Upper processing gain bound of the spreading signal in multipath fading channels

Using the joint algorithm of coherent detection and non-coherent detection, the upper processing gain bound of the spreading signal, which is two-dimensional spread spectrum signal relative to BPSK and transmitted in rich scattering multipath fading channel, was sought. Firstly, the expression of the processing gain of the spreading signal was calculated. Secondly, with increasing signal bandwidth or symbol period unlimitedly, the processing gain was bounded. At last, it was obtained that the upper processing gain bound is determined by the channel parameters and signal noise ratio. By analysis and simulation, the processing gain of the spreading signal, relative to BPSK and transmits in rich scattering multipath fading channel, is not more than 30dB, when the signal noise ratio is 20dB, the maximum Doppler shift is 100Hz, and the negative exponential factor is 5×10 ^-6.