Complexity of Verdu optimum multiuser detection algorithm in multichannel CDMA systems

A statistical characterization of the complexity function of the Verdu optimum multiuser detection (VOMD) algorithm is presented for a communication system employing a finite number of randomly accessed orthogonal channels and a finite number of simultaneous users. Multichannel code-division multiple-access (CDMA) systems are proposed. It is proved that the probability, in which the individual channel complexity is greater than A^r(1+α), approaches zero exponentially fast as the average number of simultaneous users in each channel increases, where A is the modulation alphabet size and α>0. When the number of simultaneous users is large, the complexity of applying the VOMD algorithm to each individual channel is negligible when compared with the complexity of applying the same algorithm directly to the traditional single-channel CDMA system supporting the same number of simultaneous users. The probability distribution of the joint complexity function of the aggregate system is found. It is shown that when the number of simultaneous users is large, the joint complexity function is negligible compared with applying the VOMD algorithm directly to the traditional single-channel CDMA system supporting the same number of simultaneous users. Therefore, a multichannel CDMA communication system can support a comparable population of simultaneous users to the traditional single-channel CDMA system of comparable bandwidth, while reducing the complexity of optimum multiuser detection to a practical level