Distributions of soft-decision symbols using channel-estimation based equalizers

For communications, the estimated symbols (the output of a channel equalizer) is sometimes referred to as soft-estimate of the (transmitted) symbols. The mean squared Euclidian distribution between the soft symbol and true symbols yields the mean squared symbol estimation error, sometimes referred to as the soft-decision error. The soft symbol distribution is a key measure of the equalizer performance and is used for calculating the probability of bit errors. In this paper, we apply a channel estimation (CE) based decision feedback equalizer (DFE) to at sea data. For CE-DFE, we assume channel estimation in the training mode to avoid the error feedback problem that often occurs in real data processing. The reason is to study the relationship between equalizer performance and channel estimation performance without the error feedback problem. Specifically, we investigate the relation between the soft-decision error and signal prediction error; the latter is used as a measure for the channel estimation error. For channel estimation, we used various algorithms based on signal subspace tracking as well as conventional full space tracking. For each channel estimation algorithm, we estimate the symbol distribution. We find the distributions of the soft-estimate symbols are well fitted by a Gaussian normal distribution, with a variance predictable by the signal prediction error.