE ...... 5 3.1 Tx Architecture ...... 5 3.1.1 Direct (Homodyne) Up Conversion ...... 6 3.1.2 IF (Heterodyne) Up Conversion ...... 8 3.2 Rx Architecture ...... 9 3.2.1 Super-Heterodyne Architecture ...... 10 3.2.2 Direct Conversion Architecture or Zero-IF Architecture ...... 11 3.2.2.1 Merits of Zero-IF Architecture ...... 12 3.2.2.2 De-Merits of Zero-IF Architecture ...... 12 3.2.3 Wideband-IF Architecture ...... 12 3.2.4 Low-IF Architecture ...... 13 4 MODULATION TECHNIQUES AND APPLICATIONS ...... 15 4.1 QPSK ...... 15 4.2 QAM ...... 18 4.2.1 Analog QAM ...... 18 4.2.2 Digital/Quantised QAM ...... 21 4.2.3 Drawbacks of QAM ...... 21 4.2.4 Comparison of QAM with Other Modes ...... 22 4.2.5 Constellation Diagrams for QAM ...... 23

5 SYSTEM MODEL OF MODULATOR AND DEMODULATOR AND THEIR IMPERFECTIONS ...... 24 6 IMPAIRMENTS IN THE COMMUNICATION CHANNEL ...... 26 6.1 Hardware Independent Impairments ...... 27 6.1.1 Additive White Gaussian Noise (AWGN) ...... 27 6.1.2 Multi Path...... 27 6.1.3 Phase/Frequency Offset ...... 29 6.1.3.1 Frequency Offset ...... 29 6.1.3.2 Phase Offset (Phase Error) ...... 30 6.1.4 Symbol Rate ...... 30 6.2 Hardware Inherent Impairments ...... 31 6.2.1 Non-Linearity ...... 32 6.2.2 Power Amplifier Non-Linearities ...... 32 6.2.3 Phase Noise ...... 32 6.2.4 Quadrature Skew ...... 34 6.3 Architecture Specific Impairment ...... 34 6.3.1 DC Offset ...... 34 6.3.2 IQ Imbalance ...... 36 6.3.3 I Q-Gain Imbalance...... 38 6.3.4 IF Filter Ripple or Tilt...... 41 6.3.5 Group Delay ...... 41 6.3.6 Baseband Filtering Problem ...... 44 7 SIMULATION OF THE PHYSICAL LAYER IMPAIRMENT ...... 48 7.1 Model Set Up ...... 48 7.2 Working of Graphical User Interface ...... 52 7.3 Significance of Constellation and Eye Diagram ...... 52 7.4 Simulation Results ...... 53 8 CONCLUSION AND FUTURE WORK ...... 58 BIBLIOGRAPHY ...... 59

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LIST OF TABLES

PAGE

Table 4.1. Summary of Types of Modulation with Data Capacities ...... 22

viii

LIST OF FIGURES

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Figure 2.1. Block diagram of a digital radio communication system ...... 4 Figure 3.1. Block diagram of communications system...... 5 Figure 3.2. Components of an RF Tx...... 5 Figure 3.3. Block diagram of direct up conversion RF Tx...... 6 Figure 3.4. Hardware diagram of direct up conversion...... 7 Figure 3.5. Frequency domain of direct up conversion to RF ...... 7 Figure 3.6. Hardware diagram of direct down conversion...... 8 Figure 3.7. Block diagram of homodyne up converter...... 8 Figure 3.8. Frequency domain of heterodyne up conversion to RF ...... 9 Figure 3.9. Block diagram of a typical heterodyne Rx...... 10 Figure 3.10. Block diagram of DCR architecture...... 11 Figure 3.11. Block diagram of wideband-IF Rx architecture...... 13 Figure 3.12. Low-IF Rx block diagram...... 14 Figure 4.1. Three different types of modulation ...... 16 Figure 4.2. QPSK system Tx and Rx ...... 17 Figure 4.3. QPSK constellation diagram ...... 17 Figure 4.4. Constellations affected by Rx errors ...... 19 Figure 4.5. QAM with different bits per symbol ...... 23 Figure 5.1. System model for M-QAM transceiver ...... 25 Figure 6.1. Common radio impairments linked with Tx and Rx...... 26 Figure 6.2. Eye pattern of filtered baseband signal and eye pattern of signal corrupted by AWGN channel ...... 28 Figure 6.3. Input and output of multipath fading channel ...... 29 Figure 6.4. Symbol-error-rate performances for different compensation scenarios for the frequency-independent portions of amplitude and phase ...... 31 Figure 6.5. 1-dB compression point...... 33 Figure 6.6. Power amplifier non linearities...... 33 Figure 6.7. Phase noise in 4-QAM, 16-QAM, and 64-QAM signals ...... 34

Figure 6.8. Quadrature skew in 4-QAM, 16-QAM, and 64-QAM signals ...... 35 Figure 6.9. DC offset in 4-QAM, 16-QAM, and 64-QAM signals ...... 36 Figure 6.10. IQ-offset ...... 37 Figure 6.11. Various point of IQ-imbalances...... 37 Figure 6.12. Effect of IQ-imbalance on 16-QAM constellation plot...... 38 Figure 6.13. Effects of gain imbalance...... 39 Figure 6.14. IQ-gain imbalance (excess I-gain and reduced Q-gain relative to the ideal constellation locations) ...... 40 Figure 6.15. IQ-gain imbalance in 4-QAM, 16-QAM, and 64-QAM signals...... 40 Figure 6.16. Zoomed frequency response showing ripple in the filter...... 41 Figure 6.17. Filter tilt...... 42 Figure 6.18. Inband ripple...... 42 Figure 6.19. Phase distortion ...... 43 Figure 6.20. Group delay ripple...... 43 Figure 6.21. Group delay versus deviation from linear phase ...... 44 Figure 6.22. Gain and phase contributions of IQ mismatched LPFs...... 45 Figure 6.23. Vector diagram and EVM versus time for wrong roll-off factor ...... 46 Figure 6.24. Vector diagram and EVM versus time for correct roll-off factor ...... 47 Figure 7.1. Graphical user interface for the system...... 49 Figure 7.2. Architecture of the communication system used...... 50 Figure 7.3. IQ-modulator...... 51 Figure 7.4. IQ-imbalance...... 51 Figure 7.5. DC insertion...... 52 Figure 7.6. User activity of the graphical user interface...... 53 Figure 7.7. Shaping filter output...... 54 Figure 7.8. Channel without noise output...... 54 Figure 7.9. The channel with the imbalances introduced like gain and phase imbalance...... 55 Figure 7.10. Matched filter output...... 55 Figure 7.11. Matched filter output with dc offset introduced...... 56 Figure 7.12. Matched filter output with filter tilt...... 56 Figure 7.13. Matched filter output with inband ripple...... 57 Figure 7.14. Matched filter output with mixer phase noise...... 57

LIST OF ABBREVIATIONS

ADC Analog-to-Digital Converter AGC Automatic Gain Control ASK Amplitude Shift Keying AWGN Additive White Gaussian Noise BER Bit Error Rate BP Band Pass BPSK Binary PSK Codec coder-decoder CPE Common Phase Error DAC Digital-to-Analog Converter DBPSK Differential Binary PSK DC Direct Current DCR Direct Conversion Receiver DQPSK Differential QPSK DSP Digital Signal Processor EVM Magnitude of Error Vector FSK Frequency Shift Keying GMSK Gaussian Minimum-Shift Keying GUI Graphical User Interface I In-Phase ICI Inter-Carrier-Interference IF Intermediate Frequency IR Image Rejection ISI Inter-Symbol Interference LNA Low Noise Amplifier LO Local Oscillator

LP Low Pass LPF Low Pass Filter OFDM Orthogonal Frequency-Division Multiplexing PAPR Peak-to-Average-Power-Ratio PSK Phase Shift Keying Q Quadrature Phase QAM Quadrature Amplitude Modulation QPSK Quadrature PSK RF Radio Frequency Rx Receiver SNR Signal-to-Noise Ratio TOI Third-Order Intercept Tx Transmitter UI User Interface VSA Vector Signal Analysis

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ACKNOWLEDGEMENTS

I sincerely thank my advisor Prof. fredric j. harris for his valuable guidance and encouragement throughout the time I have been working with him on my courses as well as on my thesis. He has been instrumental and been a guiding light in helping me realize my passion towards signal processing. I would also like to thank my committee members Prof. Mahashweta Sarkar and Prof. Morteza Monte Mehrabadi for agreeing to be a part of my thesis committee. Finally I would like to thank Amma, my parents, my husband and my entire family for their endless love and support. It would not have been possible without them.

