First Look at Average-Case Complexity for Planar Maximum-Likelihood Detection

In this paper, an efficient exact maximum-likelihood (ML) detection scheme is presented for a multiple-input single-output (MISO) system with real signal constellations. The proposed technique has a geometrical interpretation of exploring the points jointly "close" in all coordinate axes around the decoding hyperplane and is therefore dubbed planar detection. The fact that the lattice points which are close in all coordinate axes are much less, leads to dramatic reduction in detection complexity. Making a few approximations, this paper derives the average-case complexity exponent, e_c, for planar detection analytically in a closed form. Numerical results show that for an (n, 1) system, although the expected complexity is still exponential, complexity reduction of 2 exponents, i.e., from e_c to e_c -2, is realized and such advantage is promised irrespective of the size of the signal constellations and the received signal-to-noise ratio (SNR)