Simulating the Performance 0f Communication Links with Satellite Transponders

Bruce Elbert Application Technology Strategy, Inc. [email protected]

Maurice Schiff Elanix, Inc. [email protected]

Introduction Some time ago, the Defense Department adopted a procurement policy “fly before you buy”. In the modern world of telecommunications the equivalent concept might be termed “simulate before you build”. The economics associated with the link performance are quite severe. Even a small degradation will affect the system data rate or coverage, both of which are related to capital and operating expenses. It is crucial to have all of the system design parameters optimized before a heavy commitment to implementation. Furthermore, when things go wrong in the actual article during construction or initial operation, a simulation model can be used to track down the offending element. The simulation will also be useful for pre-testing any corrective action before attempting it either in space or on the ground. In this article we use SystemView by Elanix to explore the end-to-end simulation of communications links involving satellite transponders. We will describe the various impairments to the system and computer models used to simulate their effects.

Satellite Transponder Communications Link A transponder is a broadband RF channel used to amplify one or more carriers on the downlink side of a geostationary communications satellite. It is part of the microwave repeater and antenna system that is housed onboard the operating satellite. Examples of these satellites include AMC 4 and Telstar 5, located at 101 and 97 degrees west longitude, respectively. These satellites and most of their cohorts in the geostationary orbit have bent-pipe repeaters using C and Ku bands; a bent pipe repeater is simply one that receives all signals in the uplink beam, block translates them to the downlink band, and separates them into individual transponders of a fixed bandwidth. Figure 1 shows the basic concept. Each transponder is amplified by either a traveling wave tube amplifier (TWTA) or a solid state power amplifier (SSPA). Satellites of this type are very popular for transmitting TV channels to broadcast stations, cable TV systems, and directly to the home. Other applications include very small aperture terminal (VSAT) data communications networks, international high bit rate pipes, and rural telephony. Integration of these information types is becoming popular as satellite transponders can deliver data rates in the range of 50 to 150 Mbps. Achieving these high data rates requires careful consideration of the design and performance of the repeater.

The most significant impairments to digital transmission come about in the filtering, which constrains bandwidth and introduces delay distortion, and the power amplification, which produces AM/AM and AM/PM conversion. These effects will be discussed in detail later in this article. For maximum power output with the highest efficiency (e.g., to minimize solar panel DC supply), this amplifier should be operated at its saturation point. However, many services are sensitive and susceptible to AM/AM and AM/PM conversion, for which backoff is necessary. With such an operating point, intermodulation distortion can be held to an acceptable level, however, backoff also reduces downlink power.

The transponder itself is simply a repeater. It takes in the signal from the uplink at a frequency f1, amplifies it and sends it back on a second frequency f2. Figure 2 shows a typical frequency plan with 24-channel transponder. The uplink frequency is at 6 GHz, and the downlink frequency is at 4 GHz. The 24 channels are separated by 40 MHz and have a 36 MHz useful bandwidth. The guard band of 4 MHz assures that the transponders do not interact with each other.

System Impairments The transponder is a central element in the end-to-end communications link, illustrated in Figure 1. This drawing provides a simplified system block diagram that shows the impairments that affect the system performance. Thus, the transmitting earth station on the uplink side will cause its share of distortion as will the receiving earth station on the downlink side. Some of this distortion is uncorrelated, which means that its contribution can be added more or less algebraically. However, for this to be correct, one must know the individual contributions. Other types of distortion, notably group delay, AM/AM and AM/PM, interact with one another and independence is no longer assured. Simple link budgeting techniques are available for evaluating links with additive noise, however, a communications simulation tool like SystemView by Elanix is necessary for analyzing related impairments and their interaction. Another benefit of this approach is that both theoretical and measured data can be included in the simulation models.

Filter gain and phase distortion: These are common elements in a communication link. Most filters are designed in the frequency domain in terms of their type (Elliptic function, Chebechev, Bessel, etc.) and order. This information is linked to the filter poles and hence the frequency response. In a time domain simulator such as SystemView by Elanix the time impulse response is derived from the frequency response, and the filtering action is a convolutional operation. In a frequency domain type implementation, the data is processed in blocks, which leads to signal discontinuities at the block transitions.

