1. Miquel Payaró | NEWCOM Meeting OPTIMUM TRANSMIT ARCHITECTURE OF A MIMO SYSTEM UNDER MODULUS CHANNEL KNOWLEDGE AT THE TRANSMITTER Miquel Payaró Xavier Mestre Ana Pérez Miguel A. Lagunas CENTRE TECNOLÒGIC de TELECOMUNICACIONS de CATALUNYA CTTC

2. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 2   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 Symbol Mapper WeightingReceiver

3. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 3  Which is the optimum transmit filter, W, if only the channel modulus is known at the transmitter.  Motivation: TDD systems (exploitation of electromagnetic reciprocity). Symbol Mapper WeightingReceiver  Baseline architecture

4. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 4   We are interested in maximizing the mutual information between the transmitted and the received signals. For a particular realization of the flat-fading channel matrix, H, the mutual information is given by   We wish to find the covariance matrix that maximizes the mutual information averaged over the statistics of the unknown part of the incomplete CSI

5. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 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) SNR at the receiver Antenna selection

6. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 6  Graphical summary for the 2x2 case

7. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 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 solutions are computationally simpler to obtain.

8. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 8  Formulation for frequency selective channels (based on a multicarrier approach  capacity lossless structure) + Power Constraints!

9. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 9  Maximin formulation  Closed form solution for the 2 x n case

10. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 10  In the maximin formulation, we can make use of the following approximation (exact when min(n R,n T ) = 2)  Single carrier problem formulation  Multicarrier problem formulation  In both cases, the solution can be computed very efficiently!

11. Miquel Payaró | NEWCOM Meeting Optimum transmit architecture for MIMO Systems March 2005 | 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