On The Design of Signature Codes in Decentralized Wireless Networks

This paper addresses a unified approach towards communication in decentralized wireless networks of separate transmitter-receiver pairs. Different transmitters are connected to different receivers through channels with static and non-frequency selective gains. In general, users are unaware of each other’s codebooks and there is no central controller to assign the resources in the network to the users. A randomized signaling scheme is introduced in which each user locally spreads its Gaussian signal along a randomly generated spreading code comprised of a sequence of nonzero elements over a certain alphabet. Along with spreading, each transmitter also masks its output independently from transmission to transmission. Using a conditional version of entropy power inequality and a key lemma on the differential entropy of mixed Gaussian random vectors, achievable rates are developed for the users. Assuming the channel gains are realization of independent continuous random variables, each user finds the optimum parameters in constructing the randomized spreading and masking sequences by maximizing the average achievable rate per user. It is seen that as the number of users increases, the achievable Sum Multiplexing Gain of the network approaches that of a centralized orthogonal scheme where multiuser interference is completely avoided. An interesting observation is that in general the elements of a spreading code are not equiprobable over the underlying alphabet. This is in contrast to the customary use of binary PN codes in spread spectrum communications in which the code elements may be selected with equal probability over {−1, 1}. This particularly happens if the number of active users is greater than three. Finally, using the recently developed extremal inequality of Liu-Viswanath, we present an optimality result showing that transmission of Gaussian signals via spreading and masking yields higher achievable rates than the maximum achievable rate attained by applying masking only. ar X iv :1 00 3. 04 45 v1 [ cs .I T ] 1 M ar 2 01 0