Thermal Noise Thermal noise is the most common impairment in a wireless communication system. There are three general sources, 1) The noise that enters the antenna with the signal, aptly called antenna noise, 2) the noise generated due to ohmic absorption in the various passive hardware components, and 3) noise produced in amplifiers through thermal action within semiconductors. The noise is simulated as a Gaussian random variable with noise power spectral density No = kT = 1.381E-23T w/Hz. The system temperature T is computed by adding the contributions of the three system noise sources. This is easily simulated with SystemView by Elanix because each noise source is generated from a different key (seed) to insure that they are not correlated. Antennas and low noise amplifiers are typically rated in Kelvin (degrees above absolute zero), which allows the simple translation to noise power spectral density. If the bandwidth of the RF carrier is known, then the total noise power is simply the product NoB.

TWT AM/AM and AM/PM conversion The TWTA is a common element in earth station s and communication satellites. For an input sine wave of frequency f and amplitude r, the TWTA is characterized by the relationship

y(t)=A[r(t)]sin(2πft+φ[r(t)])

The empirical relations

2 A(r)=arr r/[1+b r ] 22 ϕ(r)=aϕϕ r /[1+b r ] describe A(r) and φ(r). The first term is called AM/AM conversion, and the second is AM/PM conversion. The four contestants [arr , b ,aϕ ,bϕ ] can be determined from the actual TWTA tube measurements via a least square fit. Another and simpler approach is to enter the measured TWTA data into a text file and use simple table look up for the required values. The term A(r)/r is the nominal gain. A plot of A(r) shows the output power increasing with the input, and then leveling off and actually decreasing as the input power continues to increase into the overdrive region. This is the saturation phenomena mentioned above. As discussed later for DVB-S, the TWTA must be operated a little bit below saturation to control sideband regeneration. Figure 3 shows the typical TWTA AM/AM curve indicating the definition of the important parameter, back off (BO). The operating point should be optimized, as described later, for the specific transmission system.

Pre-Amplifier and mixer non linearties Amplifier types other than the TWTA as well as the mixers used to translate the signal frequencies have nonlinear aspects as well. Generally the transfer function of such devices isdescribed in terms of a polynomial

2 yt()=+ a bxt () + cxt () + .... where the coefficients are chosen to satisfy common figures of merit such as the two tone third order intercept point , IP3. The coefficient, a, is the linear gain term. The problem arises when there are two or more input signals in the input x(t) of the form,

xt( )=+ A sin(2π ft12 ) B sin(2π ft )

This is common in shared transponder operation where several carriers occupy the usable bandwidth. Substituting into the above and using standard trigonometric identities show that the output y (t) can have frequency intermodulation (IM) products with frequency values ±±mf12 nf , where m and n are integers. Generally the power in the IM product decreases with increasing m and n. The worst case generally occurs in the so-called third IM product when m = 2 and n = 1 and vice versa. Using figure 2, consider two wideband signals in the uplink to the satellite, one at f1 = 6105 MHz (channel 9 uplink), and one at f2 = 6065 MHz (channel 7 uplink). The typical satellite employs a wideband frequency-translating receiver that provides about half of the 100 dB total repeater gain. Each pair of carriers creates two third order IM products: f3 = 2*6105 – 6065 MHz = 6145 MHz (uplink channel 11), and f3 = 2*6065 – 6105 MHz = 6025 MHz (uplink channel 5). Figure 4 shows the signal spectra just described. Careful modeling of these third order and higher IM products is therefore essential. Another requirement is accurate accounting of all such products that can be produced within the transponder bandwidths. Even weak, high order IM products in the wrong place can be disastrous. We want to insure that the satellite does not jam itself. This mechanism can affect multiple signals within one channel as commonly employed by single channel per carrier (SCPC) systems. The analysis above still applies where the IM from two SCPC channels within the transponder can fall into the same transponder.

