6.1 The power in RF waveforms can be compared by assuming that the waveform is supplied to a 1 load. For a sine wave V cos (t + ), the power in the 1 load is ()V^2 watts. QPSK and 8-PSK signals have a constant magnitude V for all symbols, so relative power per symbol is ()V^2 watts.

The 16-QAM and 16-APSK constellations shown in Figure 6.3 have I and Q voltage levels of V and 3V. Calculate the relative power for a 16-APSK signal compared to an 8-PSK signal, and for 16-QAM compared to QPSK, in dB. How do these results relate to the CNR values required for BER of 10^6 for these signals in Table 6.1

1101 1001 1 0001 0101 1010 1000 0000 0010 1100 1000 0000 0100 0110 1110 1100 0100 1110 0110 0010 0110 0111 1111 1101 0101 1111 1011 0011 0111 0011 0001 1011 1001 16-QAM 16-APSK Figure 6.3 Constellation diagrams for 16-QAM and 16-APSK. The Gray coding applied in each case is not unique; other Gray coded sequences can be used, and the assignment of symbols to phase states is also arbitrary. 16-APSK is the preferred choice when the transmitted signal must pass through a non-linear transponder, but 16-QAM has the advantage that a lower CNR is required for a given bit error rate than with 16-APSK. Table 6.1 Theoretical CNR and Eb/N. ratio required to achieve BER of 10-6 in an ideal link Modulation CNR (dB) Eb/N ratio (dB) BPSK 10.6 10.6 QPSK 13.6 10.6 8-QAM 17.6 10.6 8-PSK 18.5 14.0 16-QAM 20.5 14.5 16-APSK 21.0 15.0 16-PSK 24.3 18.3 32-QAM 24.4 17.4 1101 1001 1 0001 0101 1010 1000 0000 0010 1100 1000 0000 0100 0110 1110 1100 0100 1110 0110 0010 0110 0111 1111 1101 0101 1111 1011 0011 0111 0011 0001 1011 1001 16-QAM 16-APSK Figure 6.3 Constellation diagrams for 16-QAM and 16-APSK. The Gray coding applied in each case is not unique; other Gray coded sequences can be used, and the assignment of symbols to phase states is also arbitrary. 16-APSK is the preferred choice when the transmitted signal must pass through a non-linear transponder, but 16-QAM has the advantage that a lower CNR is required for a given bit error rate than with 16-APSK. Table 6.1 Theoretical CNR and Eb/N. ratio required to achieve BER of 10-6 in an ideal link Modulation CNR (dB) Eb/N ratio (dB) BPSK 10.6 10.6 QPSK 13.6 10.6 8-QAM 17.6 10.6 8-PSK 18.5 14.0 16-QAM 20.5 14.5 16-APSK 21.0 15.0 16-PSK 24.3 18.3 32-QAM 24.4 17.4