CHAPTER 1

INTRODUCTION

The impairment of communication channel in a wireless environment can affect significantly the performance of communication system. It is a widely known fact that radio channels are subject to channel impairments and they could be noise, signal fading, jamming, multipath, etc. This leads to the assigned radio channel to be unclean and full of distortion and then even the most efficient coding schemes that are available for combating these interferences can fail. These impairments directly affect the overall performance and efficiency of the system. As mentioned above about noise, it can be defined as an undesirable random fluctuation in a signal. As can be expected, the presence of noise alters a signal and, depending upon its intensity, can render it unusable. As such, signals that are being used to convey information, noise can corrupt the signal and there may be loss of information in that particular signal because of noise as an impairment. Communication systems, which exist for the purpose of information transfer, need to be able to handle noise in a way that does not degrade their performance. Noise in communication systems is measured in terms of a quantity called the signal-to-noise ratio, or SNR. A higher value of SNR corresponds to a clearer signal. In analog systems noise is cumulative. Once noise enters the system, it never leaves, and noise produced in any part of a transmission adds to the already existing noise levels whereas in digital communication systems, it convert analog signals into digital data, store and transmit them, then convert them back to analog. Digital data has the advantage of being discrete. Although they are not completely unsusceptible to noise, they lend themselves to certain techniques that can prevent noise from accumulating. All communication systems have a physical layer, composed of a transmitter (Tx), a channel and a receiver (Rx). Tx encodes digital information on to a waveform suited for transmission over the channel. Multipath present in the communication channel distort the transmitted waveform by causing inter-symbol interference (ISI) that occurs when energy from one symbol spills over into neighboring symbols and they smear into each other in time

2 domain in the received waveform. Interference and noise in the channel also contribute to distortion in the transmitted signal. ISI and the channel noise distort the amplitude and phase of the transmitted signal, causing erroneous bit detection at the Rx. The ever growing importance of data communication based devices in everyday life necessitates economical solutions that offer high data rates with high fidelity. Thesis organization is as follows:  Chapter 2 provides an overview of the communication channel, its constraint and some information on radio communication system.  Chapter 3 is based on communication system architecture, both related to Tx and Rx and what stage they get affected by the impairments or distortion.  Chapter 4 explains the various kind of modulation schemes and application and the ones used the simulation is explained in detail.  Chapter 5 deals with the impairments in the communication channel and is discussed on the basis of their hierarchy.  Chapter 6 gives a detailed explanation of a modulator and demodulator and at what point in the system does they get affected by the impairments.  Chapter 7 provides the description of the software that has been created with a help of a basic communication system and simulated for studying and visualizing the defects at various points in the communication channel.  Chapter 8 provides conclusions of the proposed work and also what further can be added to the software in future to make it more user friendly.

CHAPTER 2

THE COMMUNICATION CHANNEL

Communication systems exploit the propagation of electromagnetic waves in a medium to convey information. The medium is the electromagnetic spectrum in radio transmission and copper wire in the case of wired line communications such as those in voice band or ADSL modems. The properties of the medium determine two fundamental constraints that every communication system needs to deal with [1]: 1. Bandwidth constraint: data transmission systems work best in the frequency range over which the medium behaves linearly; over this passband a signal is guaranteed to be received with only phase and amplitude distortions, which can be remedied by linear filters. Extraneous factors such as legal or technical requirements may impose additional restrictions over the frequency range a Tx may employ. 2. Power constraint: the power of a transmitted signal is limited by factors such as range of linear operation of the medium and transmission circuitry, extraneous factors such as legal statutes, or design requirements such as operating time of battery-powered mobile devices. Besides, all analog media are vulnerable to interference from adjacent transmission bands (as in the case of radio channels) or electrical interference (as in the case of AC hum over audio lines). Noise floor, the noise level which cannot be removed and must be endured in the transmission scheme, and power constraints limit the achievable SNR with respect to the channel’s noise floor and in turn SNR determines the reliability of the data transmission scheme. The objective of communication system design is to maximize the amount of information that can be reliably transmitted across a given channel (see Figure 2.1 [2]). Digital communication system has the additional constraint [3] to operate entirely in the discrete-time domain up to the interface with the physical channel. Implying that:  At the Tx, the signal is synthesized, shaped and modulated in the discrete-time domain and is converted to a continuous-time signal just prior to transmission;  At the Rx, the incoming signal is sampled from the channel and demodulation, processing and decoding is performed in the digital domain.

Figure 2.1. Block diagram of a digital radio communication system. Source: Agilent Technologies. (n.d.). Testing and troubleshooting digital RF communications receiver designs [Online]. Available: http://my.ece.ucsb.edu/yorklab/Useful%20Stuff/ Tutorials/Testign %20DigitalRF%20Receivers%20AN1314.pdf.

CHAPTER 3

COMMUNICATION SYSTEM ARCHITECTURE

Communications signals are processed in several stages across digital domain and analog domain as shown in the Figure 3.1.

Figure 3.1. Block diagram of communications system.

3.1 TX ARCHITECTURE The radio frequency (RF) Tx section from the diagram in Figure 3.1 can be drawn as shown in Figure 3.2.

Figure 3.2. Components of an RF Tx.

In an IQ-based RF Tx, digital signal processing, signal perform modulation, interpolation, and pulse-shaped filtering to a digital baseband signal, so there is minimal error. However, in the analog domain, the signal is prone to much analog impairment. Figure 3.3 is the architecture of a typical Tx at the component level [4].

Figure 3.3. Block diagram of direct up conversion RF Tx.

As shown in Figure 3.3, a Tx processes both digital signals and analog signals [4]. On the analog side, a direct up converter requires the generation and mixing of two analog baseband signals with a local oscillator (LO). The translation of a digital message signal into digitally up converted in-phase (I) and quadrature-phase (Q) signals occurs with little or no error but once digital baseband signals enter the analog domain through digital-to-analog conversion, they become vulnerable to multiple sources of error such as frequency response of the digital-to-analog converter (DAC), baseband synchronization (quadrature skew), IQ- gain imbalance, and phase noise. The effect of each of these errors depends, at least in part, on the mechanism of up conversion or down conversion that is used in the system. Typical approaches to up conversion and down conversion are direct up conversion (shown in Figure 3.3) and heterodyne (intermediate frequency [IF]) up conversion.

3.1.1 Direct (Homodyne) Up Conversion Homodyne or direct up conversion is a common technique preferred because of its simplicity and cost effectiveness. In a homodyne up conversion implementation, analog I and Q signals are mixed with respective I and Q versions (90° out of phase) of a LO [4]. The LO is the carrier frequency of the RF signal and I and Q components that are translated are then summed (or subtracted) to produce the final RF signal. The hardware diagram of direct up conversion is given in Figure 3.4. Direct up conversion in frequency domain translates baseband I and Q signals centered at a zero frequency to an RF frequency. The frequency response of the signals centered at zero frequency is shown in Figure 3.5 [4]. Figure 3.5 illustrates that in direct up conversion each baseband signal is mixed with an LO at the center frequency of the RF signal and each baseband I and Q signal is half the

Figure 3.4. Hardware diagram of direct up conversion.

Figure 3.5. Frequency domain of direct up conversion to RF. Source: National Instruments. (2007). Sources of error in IQ based RF signal generation [Online]. Available: http://sine.ni.com/nip dfgenerator/nipdfgenerator? pageURL=http://www.ni.com/white- paper/5657/en&clientAppName =dz&dotsPerPixel=&dotsPerPoint=. bandwidth of the RF signal. Therefore when, two DACs are used in conjunction in a direct frequency translation approach, the maximum modulation bandwidth for the RF signal is exactly twice the bandwidth of each DAC. Direct down conversion [4] is the reverse of direct up conversion and uses an architecture that is reverse replica of direct up conversion as shown in Figure 3.6. Direct down converter uses two analog signal mixers as shown in Figure 3.6 to mix the RF signal with an I and Q version of the LO. These mixed signals are the baseband I and Q signals, which are filtered and then digitized with an analog-to-digital converter (ADC). As the two oscillators are mixed with RF signal that are exactly 90° out of phase, the digitized baseband I and Q signals provide the Rx with an estimation of the phase and amplitude of the RF signal.