Signal fading Uplink and downlink transmissions can experience various forms of fading as signals pass through the troposphere and ionosphere. This phenomena is sometimes called multipath fade. Basically the signal from the transmitter to the receiver can bounce off of various objects or bend due to variations in refractive index and can combine destructively at the antenna. The net received signal experiences time-varying fading. If s(t) is the transmitted signal, then the received signal r(t) can be represented by the formula;

rt()=−∑ akk ()( tstτ ()) t

The model parameters are usually determined by actual field experiments. Usually, the amplitudes are modeedl as a Rayleigh distribution with some fade dynamics. Rain attenuation does not exhibit Rayleigh fading but is an important consideration at frequencies above C band. Simulation tools allow us to consider the combined effect of different forms of fading and evaluate mitigation strategies.

Radio frequency interference (RFI) from internal and external sources There is no end to the possibilities here. Typical earth station and satellite antennas provide some selectively for the signal of interest (SOI). Any other signal in the area and on the same or adjacent frequency will ride along. The principal effect is to reduce the effective carrier-to noise (C/N) ratio at the receiver. This effect can be calculated based on assumed antenna isolation (sidelobe and cross- polarization). Depending on their frequency and strength, they can also interact via the system nonlinear elements to produce signals in the wrong place. In the case of the multi channel transponder, all other channels are potential RFI sources to the SOI. There may also be external interference signals such as radar systems and ground based microwave systems. All of these RFI components can be developed in the simulation and added to the SOI to investigate their effect.

Modulation formats Many different modulation formats are used in satellite communication links. Examples include QPSK, OQPSK, MSK, GMSK and CPFSK. Each format has its own issues that must be investigated. QPSK vs. Offset QPSK To maximize the output power in the downlink, the amplifier must operate as close to saturation as possible. To avoid destroying the signal information it is common to employ so called constant envelope modulation techniques such as FM and QPSK. In both cases, the information is in the carrier, and hard limiting the signal does no harm. But it is a little more complicated than this. To keep out unwanted signals, and to limit the spectral occupancy of the signal, each channel is band limited at the transmitting earth station using shaping such as the raised-cosine spectrum. This causes standard QPSK, which can have +/- 180-degree transitions, to have significant amplitude variations before and after these transitions. QPSK is therefore more sensitive to the filtering and limiting process. A common variation is Offset QPSK. Here, the quadrature channel is delayed by ½ of a data bit. Thus the phase transitions can never be more than 90 degrees, which alleviates this problem. Figure 5 shows the SystemView by Elanix frequency spectra of both cases at the final output of a saturated amplifier. While the spectra of both signals are the same for the basic two signals, we see that the QPSK output has higher side lobes that can affect other channels.

DVB-S The Digital Video Broadcast-Satellite (DVB-S) operates in the 11/12 GHz band. It supports data rates from 23.754 Mbps to 41.570 Mbps. The modulation is a more complicated version of the basic QPSK. In this case so-called pulse shaping filters are used to compact the signal processing bandwidth. In particular the root-raised-cosine filter (RRC) with roll of factor 0.35 is employed. This filter is commonly employed today in a variety of wireless communication systems. It compacts the signal bandwidth while simultaneously providing for matched filter pairs in the transmitter and receiver without introducing inter symbol interference (ISI). Figure 6 shows a comparison between the spectra of the standard QPSK and the filtered version. As shown in Figure 6, the spectrum with the RRC filter is much more compact. This allows for a higher data rate in a fixed operating bandwidth, a very good thing! Note that the filtered version in not a constant envelope signal, so careful choice of the transponder backoff via the simulations and analysis described must be performed.

System trade off studies The basic system figure of merit is the carrier to noise ratio C/N. If we calculate the C/N for each of the individual impairments, then the overall C/N of the system is given by, n CN/{[/]}= CN −11− ∑ k k =1

Figure 7 shows the results of combining the above equation with individual simulations used to compute the individual terms. The independent parameter in this case is the TWTA BO previously described. Note that these components have competing effects. As the BO decreases there is more output power. Since the thermal noise floor is fixed, the C/N component increases as the BO decreases. On the other hand, at the BO decreases the signal is driven further into the nonlinear region of the TWT curve. This, of course, increases the power of the IM components. The net result is an optimum operating point that is determined via the simulation.

