Linear detectors such as zero forcing (ZF) or minimum mean square error(MMSE) are imperative for large/massive MIMO systems for both the downlink anduplink scenarios. However these linear detectors require matrix inversion whichis computationally expensive for such huge systems. In this paper, we assertthat calculating an exact inverse is not necessary to find the ZF/MMSE solutionand an approximate inverse would yield a similar performance. This is possibleif the quantized solution calculated using the approximate inverse is same asthe one calculated using the exact inverse. We quantify the amount ofapproximation that can be tolerated for this to happen. Motivated by this, wepropose to use the existing iterative methods for obtaining low complexityapproximate inverses. We show that, after a sufficient number of iterations,the inverse using iterative methods can provide a similar error performance. Inaddition, we also show that the advantage of using an approximate inverse isnot limited to linear detectors but can be extended to non linear detectorssuch as sphere decoders (SD). An approximate inverse can be used for any SDthat requires matrix inversion. We prove that application of approximateinverse leads to a smaller radius, which in turn reduces the search spaceleading to reduction in complexity. Numerical results corroborate our claimthat using approximate matrix inversion reduces decoding complexity inlarge/massive MIMO systems with no loss in error performance.
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