Figure 3.6. Hardware diagram of direct down conversion.

3.1.2 IF (Heterodyne) Up Conversion The heterodyne method is the second approach for up and down conversion and it uses IF. This method involves the baseband I and Q signals first undergo direct up conversion to an IF and then mixed with an addition LO to reach the RF frequency. A typical Tx using the heterodyne approach to up conversion is illustrated in Figure 3.7.

Figure 3.7. Block diagram of homodyne up converter.

As Figure 3.7 illustrates, heterodyne (IF) up conversion [4] is a slightly more complex method of up conversion and can be done in a digital manner as well. The IF waveform in the up converter is generated by a single DAC before being up converted to the RF signal. Typical intermediate frequencies range between 15 and 170 MHz and at higher frequencies, require a high-bandwidth DAC and it also depends upon the IF frequency. The frequency response of analog up conversion is illustrated in Figure 3.8 [4].

Figure 3.8. Frequency domain of heterodyne up conversion to RF. Source: National Instruments. (2007). Sources of error in IQ based RF signal generation [Online]. Available: http://sine.ni.com/nipd fgenerator/nipdfgenerator ?pageURL=http://www.ni.com/white- paper/5657/en&clientAppName =dz&dotsPerPixel=&dotsPerPoint=.

As Figure 3.8 illustrates, the LO’s position for a single-stage IF up converter should be at the frequency difference of the RF carrier and the IF and the mixing process at the same time also produces an image at the frequency difference of the LO and the IF. Thus, for devices using this method, those filters must be used which can help to ensure that the image does not affect adjacent channels. An alternative is to use a higher frequency IF to ensure that the image is farther removed from the desired RF signal. At times, a series of mixers are used with multiple filters for signal image rejection. The sources of error in heterodyne up conversion are slightly different than from the direct up conversion approach as heterodyne uses digital signal processing to directly up convert baseband I and Q waveforms to the IF, they become immune to the phase and gain errors associated with analog signal mixing. They typically require wider bandwidth DACs, which are more susceptible to errors like passband flatness, harmonic distortion and timing errors. Therefore for most commercial applications, direct up conversion is the most common approach because of its simplicity and cost-effectiveness.

3.2 RX ARCHITECTURE A receiver is an integral part of a communication system because it is here that the incoming signal is amplified, demodulated and decoded and the various impairments are introduced [5]. It is therefore important to know the different kind of Rx architecture and they are as mentioned below.

3.2.1 Super-Heterodyne Architecture Super heterodyne Rx, is used in about 98% of all radio Rx because of its high selectivity and sensitivity. In a super heterodyne Rx, the input signal is first amplified at RF in a tuned stage, then converted by an offset-frequency LO to a lower IF, and substantially amplified in a tuned IF “strip” containing highly-selective passive band pass (BP) filters. The IF must be high enough to force the image channel in the stopband of the RF preselection filter or the antenna [6], otherwise the IF filter will pass this channel unattenuated in its own image passband. These considerations determine the familiar intermediate frequencies used in radio and TV Rx. It is dual conversion architecture, with RF being down-converted to IF in the first stage and from IF to baseband signal in the second stage. The block diagram of heterodyne Rx architecture is shown in Figure 3.9. LNA

Figure 3.9. Block diagram of a typical heterodyne Rx.

The pre selection filter removes out of band signal energy and partially rejects image band signals from the incoming RF signal. The low noise amplifier (LNA) amplifies the signal to suppress contribution of noise from the succeeding stages and the image rejection (IR) filter attenuates the signals at image band frequencies coming from LNA [7]. Mixer-I down converts the signal exiting the IR filter from RF frequency to IF frequency with the output of a LO. Next, channel selection is achieved through a BP filter to allow the IF bands of interest and reject others. This filter is critical in determining the sensitivity and selectivity of a Rx. Since channel selection is done at IF, the LO requires an external tank for good phase noise performance. I or frequency modulation, down conversion to the baseband requires both I and Q components of the signal. IF signal is down converted into I and Q

components for digital signal processing at Mixer-II. The low pass filter (LPF) acts as a channel reject filter and performs anti-aliasing. Pros include: 1. IR filter and channel selection. 2. Good sensitivity and selectivity. Cons include: 1. High Q filter. 2. High performance oscillator or LO. 3. LNA output impedance matched to 50 ohm is difficult. 4. Integration of HF image reject filter is a major problem.

3.2.2 Direct Conversion Architecture or Zero-IF Architecture Direct conversion receiver (DCR) translates the channel of interest directly from RF to baseband (IF=0) in a single stage, hence the name Direct conversion or Zero-IF [7] architecture. Double-sideband amplitude modulated signals can be, down converted using simple mixers, but frequency and phase modulated signals must be down converted using with quadrature mixers to avoid loss of information because of the overlap in the positive and negative parts of the spectra. The block diagram of homodyne or DCR architecture is illustrated in the Figure 3.10.

Figure 3.10. Block diagram of DCR architecture.

Homodyne Rx are lower cost because of their relative simplicity. The duplexing or preselection filter isolates the send and receive chains and aids in filtering out-of-band noise.

Since RF signals are directly converted to baseband, image problem does not exist and there is no IR filter. DCRs need to be DC coupled from mixer to baseband to avoid loss of information in DC and low frequency signals. But offsets in signal chain result in distortion, requiring DC offset cancellation or calibration circuits to overcome this problem.

3.2.2.1 MERITS OF ZERO-IF ARCHITECTURE 1. Less hardware requirement. 2. No image problem, so image filter is not required. 3. LPF is sufficient for filtering as there is no IF stage. 4. Amplification occurs at BB stage, resulting in power savings. 5. Because there is no image reject filter between LNA and mixer, they do not require 50-ohm impedance matching.

3.2.2.2 DE-MERITS OF ZERO-IF ARCHITECTURE 1. DC off-set error: This is the most serious problem in the baseband section of homodyne Rx. 2. LO leakage: There is imperfect isolation between LO port and input port of mixer and LNA due to capacitive and substrate coupling. This causes LO feed though from LO port to the input port of the mixer and LNA, which mixes with original LO in a phenomenon called self-mixing, and produces DC offsets in the mixer output, causing saturation of following stages in the Rx chain. 3. In ICs, circuits are realized in differential mode, mismatches in signal paths introduce DC offsets and degrade SNR. 4. Since LO frequency is same as carrier frequency, it leaks from Rx to antenna which interferes with same frequency-band Rx. 5. Flicker noise from an active device contaminates BB signal. 6. IQ mismatch. 7. Even order distortion.

3.2.3 Wideband-IF Architecture Wideband-IF Rx is a dual conversion architecture in which data is down converted from RF to IF in the first stage, and from IF to baseband in the second stage [7]. The block diagram of wideband-IF Rx architecture is shown in Figure 3.11.

Figure 3.11. Block diagram of wideband-IF Rx architecture.

In this architecture all the RF channels are complex mixed and down converted to fixed IF after preselection filtering and amplification. In the second stage, an IR mixer does complex mixing and translates IF to BB using a tunable channel select frequency synthesizer. All image frequencies are cancelled in this process. If the IF chosen is high enough, additional IR may be obtained from the RF front-end preselection filter. Channel selection is performed at baseband by using programmable integrated channel select filter. Since LO-1 is fixed frequency synthesizer generated by crystal controlled oscillator, good phase noise performance is obtained. Channel tuning is achieved by using programmable frequency synthesizer at IF.

3.2.4 Low-IF Architecture In low-IF Rx architecture all the RF signals are translated to low-IF frequency and subsequently down converted to BB signal in digital domain. Low-IF architecture [7] combines the advantages of both heterodyne and homodyne Rx. The block diagram of low-IF Rx architecture is shown in Figure 3.12. After pre selection filtering and amplification, all RF channels are quadrature mixed and down converted to low-IF containing both wanted and unwanted signals. The IF frequency is just one or two channels bandwidth away from DC [5], which is just enough to overcome DC offset problems. It is then amplified and filtered before being sampled by ADC. Since the ADC samples both desirable and undesirable signals, there are strong constraints on ADC dynamic range requirements. The AC-coupled signal path to ADC eliminates the need of DC offset compensation circuitry. Sampled digital data is fed to image reject mixer which is implemented in digital domain.

