A new approach to improve multiplexing gain in decentralized networks via frequency hopping and repetition coding

This paper addresses a distributed signaling scheme to improve the multiplexing gain (MG) in a wireless decentralized network with a fixed number u > 1 of frequency sub-bands to be shared among K transmitter-reciever pairs. 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 canceling the interference is impossible. On the other hand, decentralized networks have no fixed underlying infrastructure, i.e., there is no central management to assign certain non-overlaping portions of the spectrum to different users. As such, choosing the same sub-band by different users may result in losing the data transmitted on this sub-band. 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 repetition-frequency hopping (RFH) where all users keep transmitting the same set of independent signals over different portion of the spectrum along a certain repetition frame. Due to the dynamic nature of interference, sensing the spectrum to locate 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. We show that it is possible to achieve higher multiplexing gains in such systems if the length of the repetition frame along the time-axis is large enough. In fact, in many cases, there is a certain amount of repetition that leads to the highest multiplexing gain per user.