A Transmitted Reference System for Communication in Random of Unknown Channels

When communicating through an unknown or random channel, it often becomes advisable to utilize some of the transmitted energy to allow the receiver to measure certain channel parameters. In this paper, a set of transmitted signals are chosen of the form
\{x_{m}^{(i)}(t), x_{r}(t)\}, t\epsilon(0,T)
, where
i = 1, 2,...,l
. Here
x_{m}^{(i)}(t)
represents the message or information portion of the signal and
x_{r}(t)
represents that portion which is transmitted for the purpose of identifying the channel. The random multipath channel model is assumed, and an optimum "one-shot" Bayesian receiver is derived under the Gaussian assumption for channel filter and additive noise. An expression for error probability is derived for a special case of binary phase reversal keying, assuming that the additive noise in the channel is white. Probability of error curves are plotted as a function of various system parameters for both the optimal and a simpler suboptimal receiver. The energy sharing problem between the message and reference portion of transmitted signal is also considered. The divergence criterion is utilized and shown to be an effective method for deriving the optimum trade-off.