Figure 3.12. Low-IF Rx block diagram.

CHAPTER 4

MODULATION TECHNIQUES AND APPLICATIONS

Selection of modulation techniques depends on the requirements of a particular application, no modulation technique is always superior to another. For example, PSK is employed in the IEEE 802.11b standard for defining wireless LAN systems, Bluetooth 2, biometric passports and credit cards. Bit rate required is an important factor influencing the choice of modulation scheme. Differential binary phase shift keying (DBPSK) is typically employed for the basic rate of 1 MBit/s, differential QPSK (DQPSK) at 2 MBit/s and QPSK for bit rates of up to 11 MBit/s. Binary PSK (BPSK), a constellation with only two points, is used primarily due to its simplicity. 8-PSK, with an error rate similar to 16-quadrature amplitude modulation (QAM), but lower data rate is usually not used in standards.

4.1 QPSK Several methods of modulation exist, of which the three main types are frequency shift keying (FSK), amplitude shift keying (ASK) and phase shift keying (PSK) as illustrated in Figure 4.1 [8]. Quadrature PSK (QPSK) is a popular modulation technique as it can transmit at data rates up to 30 Mbps, and only requires 200 mW total baseband power. There are other modulation schemes said to be capable of comparable performance, such as Gaussian minimum-shift keying (GMSK) and orthogonal frequency-division multiplexing (OFDM). However, these methods are more complicated and it has been shown that OFDM is more efficient than QPSK, they have also given a number of challenges that would occur with it, such as high sensitivity to phase noise. QPSK encodes a symbol in 2 bits, thus needing four phases as shown in the constellation diagram in Figure 4.2 [8]. The I and Q components can then be modulated with carrier waves that are 90° out of phase. Figure 4.3 [8] shows how the I and Q components can be extracted at the demodulator using the same carrier waves as in the modulator.

PSK

ASK

FSK

Figure 4.1. Three different types of modulation. Source: D. Easton, J. Snowdon, and D. Spencer. (2008). Quadrature phase error in receivers [Online]. Available: http:// users.ecs.soton.ac.uk/jrs105/finalgdpreportgroup14.pdf.

Equation 4.1 gives a mathematical background behind this for the I component, and a similar calculation can be performed for the Q component: x0i(t) = (xi(t) cos(ωt) + xq(t) sin(ωt))cos(ωt) (4.1) = xi(t) cos^2(ωt) + xq(t)sin(ωt)cos(ωt) = 1/2xi(t)(1 + cos(2ωt)) + 1/2xq(t)sin(2ωt) Using a LPF to remove the 2ω terms gives the initial transmitted I signal at a lower gain, which is simple to correct if necessary [8].

Figure 4.2. QPSK system Tx and Rx. Source: D. Easton, J. Snowdon, and D. Spencer. (2008). Quadrature phase error in receivers [Online]. Available: http://users.ecs.soton.ac.uk/jrs105/finalgdpreportgroup14.pdf.

Figure 4.3. QPSK constellation diagram. Source: D. Easton, J. Snowdon, and D. Spencer. (2008). Quadrature phase error in receivers [Online]. Available: http://users.ecs.soton.ac.uk/jrs105/final gdpreportgroup14.pdf.

An ideal signal is obtained at the output only if the two components have equal gain and are out of phase by exactly 90° (orthogonal). In the real world, however, the received signal s0 (t) contains a gain error, notated by , and a phase error Ψ as shown in Equation 4.2. A DC offset can also occur as well but these are simple to correct so can be ignored: s0(t) = (1 + )xi(t) cos(ωt) + xq(t)sin(ωt + Ψ ) (4.2) Both gain and phase imbalances manifest themselves as creates a shift in the constellation as shown in Figure 4.4(a) [8] and 4.4(b) [8], respectively. Gain errors can be corrected simply by introducing a variable gain, but phase errors are more complicated and can have a greater effect on the bit-error rate (BER). Few possibilities of where these errors can be formed are inaccurate transmission lines at RF, DC offsets in mixers, and phase imbalance in the power combiner and mixers. A carrier frequency ω that is not matched to the input carrier frequency which can bring offset is illustrated by an offset δω in Equation 4.3 This results in the I and Q outputs taking the forms shown in Equation 4.4 x0i(t) = (xi(t)cos (ωt) + xq(t)sin (ωt)) cos ((ω + δω )t) (4.3) x0i(t) = 1/2xi(t)cos (δω t) - 1/2xq(t)sin (δω t) (4.4) x0q(t) = 1/2xi(t)sin (δω t) - 1/2xq(t)cos (δω t) These equations show that the Q-channel leaks into the I-channel and vice versa, where the magnitude of the leakage increases with δω. This causes rotation of the constellation diagram as shown in Figure 4.4(c) [8], which can be stopped by symbol recovery.

4.2 QAM Quadrature amplitude modulation (QAM) is a signal in which two carriers shifted I by 90° are modulated and the resultant output consists of both amplitude and phase variations [9]. Since both amplitude and phase variations are present it may also be considered a combination of amplitude and phase modulation.

4.2.1 Analog QAM Analog versions of QAM are typically used to enable carrying multiple analog signals on a single carrier. For example, it is used in PAL and NTSC television systems [10], to carry

Figure 4.4. Constellations affected by Rx errors. Source: D. Easton, J. Snowdon, and D. Spencer. (2008). Quadrature phase error in receivers [Online]. Available: http://users.ecs.soton.ac.uk/jrs105/finalgdpreportgroup14.pdf.

(a) Gain Error

(b) Phase Error

the components of chroma or color information over different channels. In radio applications a system known as C-QUAM is used for AM stereo radio. Here the different channels enable the two channels required for stereo to be carried on the single carrier.

4.2.2 Digital/Quantized QAM In digital transmission applications [9], QAM enables higher data rates than ordinary amplitude modulated and phase modulated schemes. As with phase shift keying, the number of points at which the signal can rest, i.e. the number of points on the constellation, is indicated in the modulation format description, e.g. 16-QAM uses a 16 point constellation. QAM constellation points are normally arranged in a grid with equal vertical and horizontal spacing and as a result the most common forms of QAM use a constellation with the number of points equal to a power of 2 such as, 2, 4, 8, 16 and it goes on. Using higher order modulation formats allows transmitting more bits per symbol, but has the downside of being more susceptible to noise and data errors as the points are closer together.

4.2.3 Drawbacks of QAM 1. Susceptibility to noise is more because the states are closer together, even a lower noise is sufficient to move the signal to a different decision point and cause data corruption. Rx that are used for phase or frequency modulation may use

limiting amplifiers to remove any amplitude noise and thereby improve the noise resilience. 2. When a radio Tx amplifies phase or frequency modulated signal, there is no need to use linear amplifiers, linearity must be maintained when using QAM as it contains amplitude component. However, since linear amplifiers are less efficient and consume more power, this makes them less attractive for mobile applications.

4.2.4 Comparison of QAM with Other Modes Some radio communication systems dynamically change the modulation scheme dependent upon the link conditions and requirements like signal level, noise, data rate required, etc. Table 4.1 [9] compares various forms of modulation.

Table 4.1. Summary of Types of Modulation with Data Capacities

Modulation Bits per Symbol Error Margin Complexity

OOK 1 1/2 0.5 Low

BPSK 1 1 1 Medium

QPSK 1 1 / √2 0.71 Medium

16-QAM 4 √2 / 6 0.23 High

64-QAM 6 &radix / 14 0.1 High

Source: I. Poole. (n.d.). What is QAM - quadrature amplitude modulation [Online]. Available: http://www.radio-electronics.com/info/rf-technology-design/pm-phase- modulation/what-is-qam-quadrature-amplitude-modulation-tutorial.php.

As QAM achieves greater distances between adjacent points in the IQ plane by distributing the points more evenly, points on the constellation are more distinct and data errors are reduced. Hence, it is possible to transmit more bits per symbol. However, for the energy of the constellation to remain the same, points on the constellation must be closer together and the transmission becomes more susceptible to noise. This results in a higher bit error rate (BER) than for the lower order QAM variants, thus forcing a tradeoff between obtaining higher data rates and maintaining acceptable BERs for radio communications system.

