Data sources for simulation of m-ary systems

It has been generally assumed that binary data from a maximum-length pseudo-random binary source can be grouped into m-ary symbols that will uniformly cover constellation points in a modulation scheme due to the central limit theorem. This is not the case. Sources based on the Galois field GF(16) are introduced and compared to binary, GF(2), ones in terms of the mean and variability of the resulting bit error rate (BER) estimate using a single carrier quadrature amplitude modulation (16-QAM) system as an example. The use of data sources over GF(16) for Monte Carlo simulation of the example system eliminates BER estimate variability with certain channels. Such variability is important when the channel is such that some of the constellation points cause higher probabilities of error than others. The approach is then extended to orthogonal frequency division multiplex (OFDM) m-ary systems. It is found that it is important to map separate Galois field data sources to each sub-carrier in the case of OFDM systems. There is found to be some residual BER estimate variability. The extension of the approach to systems employing forward error correction coding and interleaving is discussed.