Maximizing Mutual Information in MIMO Systems | CSI Effects & Power Allocation Strategies

1. Miquel Payaró Xavier Mestre Ana Pérez Miguel A. Lagunas CENTRE TECNOLÒGIC de TELECOMUNICACIONS de CATALUNYA CTTC

2. Weighting Receiver Symbol Mapper • If perfect CSI is assumed at the receiver end, the achievable rates of a MIMO system depend on the quality and quantity of CSI available at the transmitter side. • Generic effect of partial side information in MIMO Systems [Skoglund]. Capacity can be achieved by a structure that first maps source symbols into space-time codewords independently from CSI and then weights these codewords as a function of CSI

3. Weighting Receiver Symbol Mapper • Baseline architecture • Which is the optimum transmit filter, W, if only the channel modulus is known at the transmitter. • Motivation: TDD systems (exploitation of electromagnetic reciprocity).

4. We are interested in maximizing the mutual informationbetween the transmitted and the received signals. For aparticular realization of the flat-fading channel matrix, H, the mutual information is given by • Wewish to find the covariance matrix that maximizes the mutual information averaged overthe statistics of the unknown part of the incomplete CSI

5. First result: we prove that power allocation is a capacity achieving structure in this situation. • Second result: we give a description of the optimum power allocation strategy in the 2x2 case. • Otherwise: power allocation (roots of a fourth order polynomial) Antenna selection SNR at the receiver

6. Graphical summary for the 2x2 case

7. Technical problems: • No great capacity improvement in rayleigh i.i.d. flat fading channels w.r.t. uniform power allocation. • Closed form analysis limited to the flat fading 2x2 case. • For the general case, numerical solutions are computationally hard to obtain. • Possible solutions: • Formulation extension to frequency-selective channels. • Performance improvement w.r.t. uniform power allocation. • Maximin approach  closed form solution for the 2 x n flat fading case. • Numerical solutionsare computationally simpler to obtain.

8. Formulation for frequency selective channels (based on a multicarrier approach  capacity lossless structure) + Power Constraints!

9. Maximin formulation • Closed form solution for the 2 x n case

10. In the maximin formulation, we can make use of the following approximation (exact when min(nR,nT) = 2) • Single carrier problem formulation • Multicarrier problem formulation • In both cases, the solution can be computed very efficiently!

11. Performance of multicarrier maximin approach, for HIPERLAN/2 type A power delay profile, with 4 transmit and 4 receive antennas with 48 active subcarriers