4.2.5 Constellation Diagrams for QAM Constellation diagrams show different positions for the states within different forms of QAM. As the order of modulation increases, so does the number of points on the QAM constellation diagram. The diagrams in Figure 4.5 [11] show constellation diagrams for a variety of formats of modulation.

Figure 4.5. QAM with different bits per symbol. Source: Agilent Technologies. (2010). Digital signal analysis [Online]. Available: http://www.home.agilent.com/upload/cmc_upload/All/PPT4_AGILENT_La- modulation-numerique.pdf?&cc=US&lc=eng.

CHAPTER 5

SYSTEM MODEL OF MODULATOR AND DEMODULATOR AND THEIR IMPERFECTIONS

A full system model is composed of a QAM modulator and demodulator, a quadrature modulator and demodulator, an RF amplifier, a LNA, an automatic gain control (AGC), LPFs, and antennas (see Figure 5.1 [12]). Data streams to and from the coder- decoder (codec) form its input and output. In QAM modulators, transmitted symbols are first mapped to a constellation with M signal points differing in both phase and amplitude in the lattice. The discrete signal points excite a shaping filter to generate the baseband signal in two channels that are called I-channel and Q-channel. The received two channel baseband signals are filtered by a matching filter and sampled to get the received signal points, which are then decided to be received symbols in the QAM demodulator. The quadrature modulator up converts the two-channel baseband signals to an RF band. The carriers for both channels are generated by a Tx LO generator [12], which is typically a PLL with quadrature outputs. The baseband IQ signals are up converted using an image-rejection mixer with the single side band output. The quadrature demodulator down converts the received RF signal to IQ baseband signals by mixing it with the quadrature carriers generated by an Rx LO generator. The Tx and Rx LOs can be generated with the same PLL synthesizer if the uplink and downlink operate at the same frequency. The two LPFs in the Rx path provide the baseband filtering. The RF amplifier, the LNA, and the AGCs are used to adjust the received and transmitted signal powers. This system is vulnerable to several imperfections introduced from different components and these effects should be carefully considered. Transceiver building blocks such as the LNA, the AGC, and the RF amplifier can introduce noise and nonlinearity. Imperfections like amplitude imbalance, phase imbalance, DC offset, and phase noise is presented in the LOs in the quadrature modulator and demodulator.

Figure 5.1. System model for M-QAM transceiver. Source: Z. Q. Chen and F. F. Dai, “Effects of LO phase and amplitude imbalances and phase noise on M-QAM transceiver performance,” IEEE Trans. Industrial Electron., vol. 57, pp. 1505-1517, May 2010.

CHAPTER 6

IMPAIRMENTS IN THE COMMUNICATION CHANNEL

Impairment is anything which distorts the signal and degrades the quality of the transmission. Figure 6.1 shows the common radio impairments linked with Tx and Rx.

Figure 6.1. Common radio impairments linked with Tx and Rx.

6.1 HARDWARE INDEPENDENT IMPAIRMENTS Hardware independent impairments are those impairments that do not depend on the hardware and mostly depend on factors like frequency band.

6.1.1 Additive White Gaussian Noise (AWGN) AWGN is a simplified channel model in which the only impairment is a linear addition of wideband or white noise with constant spectral density (expressed as watts per hertz of bandwidth) and Gaussian distribution of amplitude [13]. The effects of fading, frequency selectivity, interference, nonlinearity or dispersion are ignored to create tractable mathematical models which are useful for understanding the inherent behavior of a system. Sources of wideband Gaussian noise are extremely varied, such as shot noise, black body radiation from the earth and other warm objects, and from celestial sources such as the Sun. Figure 6.2 [14] are of an eye diagram of a signal corrupted by AWGN channel. The AWGN channel [15] ignores effects of multipath, terrain blocking, interference, etc. It is a good model for many satellite and deep space communication links but not for terrestrial links. It may still be used in terrestrial path modeling to simulate background noise of the channel under study.

6.1.2 Multi Path In a radio communication system, there are multiple paths for a signal to travel from a Tx to a Rx, while some may be direct, mostly these paths are encumbered by obstructions which cause components of the signal to be reflected and refracted before reaching the Rx. Therefore, it can be said that multipath is an impairment caused by radio signals reaching the receiving antenna by more than one path. It may be caused by atmospheric ducting, ionospheric reflection and refraction and reflection from water bodies and terrestrial objects such as mountains and buildings. When the signal components merge at the Rx [14], they have each traveled different physical lengths and consequently suffered different transmission delays due to finite propagation velocity. The superposition of these signals at the Rx results in interference, which may be constructive or destructive, depending on the relative delays involved. Since the environment changes with time, it causes signal variation. Motion of terminals also influences signals- often a small change in terminal position may change the

Figure 6.2. Eye pattern of filtered baseband signal and eye pattern of signal corrupted by AWGN channel. Source: Z. Zeng. (2000). Digital communication via multipath fading channel [Online]. Available: http://www.ee.iastate.edu/~russell/cpre537xf00/Project s/Zeng.pdf. propagation paths significantly enough to impact the strength of received signals. Figure 6.3 [16] shows how the channel gets affected due to multipath. Signal fading generally causes large fluctuations in the received signal amplitude [16]. Multipath causes destructive (leading to fading) and constructive interference, and

Figure 6.3. Input and output of multipath fading channel. Source: Wikipedia. (2012). Multipath propagation [Online]. Available: http://en.wikipedia.org/wiki/Multipath_propagation. phase shifting of the signal. When the magnitudes of the signals arriving by the various paths are distributed along Rayleigh distribution, it is known as Rayleigh fading. When one component (typically a line of sight component) dominates, a Rician distribution provides a more accurate model, and the phenomenon is called fading.

6.1.3 Phase/Frequency Offset Frequency and phase offset are major deterrents to the capacity a communication system can achieve and systems need simple, economical and efficient signal processing algorithms [17] to mitigate their effect. Frequency offset and phase noise has the same impact on the signal except for the fact that frequency offset is deterministic while phase noise is random.

6.1.3.1 FREQUENCY OFFSET Frequency offset is the frequency mismatch between the RF signal received at the Rx and the Rx oscillator which is used to down convert the RF signal to IF frequency or baseband frequency. It can be caused by:

1. Frequency mismatch between the transmit and receive oscillators. 2. Time variations in the channel cause the transmitted RF frequency to vary in time, known as Doppler shift.

6.1.3.2 PHASE OFFSET (PHASE ERROR) Phase offset/phase error is the time difference between the reference input clock and the feedback input to the phase detector of a PLL [18]. It may be of two types as defined below.

6.1.3.2.1 Static Phase Offset Static phase offset (t ()) is the time difference between the averaged input reference clock and the averaged feedback input signal when the PLL is in locked mode. The time difference between the input of the PLL and its feedback is averaged over several thousand periods. This method excludes jitter.

6.1.3.2.2 Dynamic Phase Offset Dynamic phase offset (td ()) or tracking skew is the phase difference between input clock and output clock due to the PLLs inability to instantaneously update the output clock when the period of the input clock changes and dynamic and it includes jitter.

6.1.4 Symbol Rate A symbol is a waveform, a state or a significant condition of the communication channel that persists for a fixed period of time [19]. A sending device places symbols on the channel at a fixed and known symbol rate, which the receiving device should detect to reconstruct the transmitted data. A symbol may correspond directly to a unit of data such as each symbol may encode one or several binary digits or ‘bits’ or the data may be represented by the transitions between symbols or even by a sequence of many symbols, the rate of transition being the symbol rate. When taking into consideration modulation schemes [20], QPSK has four symbols each containing two bits, while 16-QAM has 16 symbols each containing four bits of data. While 16-QAM transports more data than QPSK, it is more susceptible to signal impairment because the symbols are closer together and consequently more difficult for the Rx to demodulate. Since symbols containing multiple bits of data, data rate can be defined as:

Data Rate = # Bits per Symbol * Symbol Rate Figure 6.4. [21] shows symbol-error-rate performances for different compensation scenarios for the frequency-independent portions of amplitude and phase.

Figure 6.4. Symbol-error-rate performances for different compensation scenarios for the frequency-independent portions of amplitude and phase. Source: M. Mailand, R. Richter, and H.-J. Jentschel. (2006). IQ-imbalance and its compensation for non-ideal analog receivers comprising frequency-selective components [Online]. Available: http://www.adv-radio-sci.net/4/189/2006/ars-4-189-2006.pdf.