Another system measure is the bit error rate (BER), or sometimes the message or packet error rate. Some user applications require the BER to be in the 10e-6 to 10e-9 range. To achieve such low rates the information data is usually protected by a variety of forward error correcting codes (FEC). The DVB-S system uses a concatenated code, or code within a code structure. The outer code is a [204,188, 8] shortened Reed Solomon (RS) code. This code is used because it is effective against burst errors. The inner code is a rate ½ punctured to 2/3, constraint length 7 convolutional code. The Viterbi algorithm is used as the decoder. The nature of the convolutional code and this decoder gives rise to errors occurring in bursts that are then ‘cleaned up’ by the RS code. Simulations employing Monte Carlo techniques can combine all of the impairments described here to determine the BER. Also, trade off studies can determine which impairments are the most damaging and which are not. This information leads to tolerance requirements for the various components. Thus component costs are controlled with time, energy, and money being devoted only to the extent that is required for performance.

Conclusion In this article we have described many of the real world impairments that affect the performance of a satellite based transponder communication link. By carefully implementing these effects in SystemView by Elanix computer simulations, optimum operating points and potential problems can be determined and corrected in the design process before costly mistakes occur in the finished product.

Biographies Bruce Elbert is President of Application Technology Strategy, Inc., a consultancy that assists companies and government agencies in the design and development of satellite communications systems. He held several key engineering and business management positions at Hughes Electronics where he contributed to new projects in broadband and mobile satellite technology. He holds an BEE from City College of New York, an MSEE from the University of Maryland and an MBA from the Pepperdine University.

Maurice Schiff is the Chief Scientist at Elanix, Inc. He has over 30 years of experience in the field of digital communications, spread spectrum systems, digital signal processing, communications, and radar systems. He is has designed many of the signal processing and communication system modules in SystemView by Elanix. He teaches, with Dr. Bernard Sklar, a course in advanced digital communications at UCLA extension. Along with Dr. Robert Stewart, Dr. Schiff produced the SystemView based communication theory training CD ROM which accompanies the popular text book; ‘Digital Communications, Fundamentals and Applications’ by Bernard Sklar

References

Bernard Sklar, Digital Communications – Fundamentals and Applications, 2nd Edition, Prentice Hall, Upper Saddle River, NJ, 2001.

Bruce Elbert, Introduction to Satellite Communication, 2nd Edition, Artech House, Inc., Boston Mass, 1999

Figure 1 Elements of a basic Satellite link showing ground stations and the satellite transponder. The nature and location of the various system impairments are also shown.

(downlink) 3800 3840 H 7 3780 4 V

(uplink) V

H

Channel spacing = 40 MHz Usable bandwidth = 36 MHz

COPYRIGHT © 2002 – Application Technology Strategy, Inc. 2-6

Figure 2 Basic 24 channel C-band transponder frequency plan

Figure 3 Power characteristics of a TWTA showing the saturation. The definition of the back off parameter is also shown. SystemView

SystemView by Elanix

6e+9 6.08e+9 6.16e+9 6.24e+9

Signal Signal C hannel 7 C hannel 9 6.065 GHz 6.105 GHz

-30 Power dBm -50 3rd order 3rd order Intermod Intermod C hannel 11 C hannel 5 6.145 GHz 6.025 GHz

-70

6e+9 6.08e+9 6.16e+9 6.24e+9 Frequency in Hz (dF = 5e+6 Hz)

Figure 4 Two tone 3rd order intermods in a transponder showing the IM products falling directly into adjacent bands. SystemView

Spectra of hardlimited filtered OQPSK vs QPSK

65 85 105 125

0

-10

Q PSK

-20 Amplitude

-30

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offset Q PSK

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65 85 105 125 Spectrum

Figure5 Frequency power spectra of QPSK and offset QPSK after filtering and limiting. SystemView

SystemView by Elanix

-40 -20 0 20 40

0 QPSK

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-40

-60 Power in dB

-80

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QPSK with RRC Filter

-120

-40 -20 0 20 40 Relative Frequency

Figure 6 Frequency power spectra of standard QPSK vs. QPSK with a band limiting rrc filter.

Figure 7 Trade off of the system performance as a function of intermod power and signal power