Performance analysis of DS/SS system according to the loop gain under the Nakagami-m fading channel

The performance of a direct sequence spread spectrum acoustic communications signal, operating over a multi-path Nakagami fading channel, is investigated when corrupted by phase noise as well as additive white Gaussian noise (AWGN). The phase noise arises from phase locked loop (PLL) dynamics and results in imperfect receiver phase estimates whereby the phase errors assume Tikhonov densities. The phase estimates are used by a multi-path combining RAKE receiver for demodulation. Approximate upper-bounds on the bit error probability are obtained and evaluated for different combinations of channel parameters and for various values of the average loop signal-to-noise ratio (SNR). Results indicate that the PLL loop gain was increased from 5 dB to 10 dB, the performance of system was increased by 6 dB, when increased from 5 dB to 10 dB, increased by 0.9 dB, when increased from 10 dB to 20 dB, increased by 0.8 dB, and when from 20 dB to 30 dB, increased by 0.2 dB. With the above data, it was shown that the limit of gain required in the PLL of the receiver is 30 dB