Structure of an Optimum Linear Precoder and its Application to ML Equalizer

• Published in: IEEE transactions on signal processing Vol. 56; no. 8; pp. 3690 - 3701
• Main Authors: Lokesh, S.S., Kumar, A., Agrawal, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Bit error rate; Channel capacity; Codes; Constraint optimization; Decision feedback equalizers; Detection, estimation, filtering, equalization, prediction; Equalizer; Equalizers; Error analysis; Errors; Exact sciences and technology; Feedback; Information, signal and communications theory; Invariants; Least mean squares algorithm; Maximization; maximum likelihood (ML); Mean square error methods; Mean square errors; Miscellaneous; Modulation, demodulation; multiple-input multiple-output (MIMO); Optimization; optimum beamforming; Phase shift keying; Power measurement; precoder; rotation invariance; Rotation measurement; Signal and communications theory; Signal processing; Signal to noise ratio; Signal, noise; Studies; Telecommunications and information theory; Transmitters; Performance evaluation; MIMO system; Channel capacity; Input signal; Bit error rate; optimum beamforming; precoder; Equalizer; Binary phase shift keying; Information transmission; Beam forming; Optimization; Mean square error; rotation invariance; maximum likelihood (ML); Rotational invariance; Telecommunication system; Signal processing; Minimal distance; Maximum likelihood; Signal to noise ratio; multiple- input multiple-output (MIMO)
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2008.920147

The structure of an optimum linear precoder for a rotation-invariant performance measure is obtained subject to the constraint of limited input power for a block transmission scheme. It is shown that several known performance measures of a communication system are rotation invariant. The rotation invariant property provides a unified framework for obtaining the structure of an optimum linear precoder for several criteria such as: 1) maximization of minimum distance; 2) maximization of channel capacity; and 3) optimization of different performance measures, such as bit-error rate (BER), mean square error, signal-to-noise ratio of optimum equalizers (linear minimum mean square error, zero-forcing, maximum likelihood (ML), zero forcing-block decision feedback, minimum mean square error-block decision feedback, etc.). This framework provides a method for obtaining the structure of an optimum linear precoder for BER performance measure of the ML equalizer. The structure turns out to be a channel diagonalizing structure after a prerotation of the input constellation. Using this structure, the properties of the optimum precoder that minimize the BER of the ML equalizer for two binary phase-shift keying symbols transmission under input-power constraint are studied.