On the design of PN codes in decentralized networks

This paper provides a unified measure to design binary pseudo-random (PN) codes in a wireless decentralized network in which several transmitter-reciever pairs share the spectrum. In a decentralized network, users are not aware of the code-books of each other. Hence, in the high SNR regime, interference highly degrades the achievable rates of users as interference cancellation is impossible. On the other hand, decentralized networks have no fixed underlying infrastructure, i.e., there is no central management to assign ldquogoodrdquo PN codes with appropriate cross-correlation properties to different users. As such, choosing the same PN code by different users may result in losing the packets transmitted by these users. These shortcomings motivate us to propose a decentralized scheme that enables all users to coexist fairly, while utilizing the spectrum efficiently. We introduce a distributed signaling scheme (using i:i:d: Gaussian code-books) called Bernoulli-Direct-Sequence (BDS) where all users spread their signals by locally generated binary PN codes. Due to the dynamic nature of interference, sensing the spectrum to measure the interference is practically not possible. This makes the interference plus noise probability density function (PDF) be mixed Gaussian. We obtain upper and lower bounds on the rates of users that coincide as SNR tends to infinity. This enables us to derive a general formula for the sum-rate multiplexing gain in the network. Subsequently, we propose a general rule to design the PN codes in the sense of increasing the sum-rate multiplexing gain in the network. It is shown that depending on the number of active users in the system, there is a certain amount of spreading length that leads to the highest multiplexing gain per user. Several design examples are provided at the end.