On Frame Synchronization for Multiple Access Channels

The problem of frame synchronization is formulated and investigated for multiple access channels (MAC). Several decision rules for locating the starting positions in continuously transmitted frames are proposed and compared, for both user- synchronous and user-asynchronous cases. It is shown that the common decision rule based on the correlation statistic is suboptimal, and that correction terms need be added in order to achieve an improved detection performance. For the user-asynchronous case, the optimal joint decision rule is derived in analytical form for two-user MAC and is highly complex, and is shown to suffer from a high computational complexity. To reduce the complexity, suboptimal separate decision algorithms with and without Gaussian approximation are derived, and it is illustrated using Monte Carlo simulation that those low-complexity algorithms only incur a slight degradation in optimality.