Optimal phases of maximal length sequences for asynchronous spread-spectrum multiplexing

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Abstract
Optimal phases are given for maximal length linear feedback shift-register sequences (m-sequences) of periods 31 and 63 which are to be employed as signature sequences in an asynchronous direct sequence spread-spectrum multiple access communications system. The performance measure considered is the average signal/noise ratio at the output of the correlation receiver. The data presented is applicable to various forms of direct sequence spread-spectrum modulation including binary phase-shift keying, offset quadriphase-shift keying, and minimum shift keying modulation.