Abstract: A method and apparatus for multiplying a first array including a plurality of equal-sized subgroups of elements, each including at least a minimum number of zero-elements, by a second array, by, for each subgroup of elements of the first array: loading a subgroup mask indicating locations of non-zero elements within the subgroup of elements of the first array, from memory into a first register; loading, from memory into a second register, the non-zero elements in the subgroup of elements of the first array; loading, from memory into a third register, a subgroup of elements of the second array corresponding to the subgroup of elements of the first array; and multiplying each of the non-zero elements of the first array by the corresponding elements of the second array, wherein the corresponding elements of the second array are selected according to the subgroup mask.

Abstract: A system and method for synchronizing to a received signal in an IR-UWB receiver including sampling the received signal in a frequency that is less than a Nyquist frequency of the received signal; for each part of the sampled received signal that is equal in length to a synchronization symbol: calculating a cross-correlation between the synchronization symbol and the part of the sampled received signal that is equal in length to the synchronization symbol; calculating at least one autocorrelation, where each autocorrelation is performed between the results of the cross-correlation and the results of the cross-correlation delayed by a time lag that equals one or more time-durations of the synchronization symbol; accumulating the results of each of the at least one autocorrelation to obtain at least one coarse synchronization window; and analyzing the at least one coarse synchronization window to detect presence of the synchronization symbol in the received signal.

Abstract: A method and system for performing quadrature amplitude modulation (QAM) decoding of a received signal includes finding for each layer a region in a first constellation diagram of the received signal, the region including a portion of the first constellation diagram, the portion having the same size of a second constellation diagram, and a first constellation order of the received signal is higher than a second constellation order of the second constellation diagram; and, for each layer: finding a first portion of bits based on bits that are constant among constellation points located in the region of the layer; decoding the received signal using a QAM decoder having the second constellation order to obtain a second portion of bits; adjusting the second portion of bits based on the region of the layer; and merging the first portion of bits with the second portion of bits to obtain a decoded symbol.