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An improved sphere decoder for MIMO systems

The Maximum Likelihood (ML) detector is a detection criteria which yields an optimal solution to Multiple-Input Multiple-Output (MIMO) systems but however, at the expense of its NP-hard complexity. Instead, the Sphere Decoder (SD) was proposed as an efficient algorithm for finding the solution to the ML detection problem in MIMO digital communication systems. Unlike the ML detector whose complexity rises exponentially with the number of transmit and receive antennas, the complexity of the SD is polynomial for both finite and infinite lattices which makes real-time implementation of the ML detector practical. The choice of the initial radius for the SD has a significant impact on the complexity and the performance of the SD. However, the problem of selecting the initial radius is NP-hard itself. In this paper, we propose a simple Schnorr-Euchner SD (SE-SD) with a novel radius based on the received signal, noise statistics, number of transmit antennas, the energy of the transmitted symbols and on the channel matrix. The proposed method does not only reduce the complexity of the SD, but it also improves the bit error rate performance of the SD, particularly at low signal-to-noise ratios (SNR). To demonstrate the feasibility of our proposed method, we compare our method with the conventional SD radius and with other methods proposed in the literature.