390 S. MATEJKA, ANALYSIS OF INTERMODULATION DISTORTION IN OFDM BASED TRANSMITTER USING EER TECHNIQUE Analysis of Intermodulation Distortion in OFDM Based Transmitter Using EER Technique Stepan MATEJKA Dept. of Radio Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague 6, Czech Republic [email protected] Manuscript received June 22, 2015 Abstract. During the last two decades, new digital modu- lation scheme. The implementation of such new OFDM lation systems have appeared in the audio broadcasting. based schemes caused the new high-power transmitter de- Such broadcasting systems require new transmitters’ con- signs to evolve during the past two decades. It is not only the cepts to enable the transmission of digitally modulated sig- demand for implementation of the new digital modulation nals. Moreover, the selected modulation schemes (e.g. or- schemes, but also the low efficiency of traditional linear am- thogonal frequency division multiplexing) require a high lin- plifiers due to a high peak-to-average power ratio (PAPR) [3], earity power stage, which typically exhibits low efficiency due which moves the traditional linear power stage transmitter to high peak-to-average power ratio of the modulated signal. construction to the high-power switching conception [4–6]. One of the promising transmitter concepts is the Kahn enve- Nowadays, the pulse duration modulation (PDM) and its spe- lope elimination and restoration technique, where the origi- cial case – pulse width modulation (PWM) – are the most nal Cartesian in-phase and quadrature baseband signals are common modulation techniques used in the new high-power transformed to the envelope and phase signals. The main ad- AM transmitters [7], [8]. Utilizing the envelope elimination vantage of this technique is an ability to employ suitable types and restoration (EER) modulation method proposed by Kahn of highly efficient amplitude modulation transmitters for en- in 1952 [9], it is possible to design a switching transmit- velope amplification, while the phase modulated carrier is ter convenient for digital broadcasting (e.g. DRM 30), which produced by an additional phase modulator. The substantial is still based on the PWM technique applied to the transmitter drawback of envelope elimination and restoration is non- envelope signal processing path. ideal recombination of linearly distorted amplitude signal The EER technique is also known as the polar modu- and phase modulated carrier at the output power stage. lation technique. In its basic arrangement, the amplitude The aim of this paper is twofold. Firstly, to analyze the effect and phase informations are separated from the original low- of the envelope and phase signals bandwidth limitation on the level modulated signal using an envelope detector and a hard modulated signal in-channel distortion and out-of-channel limiter. The rectangular-shaped phase modulated carrier is emission. Secondly, to present the performance results as then amplified by a highly efficient switching power ampli- a reference for transmitter designers to properly set the en- fier such as class D, E, or F. The amplitude (envelope) signal velope and phase paths to reach required in-channel signal controls the power supply voltage of the phase signal power quality and suppress out-of-channel products. amplifier. In this way, the power amplifier works as a time domain multiplier. Thus the separated amplitude and phase signals recombine and the power amplifier produces ampli- fied modulated signal. As a switching mode power amplifier Keywords can be used in the power supply block as well, the overall Envelope Elimination and Restoration (EER), Orthogo- transmitter efficiency achieves very good values. nal Frequency Division Multiplex (OFDM), transmitter, The EER transmitter architecture is attractive not only amplitude and phase modulation, intermodulation dis- for high PAPR narrowband communication systems but also tortion, Error Vector Magnitude (EVM) for wideband systems [10], [11]. Increasing envelope am- plifier bandwidth, however, means increasing the negative influence of switching characteristics of power transistors on 1. Introduction the total distortion of the power amplifier. Although a large effort has been devoted to the investigation of EER enhance- New radio broadcasting standards operating in the LW, ment [12], [13], it still holds that this undesirable effect of the MW,and SW broadcasting bands, such as Digital Radio Mon- wideband EER leads either to the construction of EER based diale (DRM) [1] and HD Radio [2], are mainly based on the amplifiers with only a low output power (e.g. WLAN 802.11 orthogonal frequency division multiplexing (OFDM) modu- standard families), or to use other techniques to reach high DOI: 10.13164/re.2016.0390 SYSTEMS RADIOENGINEERING, VOL. 25, NO. 2, JUNE 2016 391 • Bandwidth limitation and undersampling effects of the carrier frequency phase modulator. The first phenomenon, the delay mismatch, is well dis- cussed in papers [19], [20]. In the contemporary transmitter designs, where the low-level signal processing is performed in the digital domain