Abstract
This paper examines the optimum design of FIR precoders or equalizers for multiple-input multiple-output (MIMO) frequency-selective wireless channels. For the case of a left-coprime FIR channel, which arises generically when the number nT of transmit antennas is larger than the number nR of receive antennas, the Bezout matrix identity can be employed to design an FIR MIMO precoder that equalizes exactly the channel at the transmitter. Similarly, for a right-coprime FIR channel, the Bezout identity yields an FIR zero-forcing MIMO equalizer. Unfortunately, Bezout precoders usually increase the transmit power, and Bezout equalizers tend to amplify the noise power. To overcome this problem, we describe in this paper a convex optimization technique for the optimal synthesis of MIMO FIR precoders subject to transmit power constraints, and of MIMO FIR equalizers with output noise power constraints. The synthesis problem reduces to the minimization of a quadratic objective function under convex quadratic inequality constraints, so it can be solved by employing Lagrangian duality. Instead of solving the primal problem, we solve the lower-dimensional dual problem for the Lagrange multipliers. When an FIR MIMO precoder has already been selected, we also describe a technique for adding a vector shaping sequence to the transmitted signal in order to reduce the transmit power. The selection of effective shaping sequences requires a search over a trellis of large dimensionality, which can be accomplished suboptimally by employing reduced-complexity search techniques.
Highlights
The increasing demand for high data rates communication and the lack of wireless spectrum have prompted the consideration in recent years of multiantenna wireless communication systems that can support much higher data rates [1, 2, 3] than traditional single-input single-output wireless channels
Whereas earlier precoder or equalizer design techniques consider only a total transmit power constraint, the filter impulse response (FIR) design methodology we propose can handle a wider range of such constraints, which includes for example constraints on each transmit antenna power, or on the power allocated to each user
Since the same design technique is applicable to both equalizers and precoders, we only show results for the precoder case
Summary
The increasing demand for high data rates communication and the lack of wireless spectrum have prompted the consideration in recent years of multiantenna wireless communication systems that can support much higher data rates [1, 2, 3] than traditional single-input single-output wireless channels. For MIMO systems with more transmit than receive antennas, a convex optimization technique is proposed for the synthesis of FIR MIMO precoders minimizing the power of the residual channel ISI subject to various power constraints. For systems with more receive than transmit antennas, we discuss briefly the optimum synthesis of FIR MIMO equalizers minimizing the residual ISI power under various equalizer-output noise power constraints In this respect, it is worth noting that a wide range of results have already been derived concerning the separate or joint optimization of precoders and/or equalizers for frequency-selective channels. The case of multiantenna systems with more receive than transmit antennas is examined in Section 5 where a design technique is presented for minimizing the residual ISI while ensuring that noise power constraints for the output signal are satisfied.
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