R
21sc
Carrier transmitted tor Doppler measurement
Requires extra power and bandwidth.
memory a sequence (typically 62 bits long). As time goes on, additional bits aie received and stored. These sequences are compared with coded sequences which could have been transmitted. The possible sequence which most closely resembles the received sequence is chosen as the most likely sequence transmitted. This process is repeated a number of times to reduce the probability of error. As shown in Fig. 139, Viterbi decoding gready reduces the £yW0 required to obtain a specified BER. For example, a BER of 10~5 is achieved with an Eb/N0 of 4.4 dB. This represents an improvement, or coding gain, of 5.2 dB below the 9.6 dB required for uncoded BPSK.
There is a value of equal to 1.6 dB, known as the Shannon limit, below which no errorfree communication at any information rate can take place. This is derived from the ShannonHartley theorem, which states that the maximum theoretical data rate, Rmax, which can be transmitted over a transmission channel with bandwidth, B, is
where CIN is the average carriertonoise power ratio in the channel (see Panter [1965], Sec. 19.2; or Sklar [1988], Sec. 7.4).
We cannot reach the Shannon limit in practice because the transmission bandwidth and coding complexity increases without bound. But we can approach this limit by using a double, or concatenated, coding scheme. The Pioneer deepspace communication link uses this technique to obtain the performance required to overcome die large space loss [Yuen, 1983, Sec. 5.4.4]. The binary signal is first block encoded using a 255bit ReedSolomon code with 32 parity bits. The blockencoded signal is then encoded using the rate1/2 convolution^ code. The data is recovered at the receiver with a Viterbi decoder followed by a ReedSolomon decoder. As shown in Fig. 139, the BER performance for the concatenated code is only 4.2 dB above the Shannon limit at a BER of 10~5. Longer and more complex codes can be used to push performance even closer to the Shannon limit This technique is not presendy used for data rates much above 100 bps due to the complexity and cost of the decoding process. However, we expect this limitation to disappear in the future with the development of highspeed, lowcost digital processing circuits.
Figure 139 demonstrates that the BER is sensitive to the Eb/N0 level. At error rates below 10*4, a decrease of 1 dB in Eb/N0 will increase the BER about one order of magnitude. Thus, providing adequate link margin in our design (discussed later) is very important. Note that the Eb/N0 values given are theoretical, based on infinite bandwidth transmission channels and ideal receivers. In practice, we must account for bandlimiting effects, deviations from ideal filter responses, phase noise and frequency drift in local oscillators, noise in carrier tracking loops, and bit synchronizing errors. Thus, we must add 1 or 2 dB to the theoretical Eb/N0 to allow for these losses.
Choosing which modulation and coding technique to use depends on cost, complexity, difficulty of acquiring the signal, limits on transmission bandwidth, and susceptibility to interference or fading. In the case of powerlimited systems, where power is scarce but bandwidth is available, coding makes sense. Most systems today use some forward error correction coding to save transmitter power unless the data rate is greater than several hundred Mbps, in which case limits on both bandwidth and hardware speed become significant
Table 1311 showed that to obtain a low value of EbfNa for a BER of 10~s, we must be less efficient in using the spectrum, which means the transmission bandwidth must increase. This is the result of adding forward error correction check bits to the signal before modulation, thus increasing the transmission rate through the channel. However, recent techniques can achieve significant coding gains without increasing the bandwidth [Ungerboeck, 1982; Sklar, 1988, Sec. 7.10.6]. The basic idea is to combine the coding and modulation process to generate a set of possible coded signal patterns at RF, each pattern corresponding to an nbit word. The receiver knows the set of possible patterns and chooses the pattern that most closely resembles what it receives. For example, a fourstate, rate2/3, encoder combined with 8PSK modulation achieves a 3 dB coding gain over uncoded QPSK modulation with the same bandwidth. (8PSK is like QPSK except the carrier phase is set at one of 8 possible phases separated by 45deg intervals.) Such schemes have been proposed for highspeed data communication on satellite channels and are likely to be used in future space systems [Deng and Costello, 1989].
