Source: Reference 5.

Source: Reference 5.

Table 4.5 shows the maximum free distance for R = 1/2 systematic and nonsystematic codes for K = 2 through 5. It should be noted that for large constraint lengths the results are even more widely separated.

4.2.5 Channel Performance of Uncoded and Coded Systems

4.2.5.1 Uncoded Performance. For uncoded systems a number of modulation implementations are reviewed in the presence of additive white Gaussian noise (AWGN) and with Rayleigh fading. The AWGN performance of BPSK, QPSK, and 8-ary PSK is shown in Figure 4.12. AWGN is typified by thermal noise or wideband white noise jamming. The demodulator for this system requires a coherent phase reference.

Another similar implementation is differentially coherent phase-shift keying. This is a method of obtaining a phase reference by using the previously received channel symbol. The demodulator makes its decision based on the change in phase from the previous to the present received channel symbol. Figure 4.13 gives the performance of DBPSK and DQPSK with values of BER versus Eb/N0.

Figure 4.12. Bit error probability versus Eb/N0 performance of BPSK, QPSK, and octal-PSK (8-ary PSK). (From Ref. 5.)

Figure 4.12. Bit error probability versus Eb/N0 performance of BPSK, QPSK, and octal-PSK (8-ary PSK). (From Ref. 5.)

Independent Rayleigh fading can be assumed during periods of heavy rainfall on satellite links operating above about 10 GHz (see Chapter 9). Such fading can severely degrade error rate performance. The performance with this type of channel can be greatly improved by providing some type of diversity. Here we mean providing several independent transmissions for each information symbol. In this case we will restrict the meaning to some

Figure 4.13. Bit error probability versus Eb/N0 performance of DBPSK and DQPSK. (From Ref. 5.)

Figure 4.13. Bit error probability versus Eb/N0 performance of DBPSK and DQPSK. (From Ref. 5.)

form of time diversity that can be achieved by repeating each information symbol several times and using interleaving/deinterleaving for the channel symbols. Figure 4.15 gives binary bit error probability for several orders of diversity (L = order of diversity; L = 1, no diversity) for the mean bit energy-to-noise ratio (Eb/N0). This figure shows that for a particular error rate there is an optimum amount of diversity. The modulation is binary FSK.

Figure 4.14. Bit error probability versus Eb/N0 for M-ary FSK: M = 2 for BFSK. (From Ref. 5.)

Figure 4.14. Bit error probability versus Eb/N0 for M-ary FSK: M = 2 for BFSK. (From Ref. 5.)

Table 4.6 recaps error performance versus Eb/N0 for the several modulation types considered. The reader should keep in mind that the values for Eb/N0 are theoretical values. A certain modulation implementation loss should be added for each case to derive practical values. The modulation implementation loss value in each case is equipment driven.

4.2.5.2 Coded Performance. Figures 4.16, 4.17, and 4.18 show the BER performance K = 7, R = 1/2; K = 7, R = 1/3; and K = 9, R = 3/4 convo-

Figure 4.15. Bit error probability versus Eb/N0 performance of binary FSK on a Rayleigh fading channel for several orders of diversity. L = order of diversity. (From Ref. 5.)

Figure 4.15. Bit error probability versus Eb/N0 performance of binary FSK on a Rayleigh fading channel for several orders of diversity. L = order of diversity. (From Ref. 5.)

lutional coding systems on an AWGN channel with hard and 3-bit soft quantization. Figures 4.16 and 4.18 again illustrate the advantages of soft quantization discussed in Section 4.2.2.2.

Reference 5 reports that simulation results have been run for many other codes (from those discussed) on an AWGN channel. The results show that for rate 1/2 codes, each increment increase in the constraint length in the

Channel |
Modulation / Demodulation |
Eb / N0 (dB) Required for Given Bit Error Rate | ||||||

10 - 1 |
10 - 2 |
10 - 3 |
10 - 4 |
10 - 5 |
10 - 6 |
10 - 7 | ||

Additive white |
BPSKand QPSK |
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