The symbol clock of a digital radio determines the sampling rate of the baseband I and Q waveforms required to accurately interpret the symbols and recover the digital data at the Rx. In the Tx, the symbol rate [2] is responsible for the creation of baseband I and Q waveforms and correct placement of valid states, ensuring proper encoding of the digital data. Therefore, the Tx and Rx must have the same symbol rate to be compatible, otherwise symbol rate errors may occur.

6.2 HARDWARE INHERENT IMPAIRMENTS Hardware inherent impairments are those impairments that exist within hardware and imbalances are created by any active circuit.

6.2.1 Non-Linearity Non-linear distortions occur when a signal is subjected to poor frequency response, bent-line phase response or both. If the amplitude of the impairment relative to the desired signal varies while varying the amplitude of the input signal, it is probably a nonlinear distortion. The behavior is considered non-linear when its output amplitude or phase is no longer proportional to its corresponding input. Non-linear distortions are commonly observed in high level QAM modulation formats, and may be caused by any active circuit, especially microwave power amplifiers [22]. Usually, third order and fifth order inter-modulation products cause limited non-linearity in linear systems. If the input to a Rx is expressed as two pure tones at two distinct frequencies

The output y(t) of a non-linear device can be represented as:

Implying that for a small signal gain, output signal is mostly linear, but with increasing input signal power, the compressive effects of third-order intercept (TOI) causes the output to become non-linear. The output power will eventually drop off after a particular level of input signal power and this point is called the 1-dB compression point. This is shown in the Figure 6.5.

6.2.2 Power Amplifier Non-Linearities Power amplifiers are used for boosting the signal power before transmission, but being inherently non-linear, they cause distortion of the input signal. Signals with large peak-to-average-power-ratio (PAPR) [17] get impacted more and experience clipping when passed through the power amplifier because of the level of saturation of the amplifier. This causes in-band distortion and out-of-band spectral regrowth. Figure 6.6 shows the compression of a power amplifier (non-linearity).

6.2.3 Phase Noise Phase noise is random disturbance in the phase of the carrier signal. In phase noise the spectrum of the signal is convolved with the complex exponential of the LP phase noise process and results in interference from the neighboring subcarriers [23]. This causes a

Figure 6.5. 1-dB compression point.

Figure 6.6. Power amplifier non linearities.

rotation and noise like blurring of the signal constellation which are termed as common phase error (CPE) and inter-carrier-interference (ICI), respectively. When phase noise [17] is present in the LO, rotation and blur due to noise can be observed. Phase noise creates instantaneous frequency error of the baseband signal. Modulation schemes that are higher in order like 64-QAM, 128-QAM, and phase noise prevents carrier recovery and causes the spinning of the constellation plot. Figure 6.7 [4]

Figure 6.7. Phase noise in 4-QAM, 16-QAM, and 64-QAM signals. Source: National Instruments. (2007). Sources of error in IQ based RF signal generation [Online]. Available: http://sine.ni.com/nipdfgenerator/nipdfgenerator?pageURL=http:// www.ni.com/white-paper/5657/en&clientAppName=dz&dotsPerPixel=&dotsPerPoint=.

illustrates the constellation plots of two modulation schemes when a phase noise of -50 dB at a 1 KHz offset is observed.

6.2.4 Quadrature Skew Quadrature skew is a source of error which is observed particularly in the LO splitter, which divides the LO into an I and a Q signals. While an ideal system would result in each of these being exactly 90° out of phase, some systems specify up to three degrees or more of skew. Lower order modulation schemes like QPSK and 16-QAM, quadrature skew has relatively little effect on system throughput. However, like other sources of error, higher order modulation schemes such as 64-QAM is significantly impaired. Figure 6.8 [4] is a contrast to the performance of lower order and higher order modulation schemes, two systems with a quadrature skew of 16%.

6.3 ARCHITECTURE SPECIFIC IMPAIRMENT These impairment are associated with the kind of architecture that they follow and they are listed below.

6.3.1 DC Offset DC offset is when a waveform has unequal amounts of signal in the positive and negative domains. Normally, the signal should have a middle point at zero to allow a maximum dynamic range but if the mean amplitude is zero, there is no DC offset [24].

Figure 6.8. Quadrature skew in 4-QAM, 16-QAM, and 64-QAM signals. Source: National Instruments. (2007). Sources of error in IQ based RF signal generation [Online]. Available: http://sine.ni.com/nipdfgenerator/nipdfgenerator?pageURL=http:// www.ni.com/white-paper/5657/en&clientAppName=dz&dotsPerPixel=&dotsPerPoint=.

DC offset is undesirable when it causes saturation in the amplifier or changes the operating point of an amplifier. Often, very low frequencies are called “slowly changing DC” or “baseline wander.” It is also an imbalance that sometimes occurs in A/D converters. Considering I and Q as stream of 1s and 0s, taking them as two streams switching between a value of +1 and –1. So, the output of the I multiplier consists of a vector which is flipping I between 0° and 180° as the bit stream alternates. Likewise, the output of the Q multiplier is a vector that flips between +90° and –90° as the bit stream modulates the original 90° vector. Thus, if at a particular instant, both the I and Q bit streams are equal to +1, the result at the output of the IQ-modulator is the sum of the 90° and 0° vectors, that is, a +45° vector. Likewise, I and Q bit combinations of −1/+1, −1/−1, and +1/−1 produce vectors (commonly called symbols) all of equal amplitude at +135°, −135°, and −45°, respectively [25]. If either I or Q paths have unwanted DC offset errors, this would result in the +1/−1 multiplication being skewed. If there is an offset that is equal to 1% of the baseband signal amplitude, it causes the +1/−1 multipliers to be modified to +1.01/−0.99. This has the effect of shifting the center of the constellation plot off the origin, on either I or Q axis, most likely it occurs on both the axis. In the frequency domain, this manifests itself as a small portion of the unmodulated carrier appearing at the output of the modulator and this LO leakage (also referred to as LO feed through) appears at the center of the modulated spectrum.

For a 4-QAM modulation scheme, the DC error in Figure 6.9 [4] is insignificant and the signal can be successfully demodulated. However, for a 64-QAM modulation scheme, the error is significant enough to prevent carrier recovery. Thus, the constellation plot begins to spin when the demodulation algorithm is unable to accurately estimate the phase or frequency of the baseband signal. Figure 6.10 [2] shows IQ-offset in 16-QAM.

Figure 6.9. DC offset in 4-QAM, 16-QAM, and 64-QAM signals. Source: National Instruments. (2007). Sources of error in IQ based RF signal generation [Online]. Available: http://sine.ni.com/nipdfgenerator/nipdfgenerator?pageURL=http:// www.ni.com/white-paper/5657/en&clientAppName=dz&dotsPerPixel=&dotsPerPoint=.

6.3.2 IQ Imbalance IQ mismatch or imbalance is a common reason for the introduction of noise through hardware being generated during IQ modulation at the Tx and IQ demodulation at the Rx. It consists of IQ-gain, IQ-delay and IQ-phase mismatch. The IQ-gain and IQ-delay mismatches are caused by the gain and delay difference respectively between the I-rail and Q-rail, IQ- phase mismatch is caused by the 90° phase shifter in analog IQ-modulator and demodulator. These differences may be attributed to mixers, filters, or ADCs [26]. Figure 6.11 shows various point of IQ-imbalances and the effect of gain and Figure 6.12 phase on 16-QAM. In heterodyne or IF reception, when IF-down conversion takes place IQ-imbalance causes the respective image channel to mix partially with the desired signal. Within homodyne, direct conversion or zero-IF reception, the IQ-signals gets distorted by IQ-imbalance within the respective desired channel. In both cases, IQ-imbalance degrades reception performance. This effect may be caused by amplitude- and

Figure 6.10. IQ-offset. Source: Agilent Technologies. (n.d.). Testing and troubleshooting digital RF communications receiver designs [Online]. Available: http://my.ece.ucsb.edu/yorklab/Useful%20Stuff/ Tutorials/Testign%20DigitalRF%20Receivers%20AN1314.pdf.

Figure 6.11. Various point of IQ-imbalances.

