An algorithmic approach to preamble sequence optimization

When using coherent demodulation techniques, it is often necessary to include sequences of known symbols within the transmission in order to facilitate synchronization and, when advanced equalization algorithms are employed, channel estimation. In many cases it is possible to employ well-known sequences with desirable properties for use in synchronization. In some cases, however, to remove the overt signature that the repeated use of these known sequences causes, pseudo-random sequences are required. The conventional method of choosing such pseudo-random sequences relies on an exhaustive search algorithm. However, the computational requirements for a search of moderate length sequences are immense. In practice, for sequences of moderate length, the usual procedure is to evaluate sequences generated at random against several well-defined criteria. We present a computationally efficient method for deriving PSK sequences with good properties for signal detection and channel estimation. From an initial random sequence, a gradient descent algorithm is used to iteratively improve the sequence, based on the evaluation criteria. This algorithmic approach is shown to reduce the time required to generate a set of sequences, meeting the specified performance criteria, by more than two orders of magnitude in some cases. The method is particularly applicable to the design of pseudorandom sequences for preamble and training segments in serial-tone HF waveforms. Although the technique is general in nature, examples provided focus on the design of 8PSK sequences for serial-tone HF waveforms