Near-optimal uniqueword design in single-carrier block transmission systems

The problem of designing short sequences for nearoptimal training arises in single-carrier block transmission systems that use a unique word (UW) extension to facilitate frequency-domain equalization and channel estimation. Effectively, this problem involves constructing sequences of length Q ≤ N/2 that, when padded with zeros to make a length-N sequence, have good periodic autocorrelation properties and, thus, a (nearly) flat power spectrum. Using training sequences with a flat power spectrum allows each channel frequency response coefficient to be estimated with the same accuracy. In this paper, convex optimization theory is used to find near-optimal (in terms of channel estimation mean-square error) sequences with a constrained peak-to-average power ratio that can be used as UWs. The approach used here is a powerful method of solving optimization problems, and it is conjectured that this approach can be extended to similar problems in the field of communications.