using the digital signal processors (DSP) or FPGA [21], [22], it is not problematic to compensate for such type of distortion. Fig. 1. Generalized block diagram of a PWM based switching The second phenomenon referred to as linear distor- transmitter for OFDM modulation scheme. tion is a result of filtering process in the digital part of the linearity and high power efficiency (e.g. Doherty amplifier transmitter envelope section, the PWM modulator, and the for COFDM broadcasting standards [14]). low-pass LC filter, which works as a PWM demodulator gen- erating a high-level amplitude signal. Due to its analog form, The simplified block diagram of a typical PWM based the low-pass LC filter exhibits not only the bandwidth limita- switching transmitter for OFDM modulation scheme follow- tion (it must reject PWM spectral components located at the ing the Kahn EER modulation method is shown in Fig. 1. vicinity of the PWM switching frequency multiples), but The Cartesian modulating signals – digital in-phase (I) and a non-linear phase of the transfer function resulting in a non- quadrature (Q) signals from IFFT based OFDM modula- constant group delay. Both effects can be corrected up to tor – are converted to their amplitude (A) and phase (Ph) the LPF cut-off frequency, which is determined by the PWM equivalents by means of the specialized digital signal pro- switching frequency and by the PWM out-of-baseband spec- cessing algorithm (e.g. CORDIC, [15]) with simultaneous tral components rejection requirements. This effect is dis- sampling rate conversion (up-sampling) due to increased am- cussed in [19], [20] only partially and author focuses on the plitude and phase signals bandwidth. The amplitude base- out-of-band distortion only. band signal feeds the envelope path of the transmitter, while the phase baseband signal feeds the carrier frequency path. The third phenomenon appears in the case of the carrier The main building blocks of the envelope path are a low-level phase modulator working with a low sampling frequency. PWM generator (PWM) driving a class-D switching ampli- The best way is to implement a numeric modulator, which fier (SW), which produces a high-level PWM pulse train exactly calculates edge positions of the rectangular shaped proportional to the modulating signal amplitude, and a low- carrier signal. This modulator in conjunction with direct pass filter (LPF), which rejects unwanted frequency compo- carrier signal synthesis ensures low distortion of the phase nents to reconstruct amplified amplitude signal. The carrier modulated carrier. path consists of a carrier frequency generator (FCG), which In this paper, the effect of the amplitude and phase sig- generates phase modulated carrier signal, followed by an in- nal bandwidth limitation is studied and its impact on the verter (RFSW) powered from the envelope path LPF. The modulated signal in-channel and out-of-channel distortion is inverter is typically constructed as a set of full-bridge MOS- described. The rest of the paper is organized as follows. FET switching stages, where the outputs from all stages are In Sec. 2, a simplified mathematical model of the envelope summed, filtered, and matched to a connected transmitting and phase signal processing paths is proposed, some proper- antenna. The RFSW works as a combiner (multiplier), whose ties of the amplitude and phase signals are specified and the output produces desired high-power band-limited modulated power spectral properties of both polar components are de- signal. termined. The simulation results of the amplitude and phase Inside the real transmitter, the recombination of the am- signal bandwidth limitations are given in Sec. 3. Both effects plitude signal and the phase modulated carrier to narrowband – the out-of-channel emission and the in-channel distortion modulated signal is not perfect, which results in intermodula- due to bandwidth limitations – are demonstrated. The sim- tion distortion [16–18]. There are several effects producing ulation results are discussed and summarized in the form of both the in-channel distortion, which results in modulated transmitter design recommendations in Sec. 4, and the paper signal Error Vector Magnitude (EVM) increase, and the out- concludes in Sec. 5. of-channel emission, which decreases not only the transmitter Adjacent Channel Power Ratio (ACPR), but produces wide- band transmitter noise: 2. Problem Statement • Delay mismatch between the amplitude signal and the The proposed simplified model of a transmitter based phase modulated carrier signal at the output power on the ERR technique is shown in Fig. 2, [21], where the stage. band-limiting low pass filters for the amplitude and phase paths are added. • Bandwidth limitation and non-constant group delay of The input Cartesian in-phase and quadrature compo- the transmitter envelope path. nents, i(t), q(t), produced by preceding baseband OFDM 392 S. MATEJKA, ANALYSIS OF INTERMODULATION DISTORTION IN OFDM BASED TRANSMITTER USING EER TECHNIQUE signals. Unfortunately, such type of distortion has consider- able impact on a resultant modulated signal.