A Linear Network Coding Approach for Uplink Distributed MIMO Systems: Protocol and Outage Behavior

A distributed multiple-input-multiple-output (MIMO) system consists of M users served by L distributed base stations (BSs), where the BSs are connected to a central unit (CU) via L independent backhaul (BH) links. In this paper, we consider the design of an uplink distributed MIMO system where 1) the channel state information is not available at the transmitters and 2) the BH links are rate constrained. We propose a new linear network coding (LNC)-based protocol: the M users transmit simultaneously. Each BS generates N linear functions of the M users' messages, based on a preassigned LNC coefficient matrix. The CU collects N · L linear functions from the L BSs and recovers all M users' messages by solving these linear functions. The decoding becomes successful if the linear functions has full rank M and fails if the linear functions are rank deficient. We derive the preassigned LNC coefficient matrix that minimizes the probability of rank deficiency. We then analyze the outage probability (OP) of the proposed scheme over a Rayleigh fading channel. We analytically show that as long as the BH rate is greater than the individual data rate of one user, the OP of the proposed scheme decays like 1/SNR^L at high SNR. This is in contrast to the existing scheme whose OP decays like 1/SNR. As the BH rate constraint approaches M times the data rate of one user, the performance of the proposed scheme is 10/L log₁₀(L!) dB away from that of the full MIMO scenario at high SNR. We also develop a structured way to efficiently construct the preassigned LNC coefficient matrix that yields the optimized OP performance. Numerical results show that the proposed scheme has significantly improved performance over existing schemes.