CHEBYSHEV OPTIMIZATION OF SPARSE FIR FILTERS USING LINEAR-PROGRAMMINGWITH AN APPLICATION TO BEAMFORMING

Sparse FIR filter design, where some tap weights are zero, is of inter est as a means of reducing the expense or enhancing the performance of a filter, as a result of fewer or more efficiently placed multipliers , We show that for certain classes of filters with moderately wide pas sbands, it is possible to increase the stopband suppression by up to 2 0 dB without increasing the number of multipliers, simply by increasin g the number of delay elements, zeroing the appropriate taps, and opti mizing the other taps using linear programming, Another use for sparse FIR filters is for the case where multipliers have faded, Graceful de gradation can be achieved in some types of FIR filters by optimally ad justing the functional elements to compensate for the failed multiplie rs, This approach can also be used to minimize the peak sidelobe level for beamformers that may have failed elements, For the beamforming ca ses considered, the peak sidelobe level was decreased by as much as 5 dB.