Miquel Payaró | NEWCOM Meeting OPTIMUM TRANSMIT ARCHITECTURE OF A MIMO SYSTEM UNDER MODULUS CHANNEL KNOWLEDGE AT THE TRANSMITTER Miquel Payaró Xavier Mestre

Miquel Payaró | NEWCOM Meeting

OPTIMUM TRANSMIT OPTIMUM TRANSMIT ARCHITECTURE OF A MIMO ARCHITECTURE OF A MIMO SYSTEM UNDER MODULUS SYSTEM UNDER MODULUS

CHANNEL KNOWLEDGE AT THE CHANNEL KNOWLEDGE AT THE TRANSMITTERTRANSMITTER

Miquel PayaróMiquel Payaró

Xavier MestreXavier Mestre

Ana PérezAna Pérez

Miguel A. LagunasMiguel A. Lagunas

CENTRE TECNOLÒGIC de TELECOMUNICACIONS de CATALUNYACENTRE TECNOLÒGIC de TELECOMUNICACIONS de CATALUNYA

CTTCCTTC

March 2005 | 2Miquel Payaró | NEWCOM Meeting

Optimum transmit architecture for MIMO Systems

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

SymbolMapper

Weighting Receiver t

x

( ) ( )CSI x W t

y



Which is the optimum transmit filter, W, if only the Which is the optimum transmit filter, W, if only the

channel modulus is known at the transmitter.channel modulus is known at the transmitter.

Motivation: TDD systems (exploitation of Motivation: TDD systems (exploitation of

electromagnetic reciprocity).electromagnetic reciprocity).

SymbolMapper

Weighting Receiver t

x

( ) ( )CSI x W t

y

Baseline architectureBaseline architecture



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



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

Antennaselection



Graphical summary for the 2x2 case



• 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.



Formulation for frequency selective channels (based on Formulation for frequency selective channels (based on

a multicarrier approach a multicarrier approach capacity lossless structure) capacity lossless structure)

+ Power Constraints!



Maximin formulationMaximin formulation

Closed form solution for the 2 x n caseClosed form solution for the 2 x n case



In the In the maximin formulationmaximin formulation, we can make use of the , we can make use of the

following approximation (exact when min(nfollowing approximation (exact when min(nRR,n,nTT) = 2)) = 2)

Single carrier problem formulationSingle carrier problem formulation

Multicarrier problem formulationMulticarrier problem formulation

In both cases, the solution can be computed very In both cases, the solution can be computed very

efficiently!efficiently!



Performance of multicarrier maximin approach, for Performance of multicarrier maximin approach, for

HIPERLAN/2 type A power delay profile, with 4 transmit HIPERLAN/2 type A power delay profile, with 4 transmit

and 4 receive antennas with 48 active subcarriersand 4 receive antennas with 48 active subcarriers

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Miquel Payaró | NEWCOM Meeting OPTIMUM TRANSMIT ARCHITECTURE OF A MIMO SYSTEM UNDER MODULUS CHANNEL KNOWLEDGE AT THE TRANSMITTER Miquel Payaró Xavier Mestre