Figure 6.12. Effect of IQ-imbalance on 16-QAM constellation plot.

phase impairments between the LO paths, or mismatches between respective IQ-branches after analog down conversion [2]. In wideband transmission, the distorting IQ-imbalance mixing becomes an IQ-imbalance convolution, due to the frequency selectivity of the analog frontend components following the down conversion. Therefore, different impulse responses of filters and IF or baseband amplifiers have significant influence. With the help of constellation characteristics [26], the signal impairments related to I and Q can be displayed. Matching problems due to subtle imbalances [23] can be detected by viewing the constellation diagram of the symbol time and comparing with the ideal grid of the constellation, which indicates where the symbol states should occur.

6.3.3 I Q-Gain Imbalance I and Q being two separate signals, each one is created and amplified independently. Inequality of this gain between the I and Q paths results in incorrect positioning of each

symbol in the constellation [2], causing errors in recovering the data. IQ-gain imbalance results in a distorted measured constellation relative to the reference. It may be caused by slightly different conversion losses in I and Q mixers [23] or by different filter losses in I and Q signal paths of an IQ demodulator. Even subtle imbalances are often visually detectable on zooming in on the constellation and using markers. For detecting small imbalances, ideal grids are important. Figure 6.13 speaks about the image spectrum that gets created due to gain mismatch between I and Q.

Figure 6.13. Effects of gain imbalance.

IQ-modulators and demodulators being analog usually have imperfections that result in an imperfect match between the two baseband analog signals, I and Q, which represent the complex carrier. Gain mismatch typically causes I signal to be slightly smaller than the Q. In a single-carrier modulation system, these results in a visible distortion [23] in the constellation plot where the square constellation of a 64-QAM signal becomes rectangular.

Such mismatch errors are caused by amplitude errors in the DACs or because of inconsistencies between each of the analog mixers. Higher order modulation schemes such as 64-QAM, IQ-gain imbalance of even a few dB can prevent proper demodulation of the signal [25]. This is illustrated in Figures 6.14 [2] and 6.15 [4].

Figure 6.14. IQ-gain imbalance (excess I-gain and reduced Q- gain relative to the ideal constellation locations). Source: Agilent Technologies. (n.d.). Testing and troubleshooting digital RF communications receiver designs [Online]. Available: http://my.ece. ucsb.edu /yorklab/Useful%20Stuff/ Tutorials/Testign% 20DigitalRF%20Receivers%20AN1314.pdf.

Figure 6.15. IQ-gain imbalance in 4-QAM, 16-QAM, and 64-QAM signals. Source: National Instruments. (2007). Sources of error in IQ based RF signal generation [Online]. Available: http://sine.ni.com/nipdfgenerator/nipdfgenerator?pageURL=http:// www.ni.com/white-paper/5657/en&clientAppName=dz&dotsPerPixel=&dotsPerPoint=.

6.3.4 IF Filter Ripple or Tilt Problems in IF filter (that is meant to attenuate out-of-channel interference) design may cause filter tilt or ripple in the frequency response and variations in group delay [2]. The filter should be flat with a constant group delay across the relevant frequency band. Filter tilt or ripple may be caused by improper matching of components between the antenna and the IF filter and results in linear distortion in the signal. For example, mismatch between the preselecting filter and the LNA causes reflections that result in distortion of the overall frequency response of the Rx. Distortion in the demodulated baseband signal due to filter tilt or ripple is discernible in the constellation diagram and in the higher than expected magnitude of error vector (EVM) at the symbol points and symbol transitions. Filter inband ripple in the frequency response causes linear distortion in the signal which is shown in Figure 6.16 which the zoomed plot is showing the ripple. Since the frequency response of the Rx is largely dependent on the IF filter, its shape distortion may be observed and analyzed by performing a frequency response measurement on the filter alone, as shown in Figure 6.17. Figure 6.18 shows the inband ripple effect on the constellation plot.

Figure 6.16. Zoomed frequency response showing ripple in the filter.

6.3.5 Group Delay Group delay is a measure of device phase distortion, computed as the derivative of the device’s phase characteristic with respect to frequency. It can be thought of as the transit time of a signal through a device, versus frequency. See Figure 6.19 [27] for group delay measurements and its effect as impairment.

Figure 6.17. Filter tilt.

Figure 6.18. Inband ripple.

The phase characteristic of a device typically consists of both linear and higher order (deviations from linear) phase-shift components. The linear phase-shift component represents average signal transit time and can be attributed to the electrical length of test device where as the higher order phase-shift component represents variations in transit time for different frequencies and is the source of signal distortion [27]. In a group delay measurement, the linear phase shift component is converted to a constant value (representing the average delay) and the higher order phase shift component is transformed into deviations from constant group delay (or group delay ripple). The deviations in group delay cause signal distortion, just as deviations from linear phase cause

Figure 6.19. Phase distortion. Source: Agilent Technologies. (n.d.). Group delay [Online]. Available: http://na.tm.agilent.com/pna/help/WebHel p7_5/Tutorials/Group_Delay6_5.htm. distortion. In Figure 6.20 [27], the measurement trace depicts the amount of time it takes for each frequency to travel through the device under test.

Figure 6.20. Group delay ripple. Source: Agilent Technologies. (n.d.). Group delay [Online]. Available: http://na.tm.agilent.com/pna/help/W ebHelp7_5/Tutorials/Group_Delay6 _5.htm.

Group delay is often a more accurate indication of phase distortion than phase. Deviation from linear phase results are shown in the upper region of Figure 6.21 [27]: device 1 and device 2 have same value, despite different appearances. Group delay results are shown in the lower region of Figure 6.21: device 1 and device 2 have different values of group delay. This is because in determining group delay, the analyzer calculates slope of phase ripple, which is dependent on number of ripples which occur per unit of frequency.

Figure 6.21. Group delay versus deviation from linear phase. Source: Agilent Technologies. (n.d.). Group delay [Online]. Available: http://na.tm.agilent.com/pna/help/WebHelp7_5/ Tutorials/Group_Delay6_5.htm.

6.3.6 Baseband Filtering Problem Errors in baseband filtering may cause ISI as well or overshoot of the baseband signal in time [2]. See Figure 6.22 for intentionally mismatched I and Q filters by applying different roll off factors. The alpha parameter in a raised-cosine filter defines the shape of the filter in the frequency domain. Low values create a sharp filter shape in the frequency domain, but also cause high overshoot in the time domain, which can be detected in a vector diagram. The Rx must have appropriate baseband frequency response and time characteristics for the given alpha. When baseband filtering is shared between the Tx and the Rx, filters must be compatible with respect to roll-off factor (alpha) and correctly implemented in each. Filtering errors due to a bad roll-off factor may affect the amount of interference from adjacent channels leading to Rx failing performance verification tests. Excessive overshoot of the signal trajectory between symbol states in the vector constellation diagram indicates poor baseband filter performance. The EVM versus time indicates roll-off factor discrepancies, a high EVM between symbol points and low at the symbol points indicates a wrong roll off factor. The correct roll-off factor can be found by using different roll-off factors in the vector

Figure 6.22. Gain and phase contributions of IQ mismatched LPFs. signal analysis (VSA) while viewing the error vector time display. The value for which the EVM between symbol decision points approximately equals the EVM at the decision points is the right value. See Figures 6.23 [2] and 6.24 [2] for correct and incorrect alpha values i.e., the roll-off factors.

Figure 6.23. Vector diagram and EVM versus time for wrong roll-off factor. Source: Agilent Technologies. (n.d.). Testing and troubleshooting digital RF communications receiver designs [Online]. Available: http://my.ece.ucsb.edu/yorklab/Useful%20Stuff/ Tutorials/Testign%20DigitalRF%20Receivers%20AN1314.pdf.

Figure 6.24. Vector diagram and EVM versus time for correct roll-off factor. Source: Agilent Technologies. (n.d.). Testing and troubleshooting digital RF communications receiver designs [Online]. Available: http://my.ece.ucsb.edu/yorklab/Useful%20Stuff/Tutorials/Testign%20 DigitalRF%20Receivers%20AN1314.pdf.

