New, simple bounds are presented for the probability of error in a binary hypothesis test for communications using diversity signaling in correlated Rayleigh fading. The bounds are developed in the context of pairwise error-event probabilities in decoding an error-correction code. A long-standing conjecture regarding the form of worst-case error events in exponentially correlated Rayleigh fading is also proven. The utility of the results is illustrated by their application to transfer-function bounds on the probability of bit error for a system using a convolutional code. The closed-form transfer-function bounds are shown to be tighter than previously developed transfer-function bounds for communications in exponentially correlated Rayleigh fading.
Communication systems must maintain tight timing synchronization between the transmitter and receiver. Systems typically pull-in timing from a large timing offset and then track timing once it has been sufficiently pulled in. When timing errors are large, additional reference symbols are needed to pull-in time. In some frequency hopping systems, the time pull-in step must be repeated for every hop and could occur many times a second. It then becomes important to develop rapid time pull-in algorithms that can operate on a limited number of data and reference symbols. This paper presents two algorithms for rapid time pull-in. The performance as a function of the number of data and reference symbols is shown.
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