Performance of anM-ary orthogonal communication system using stationary stochastic signals
Andrew J. Viterbi · IEEE Transactions on Information Theory · 1967
This paper considers the performance of a communication system which transmits forTseconds the real part of a sample function of one ofMstationary complex Gaussian processes whose spectral densities are all frequency translations of the functionS_{\xi (f). At the receiver white Gaussian noise of one-sided densityN_{0}is added. The center frequencies of the processes are assumed to be sufficiently separated that theMcovariance functions are orthogonal overT. Exponently tight bounds are obtained for the error probability of the maximum likelihood receiver. It is shown that the error probability approaches zero exponentially withTfor all ratesR = (\ln M)/Tup toC= \int_{-\infty}^{\infty} [S_{\xi (f)/N_{0}] df - \int_{- \infty}^{\infty} \ln [1 + S_{\xi}(f)/N_{0}] dfwhich is shown to be the channel capacity. Similar results are obtained for the case of stochastic signals with specular components.