Multiplicative mismatched filter for optimum sidelobe suppression in Barker codes

Barker codes are the only known bi-phase codes with the smallest achievable sidelobes. However, the longest Barker code of odd length is proven to be that of length 13. There is also a strong conjecture that the Barker codes of length 2 and 4 are the only ones there are of even length. The code of length 13 achieves a mainlobe to peak sidelobe ratio of only 22.28 dB which is less than the practical requirement of at least 30 dB. Mismatched filters have been proposed in the literature to improve this ratio. This is achieved at the cost of some deterioration in the signal to noise ratio at the filter output. In this paper, very efficient sidelobe suppression of Barker codes of length 13 is achieved through the use of a novel mismatched filter. This mismatched filter is comprised of a conventional matched filter cascaded with a computationally efficient filter based on multiplicative expansion. Several parameters are introduced in the terms of the expansion and are optimized to improve the performance of the filter. A version of this filter with three stages is shown to achieve a mainlobe to peak sidelobe ratio of almost 61.9 dB. This is achieved at the cost of some deterioration in the signal to noise ratio at the filter output. The loss in signal to noise ratio (SNR) is shown to be only 0.2 dB. It is suggested that by applying the proposed technique to compound Barker codes, the mainlobe to peak sidelobe ratio could be maintained while improving the signal to noise ratio performance.