Performance and complexity analysis of infinity-norm sphere-decoding


Dominik Seethaler and Helmut Bölcskei


IEEE Transactions on Information Theory, Vol. 56, No. 3, pp. 1085-1105, Mar. 2010.

DOI: 10.1109/TIT.2009.2039034

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Promising approaches for efficient detection in multiple-input multiple-output (MIMO) wireless systems are based on sphere-decoding (SD). The conventional (and optimum) norm that is used to conduct the tree traversal step in SD is the l2-norm. It was, however, recently observed that using the l-infinity-norm instead reduces the hardware complexity of SD considerably at only a marginal performance loss. These savings result from a reduction in the length of the critical path in the circuit and the silicon area required for metric computation, but are also, as observed previously through simulation results, a consequence of a reduction in the computational (i.e., algorithmic) complexity. The aim of this paper is an analytical performance and computational complexity analysis of l-infinity-norm SD. For independent and identically distributed (i.i.d.) Rayleigh fading MIMO channels, we show that l-infinity-norm SD achieves full diversity order with an asymptotic SNR gap, compared to l2-norm SD, that increases at most linearly in the number of receive antennas. Moreover, we provide a closed-form expression for the computational complexity of l-infinity-norm SD based on which we establish that its complexity scales exponentially in the system size. Finally, we characterize the tree pruning behavior of l-infinity-norm SD and show that it behaves fundamentally different from that of l2-norm SD.


Algorithmic complexity, data detection, hardware complexity, infinity norm, maximum-likelihood, multiple-input multiple-output (MIMO) wireless

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