Multidimensional signal constellation design for periodic channel impairments

We address the problem of designing a multidimensional signal constellation for the efficient transmission of symbols over periodic time-varying channels. The PCM telephone network is a classic example of such a channel. We describe a computationally efficient algorithm for designing the multidimensional signal constellation to maximize the data transmission rate over the channel. The algorithm takes into account constraints on the average error rate as well as the average transmit energy in designing the signal constellation. We provide simulation results on the performance of the proposed algorithm for PCM transmission over typical telephone channels