Random Projection based Fast Multi-User Detectors in Uplink massive MIMO Communication Networks

This work proposes a novel random projection (RP) framework based linear detection techniques in massive multiple-input multiple-output (MIMO) communication networks. Under this framework, exploiting the variants of random projection techniques, this work proposes a series of detectors namely, rademacher projection, very sparse random projection (VSRP), fast Johnson-Lindenstrauss transform (FJLT), and count-sketch projection based detectors. Recently proposed zero-forcing (ZF) and minimum mean squared error (MMSE)-based linear detectors approximate the matrix inversion that results in the same asymptotic detection run-time complexity. The detectors proposed in this work achieve asymptotically faster detection than these detectors with a trade-off in the error performance. This work presents a closed-form expression for the symbol error probability (SEP) along with an upper bound on the error probability to characterize the detection performance of the mentioned RP-based detectors in the massive MIMO networks. Further, an upper bound on the Euclidean distance between the test statistic of the proposed detector and the ZF detector is obtained that establishes a relation between the approximation error vs. speed-up achieved by using RP-based detectors. The proposed random projection-based detectors achieve asymptotically faster run time complexity than the state-of-the-art linear massive MIMO detectors. Finally, simulation results obtained for average symbol error probability highlight the comparable performance of proposed random projection-based detectors with the existing linear massive MIMO detectors.