here. Requires Adobe Acrobat Reader,

free download.]

Fly before you buy. The Defense Department adopted that procurement policy some time ago. In the modern world of telecommunications, an equivalent concept might be: simulate before you build.

Because the economics associated with link performance are severe (even a small amount of degradation will affect a system's 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 committing to implementation.

Additionally, when things go wrong during construction or initial operation, a simulation model can be used to track down the offending element. The simulation is also useful for pre-testing any corrective action before implementation, either on the ground or in space.

First, a discussion of the transnponder is in order. The 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.

Most satellites in a geostationary orbit have what are called bent-pipe repeaters using C and Ku bands (a bent pipe repeater is one that simply receives all signals in the uplink beam, block translates them to the downlink band and separates them into individual transponders of a fixed bandwidth — see Figure 1). The figure provides a simplified system block diagram that shows the impairments affecting the system performance.

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 Mb/s.

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(see Figure 2). In this case, 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 ensures that the transponders do not interact with each other.

The transponder is a central element in the end-to-end communications link and is one of the key elements in overall performance. Therefore, 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.

To obtain maximum power output with the highest efficiency (e.g., to minimize solar panel DC supply), the amplifier should be operated at its saturation point. While this interjects some distortion, the most significant impairments to digital transmission come about in the filtering. Filtering constrains bandwidth and introduces delay distortion while the power amplification produces AM/AM and AM/PM conversion. These effects will be discussed in detail later in this article.

Many services are sensitive and susceptible to AM/AM and AM/PM conversion. This necessitates operation at some backoff from the optimal operating point. With such backoff, intermodulation distortion can be held to an acceptable level. However, backoff also reduces downlink power.

RF channel distortions, notably group delay and 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 more robust communications simulation tool is necessary for analyzing non-linear impairments and their interaction.

These are common elements in a communication link. Most filters are designed in the frequency domain in terms of their type (elliptical function, Chebechev, Bessel, etc.) and order. This information is linked to the filter poles, and hence the frequency response. In a time-domain simulator, 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. This leads to signal discontinuities at the block transitions.

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. 3) Noise produced in amplifiers through thermal action within semiconductors.

The noise is simulated as a Gaussian random variable with noise power spectral density N_o = 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 because each noise source is generated from a different key (seed) to ensure that they are not correlated.

Antennas and low-noise amplifiers are typically rated in degrees, 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 N_oB.

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

The empirical relationships:

describe A(r) and φ(r).

The first term is called AM/AM conversion, and the second is AM/PM conversion. The four contestants a_r, b_r, a_φ and b_φ can be determined from the actual TWTA tube measurements via a least square fit. Another, 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.

Amplifier types other than the TWTA and the mixers used to translate the signal frequencies have nonlinear aspects as well. Generally the transfer function of such devices is described in terms of a polynomial:

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:

This is common in shared transponder operation where several carriers occupy the usable bandwidth. Substituting into the above and using standard trigonometric identities shows that the output y(t) can have frequency intermodulation (IM) products with frequency values, 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-order 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. The satellite must 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 applies, except that the IM from two SCPC channels can fall into the same transponder.

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;

The model parameters are usually determined by actual field experiments. Usually, the amplitudes are modeled 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 consideration of the combined effect of different forms of fading and evaluate mitigation strategies.

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, or on the same or adjacent frequency, will ride along.

The principal effect is to reduces 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's nonlinear elements to produce signals in the wrong place. In the case of the multichannel 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.

Many different modulation formats are used in satellite communication links. Examples include quadrature phase-shift keying (QPSK,) offset quadrature phase-shift keying (OQPSK), minimum-shift keying (MSK), Gaussian minimum-shift keying (GMSK) and CPFSK. Each format has issues that must be investigated.

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 to address this is to use offset QPSK. Here, the quadrature channel is delayed by ½ of a data bit. Thus the phase transitions can never be more than 90°, which alleviates this problem. Figure 5 shows 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.

The digital video broadcast satellite (DVB-S) format most frequently operates in the 11 to 12 GHz band. It supports data rates from 23.754 Mb/s to 41.570 Mb/s.

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 used. This commonly used filter 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 the figure, the spectrum with the RRC filter is much more compact. This allows for a higher data rate in a fixed operating bandwidth, which is a good thing. Note that the filtered version is not a constant envelope signal, so careful choice of the transponder backoff via the simulations and analysis described must be performed.

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:

Figure 7 shows the results of combining the above equation; some of the terms can be estimated using the simulations. 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. Because the thermal noise floor is fixed, the C/N component increases as the BO decreases. On the other hand, as 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 are 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 1/2 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. Therefore, component costs are controlled with time, energy, and money being devoted only to the extent that is required for performance.

This article has described many of the real world impairments that affect the performance of a satellite based transponder communication link. By carefully implementing these effects via computer simulation, optimum operating points can be determined and and potential problems corrected in the design process before costly mistakes occur in the finished product.

1. Bernard Sklar, “Digital Communications — Fundamentals and Applications, 2nd Edition,” Prentice Hall, Upper Saddle River, NJ, 2001.
2. Bruce Elbert, “Introduction to Satellite Communication, 2nd Edition,” Artech House, Inc., Boston Mass, 1999.

Bruce Elbert is president of Application Technology Strategy, a consultancy that assists companies and government agencies in the design and development of satellite communications systems. He has held several key engineering and business management positions at Hughes Electronics. He holds an B.E.E. from City College of New York, an M.S.E.E. from the University of Maryland and an M.B.A. from Pepperdine University. He can be contacted at: bruce@applicationstrategy.com.

Maurice Schiff is the chief scientist at Elanix. He has more than 30 years of experience in the field of digital communications, spread spectrum systems, digital signal processing, communications and radar systems. He has designed many of the signal processing and communication system modules in SystemView by Elanix. He teaches, along with Bernard Sklar, Ph.D., a course in advanced digital communications at UCLA extension. Along with Robert Stewart, Ph.D., Schiff produced the SystemView-based communication theory training CD ROM which accompanies the popular text book; “Digital Communications, Fundamentals and Applications” by Bernard Sklar. He can be reached at: maury@elanix.com