Accurate Approximation of QAM Error Probability on Quasi-Static MIMO Channels and Its Application to Adaptive Modulation

• Published in: IEEE transactions on information theory Vol. 53; no. 3; pp. 1151 - 1160
• Main Authors: Kharrat-Kammoun, F., Fontenelle, S., Boutros, J.J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive modulation; Antennas; Applied sciences; Approximation; Channels; Constellations; Covariance matrix; Eigenvalues and eigenfunctions; Error probability; Errors; Exact sciences and technology; H infinity control; Information theory; Information, signal and communications theory; Input output; Interference suppression; lattice constellations; Mathematical analysis; MIMO; Modulation; Modulation, demodulation; Multiaccess communication; multiple-input multiple-output (MIMO) antenna channels; Nonlinear filters; Probability; Quadrature amplitude modulation; Radiocommunications; Series (mathematics); Signal and communications theory; Signal to noise ratio; sphere decoding; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Performance evaluation; MIMO system; AWGN; Quadrature amplitude modulation; Error probability; Quasi static theory; Decoding; Conditional probability; Hyperplane; sphere decoding; multiple-input multiple-output (MIMO) antenna channels; Approximation error; lattice constellations; Antenna array; Multiple channel; Adaptive modulation
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2006.890731

An accurate approximation for the conditional error probability on quasi-static multiple-input multiple-output (MIMO) antenna channels is proposed. For a fixed channel matrix, it is possible to accurately predict the performance of quadrature amplitude modulations (QAM) transmitted over the MIMO channel in presence of additive white Gaussian noise. The tight approximation is based on a simple Union bound for the point error probability in the n-dimensional real space. Instead of making an exhaustive evaluation of all pairwise error probabilities (intractable in many cases), a Pohst or a Schnorr-Euchner lattice enumeration is used to limit the local theta series inside a finite radius sphere. The local theta series is derived from the original lattice theta series and the point position within the finite multidimensional QAM constellation. In particular, we take into account the number of constellation facets (hyperplanes) that are crossing the sphere center. As a direct application to the accurate approximation for the conditional error probability, we describe a new adaptive QAM modulation for quasi-static multiple antenna channels