Abstract: The present solution provides methods and systems for realizing hardware efficient mismatched filters for pulse compression codes. For pulse compression codes with sufficiently small sidelobe structures, such as in the cases of odd length Barker codes, the proposed filters require a small number of adders and multipliers per output. This translates to significantly reduced chip-area and lower power consumption when implemented on a chip. In one aspect, the present application features a method for suppressing an undesired part of a waveform. The method includes filtering a signal via a filter. In one embodiment, the signal includes an expected waveform that can be represented as a sum of the desired part and the undesired part. The impulse response of the filter can be represented a sum of the desired part and a negative of the undesired part.

Abstract: The present solution provides methods and systems for realizing hardware efficient mismatched filters for pulse compression codes. For pulse compression codes with sufficiently small sidelobe structures, such as in the cases of odd length Barker codes, the proposed filters require a small number of adders and multipliers per output. This translates to significantly reduced chip-area and lower power consumption when implemented on a chip. In one aspect, the present application features a method for suppressing an undesired part of a waveform. The method includes filtering a signal via a filter. In one embodiment, the signal includes an expected waveform that can be represented as a sum of the desired part and the undesired part. The impulse response of the filter can be represented a sum of the desired part and a negative of the undesired part.

Abstract: Very efficient sidelobe suppression of Barker codes is achieved through the use of a mismatched filter, which is comprised of a conventional matched filter cascaded with a computationally efficient filter based on multiplicative expansion. Several constant parameters are introduced in the terms of the expansion and are optimized to improve the performance of the filter. Optimized mismatched filters for length 13, 11, 7 and 5 Barker codes are presented. For each of these codes, filters with one, two and three stages are studied. The technique is extended to compound Barker codes based on their representation in a factored form in the z-domain. Hardware requirements for the filters discussed in the disclosure are also presented.

Abstract: A new class of biphase complementary code sets is proposed. Individual codes in each set have peak sidelobes of unity magnitude. The individual codes could have gaps of zeros but they are interlaced together without gaps in the final scheme. A number of such codes, as introduced here, use Barker codes as building blocks with additional elements from {+1,?1,0}. The main drawback of regular complementary codes longer than 4 is that they have sidelobe magnitude greater than unity. In the presence of frequency selective fading, inexact sidelobe cancellation results in non-zero sidelobes at the output. These sidelobes are minimized by using sets with individual codes that have peak sidelobes of unity magnitude. The constituent codes are transmitted at different frequencies. They are transmitted in parallel or using an appropriate combination of frequency division multiplexing (FDM) and time division multiplexing (TDM) such that the final transmission scheme is free of gaps.

Abstract: Very efficient sidelobe suppression of Barker codes is achieved through the use of a mismatched filter, which is comprised of a conventional matched filter cascaded with a computationally efficient filter based on multiplicative expansion. Several constant parameters are introduced in the terms of the expansion and are optimized to improve the performance of the filter. Optimized mismatched filters for length 13, 11, 7 and 5 Barker codes are presented. For each of these codes, filters with one, two and three stages are studied. The technique is extended to compound Barker codes based on their representation in a factored form in the z-domain. Hardware requirements for the filters discussed in the disclosure are also presented.