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8/4 X (1 + r 8/5 X (1 + r 8/6 X (1 + r 8/7 X (1 + r 8/8 X (1 + r 8/9 X (1 + r theoretical W and S/N values at 10"6 BER; calculated values may differ slightly due to different assumptions.

bQPR = quadrature partial response.

cAs an example, BCH error correction with a redundancy of 6.7% (r = 6.7%) is used for calculations in this table.

Source: Table 1a, p. 241, ITU-R Rec. F.1101, 1994 (Ref.1).

The actual signal-to-noise parameter is related to the average RSL (receive signal level), for the relevant BER, through the noise figure of the receiver and the bit rate relationship:

RSLber s 10 log kT* q 10 log bn q NF(db) q s/Nber (3.11)

### 3.4.4 Notes on Implementation and BER Performance

An ideal digital radio system using quadrature modulation is shown in Figure 3.9. The system is ideal in the sense that the filters used are bandlimited to

*In many texts this is taken as —204 dBW or —174 dBm, the noise temperature of an uncooled (room temperature) ''perfect'' receiver in 1 Hz of bandwidth.

the Nyquist bandwidth (i.e., a = 0). The transmitted RF spectrum resulting from the use of such a filter is thus ideally band-limited to a bandwidth of 1 /T, where T is the transmitted symbol (baud) rate.

As shown in Figure 3.9 (see also Figure 3.2), the two baseband signals resulting from a pair of data bits are used (in its simplest configuration, QPSK) to modulate quadrature carriers. At the far end receiver, the RF signal is down converted back to baseband by the use of coherent quadrature mixer references. Because of the ideal Nyquist character of the channel, samples of the baseband signals will be transmitted with impulse weights corrupted by the channel noise, but with zero intersymbol interference (ISI). The sampled quadrature components at the receiver are fed to a decision device that optimally decides which quadrature pair was transmitted given the receiver pair of samples.

Figure 3.10 is a conceptual block diagram of a 16-QAM modulator. It is similar to the QPSK modulator shown in Figure 3.9 except that the I

(in-phase) and Q (quadrature) carrier are each modulated by 4-level signals. Two serial bits are converted to one of four voltage levels, which control the output of the balanced modulators. This shows how the symbol rate (baud rate) becomes Rb/4. In 64-QAM, 3 bits are taken to generate one of eight voltage levels on both the I and Q streams. For such systems it is necessary to use linear modulators; otherwise, the phase state diagram will be distorted since the four voltage levels will not translate directly to the correct carrier level.

Bit error rate performance for various QAM and PSK waveforms for a BER of 1 X 10"6 is shown in Table 3.1. The column W in the table is defined the same way as Eb/N0, equation (3.8). Some channel capacity limits are shown in Figure 3.11. Typical error performance curves are shown in Figure 3.12.

Figure 3.11 shows plots comparing ideal M-QAM and M-PSK systems. The figure gives values of Cj (bit packing) in bits/s/Hz versus Eb/N0 for error rates of 1 X 10 "5, 1 X 10 "7, and 1 X 10 "9. At the left in the figure is a plot of Shannon's channel-capacity curve. Shannon's curve represents a theoretical bound on the absolute maximum capacity at zero error rate for

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