CHAPTER 7

SIMULATION OF THE PHYSICAL LAYER IMPAIRMENT

This thesis is basically about the study of various impairments linked with the Tx as well as the Rx and how they affect the overall accuracy and the efficiency. To validate those impairments and for a real time purpose out of the many impairments listed above few important ones are tested and evaluated. To test the various impairments in system we ran a couple of simulations For any simulation to work, a design and their architecture is one of the most important criteria and ours basically focuses on the points where the chances of those defects are the maximum. Therefore, a test bench setup was developed in MATLAB and this set was used with the help of graphical user interface to check the impairments at various points in the model. Figure 7.1 shows the graphical user interface that has been used.

7.1 MODEL SET UP The above discussed modulation schemes have been used in the model i.e. the test has been done on both QPSK and QAM. Beyond 64-QAM was not taken into account as this model is just for analyzing the basic impairments that a signal goes through while it takes its path from the shaping to the matching passing through a channel with noise and the imbalances that it has to deal with. The system includes digital and analog segments of the Tx, the analog channel with its various impairments, and the analog and digital segments of the Rx. Probe and display options include spectral plots, eye-diagrams as well as constellation diagrams at various points in the signal conditioning, signal processing, and signal transformation chain. The system simulation is performed by introducing channel impairments like IQ-gain and phase imbalance, DC offset, mixer phase noise, channel noise, in-band ripple and filter tilt. All simulations are conducted with base band signals and channel models. The transparency of the modulator up-conversion and the demodulator down-conversion to the

Figure 7.1. Graphical user interface for the system. modulation, acquisition, and demodulation process has been carefully illustrated and explained above. The aspects related to the missing conversions that are not simulated by the complex base band model, namely distortion terms due to non-linear power amplifiers at the Tx and nonlinear mixing with strong adjacent channels in the analog mixers at the Rx have also been identified and discussed above and will be included in the future work. The modulator design and simulation consists of a random binary data generator, a mapping to constellation points, Square-Root Nyquist Shaping and 1-to-16 Up-Sampling filters and IQ modulation [28]. This simulation gives the user to examine the constellations at all points taking from shaping input to shaping output, channel input to channel output, channel with noise input to channel with noise output and finally the matching filter input and output. At the finest detail the signal conditioning path with or without impairments can be observed. The simulation gave a platform to understand the relationships between the sample rates and symbol rates, and between spectral span and symbol bandwidth observed at each probe point. The relationship between each component at different times are different at

various points in the system and analyzing those changes taking place gives a better understanding of the causes behind the interferences. In a standard radio Rx, the input signal passes through an image reject filter, amplifies, and then down converts a selected RF channel to an IF filter that performs initial bandwidth limiting. The IF filter output is again down converted to baseband [23] by matched quadrature mixers that are followed by matched analog baseband filters that perform final bandwidth control. Each of the quadrature down-converted signals is then converted to its digital representation by a pair of matched ADCs. The output of the ADCs is processed by DSP engines that perform the required synchronization, equalization, demodulation, detection, and channel decoding. The impairments like gain and phase imbalance between the two paths containing the quadrature mixers, the analog baseband filters, and the ADCs in the Rx are the cause of cross talk between the I and Q (IQ) components. In addition, the ADCs inject a DC term in the center of the baseband signal, and the analog filters introduce group delay distortion path imbalance due to analog component tolerance, avoiding performance degradation due to component parameter drift with time and temperature, avoiding the cost of quadrature mixers, and avoiding group delay distortion associated with analog filters, DSP insertion also offers the attraction of flexibility related to filters with programmable bandwidth and sample rates. Figure 7.2 is of an ideal communication system and the system that has been used.

Figure 7.2. Architecture of the communication system used.

In the simulation QPSK and QAM which are independent modulated signal was passed through a communication path which while passing through experiences the various imbalances associated. The signals are sampled at 4-samples per symbol and shaped with a SQRT Nyquist filter with excess bandwidth 0.5. IQ-signal processing is vulnerable and prone

51 to mismatches between I and Q-channels which introduces phase and gain differences. The quadrature 90° phase-splitter used to generate the I and Q Local-Oscillator (LO) signals that drive the I and Q-channel mixers may not be exactly 90°. Differences in conversion losses between the output ports of the I and Q-channel mixers may also contribute to the mismatch. Also, filters and ADCs in the I and Q paths are not perfectly matched. An IQ down converter, which forms IQ signal components from a real input signal, is shown in Figure 7.3. The I and Q components are not orthogonal due to gain and phase imbalance as well as DC insertion (DC offset) in the paths.

Figure 7.3. IQ-modulator.

Phase Noise and IQ-Gain or Phase Error is typically caused by improper setup or operation of head-end QAM modulators or up-converters or mostly the difference in the paths (see Figure 7.4).

Figure 7.4. IQ-imbalance.

To maximize the signal to noise ratio (SNR), the Rx filter must be matched to the Tx shaping filter. The matched filter is time reversed and delayed version of the shaping filter. The main purpose of the matched filter to minimize the probability of undetected errors received from a signal. Figure 7.5 shows how some of the imbalances like DC offset, gain imbalance and phase imbalance are inserted in the system.

Figure 7.5. DC insertion.

7.2 WORKING OF GRAPHICAL USER INTERFACE Figure 7.6 gives a picture of how the frontend and the backend relates with each other. The UI remains inert till the plot button on the UI is released. As soon as plot’s push button call back is called, all parameters that the user selects from signal types, stage and the imbalances are all read from the GUI with plot call back function. The next step is calling the test function (passing values of all parameters in the UI) in it and reads the value returned from it and stores it in variable (result). Result refers to the output signal after applying all the transformation selected from the UI which passes and this function runs as soon as the plot is clicked and returns the output.

7.3 SIGNIFICANCE OF CONSTELLATION AND EYE DIAGRAM The constellation analysis provides a powerful tool for analyzing the impairments. In it every nth sample of I and Q are plotted on the screen. They can be zoomed in for a better display of the transition in the signal path with or without the imbalances. I and Q pairs can be connected with a line or they can be plotted with circles or crosses. On the other hand, the eye diagram is created by taking the time domain signal and overlapping the traces for a

Figure 7.6. User activity of the graphical user interface. certain number of symbols. The open part of the eye clearly indicates that it can be sampled over that time with fidelity. The slope of the eye diagram determines how sensitive the signal is to timing errors. A smaller slope allows eye to be opened more and hence less sensitive to timing errors.

7.4 SIMULATION RESULTS The simulation results with different impairments are shown in Figures 7.7 to 7.14. All the impairment parameters can be slid anywhere in the mentioned range and the results can be observed as constellation, eye and spectrum plots at any of the given stages.

Figure 7.7. Shaping filter output.

Figure 7.8. Channel without noise output.

Figure 7.9. The channel with the imbalances introduced like gain and phase imbalance.

Figure 7.10. Matched filter output.

Figure 7.11. Matched filter output with dc offset introduced.

Figure 7.12. Matched filter output with filter tilt.

Figure 7.13. Matched filter output with inband ripple.

Figure 7.14. Matched filter output with mixer phase noise.

CHAPTER 8

CONCLUSION AND FUTURE WORK

The tests that were performed has presented the most common physical layer impairment including the channel, Tx and the Rx and a general measurement methodology carried out to detect those defects by the simulations. Certain signal impairments appear in specific measurements and variations from the expected results can help locate problems in different parts of the Rx. By seeing the plots in Figures 7.8 to 7.13, it can be validated that differences between the I-side and Q-side of an Rx can cause gain imbalance or quadrature errors. These differences are mainly because of mixers, filters, or ADCs. There were certain imbalances like the one with channel noise and one without the channel noise which could be predicted by viewing the constellation diagram of the symbol time and comparing with the ideal grid of the constellation. These ideal grids indicate where the symbol states should occur. This simulation is a learning tool for students, design engineers and system engineers studying physical layer and it does not cover impairments like non linearity, third order input, adjacent channel interference, timing errors, frequency errors, filter mismatch (shaping and the match filter) and Bit-width in A/D convertor. More modulation schemes can be included to improve variety such as OFDM, offset QAM, VSB (vestigial side band), and CDMA. Instead of using a pre built simplistic communication system user can be allowed to define his own communication system This thesis also gives an overview of research on basic channel impairments their causes and effects on how they affect the overall flexibility of a communication system and signal conditioning. Architecture specific impairment, hardware specific impairment was analyzed with constellation plots and eye diagrams. An introduction to Rx architectures and the important factors that help characterize Rx performance was also discussed.

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