13.3.4 Atmospheric and Rain Attenuation
The transmission path loss caused by the Earth's atmosphere, La, is a function of frequency as shown in Fig. 1310. This figure gives the attenuation at 90deg elevation, that is, zenith. To determine the loss at elevation angles, fi, above 5 deg, divide the zenith attenuation by sin fi. At frequencies below 1,000 MHz, ionospheric scintillation can cause significant fluctuations in received amplitude and phase. These effects are most severe at frequencies below 200 MHz during periods of high sunspot activity, when they can disrupt communications (see Ippolito [1986], Chap. 8). Above 50 GHz, high attenuation occurs at frequencies corresponding to the oxygen absorption band. Virtually all Earthspace communications use frequencies between these two extremes, though some projects have considered the 90GHz band. Of special note is the high absorption band of oxygen at 60 GHz. Intersatellite links often operate at 60 GHz, using the atmosphere to shield from interference or jamming originating on the Earth's surface.
Figure 1311 shows that clouds and rain attenuation also add to losses, increasing with frequency, in the transmission path. This figure comes from the Crane model—a set of tables and equations based on observed climatic data used to estimate the rain attenuation (see Crane [1980], or Ippolito [1986]). This attenuation becomes an important consideration when designing systems employing satelliteEarth link frequencies above 10 GHz. Figure 1311 also shows that the attenuation increases rapidly as the antenna elevation angle decreases below 20 deg. When operating at frequencies above 20 GHz, the minimum elevation angle to the satellite should be specified at 20 deg, especially in high rainfall areas. Note, however, that increasing the minimum elevation angle dramatically reduces the size of the satellite's coverage area (see Sees. 5.3 and 5.4).
Frequency (GHz)
Fig. 1311. Rain Attenuation Predicted by Crane Model for Rain Climate Typical of the Northern United States. Ground station altitude = 0 km, latitude = 40°. For other cases, see Ippolito [1986],
Frequency (GHz)
Fig. 1311. Rain Attenuation Predicted by Crane Model for Rain Climate Typical of the Northern United States. Ground station altitude = 0 km, latitude = 40°. For other cases, see Ippolito [1986],
The percentage of time the link is available depends on the margin which the link has in clear weather. A higher link availability demands a greater margin. The availability numbers shown in Fig. 1311 correspond to the climate of northeastern United States. The availability for a specified link margin will be higher in the Midwest and lower in the Southeast, compared to those shown in the figure. (Bear in mind that these availability numbers come from average weather conditions over many years; they do not account for the possibility that this year the rainfall may be higher or lower than a normal year.)
A byproduct of rain attenuation is an increase in antenna temperature, Ta given by
where La is the rain attenuation given as a power ratio, and Ta is the temperature of the rain, usually assumed to be 290 K. The significance of this noise increase depends on the system noise in clear weather. For example, if a receiving system with a normal system temperature of727 K experienced 10 dB rain attenuation, its noise temperature would increase to 988 K, increasing N0 by 1.3 dB. The decrease in C/N0 would then be the sum of the rain attenuation (10 dB) and the increased noise (1.3 dB) totaling 11.3 dB.
13.3.5 Frequency Selection
Regulatory constraints exist on the selection of frequency band, transmission bandwidth, and power flux density. For example, international agreements have allocated frequency bands for space communications, as listed in Table 1312. These agreements originated with the International Telecommunications Union (ITU) and the
World Administrative Radio Conference (WARQ. They are administered in the United States by the Federal Communications Commission (FCC) for commercial users, and by the Interdepartmental Radio Advisory Committee for military users. The system designer must apply for and receive permission from the appropriate agency to operate at a specified frequency with the specified orbit and ground locations. This is often a timeconsuming procedure (see Chap. 21.1). For an excellent summary of this complex subject, see Morgan and Gordon [1989].
Frequency Band 
Frequency Range (GHz) 
Service 
Downlink Power Flux Density Limit (dBW/m2)  
Uplink 
Downlink  

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