NEWCOM – SWP2 MEETING 1 Impact of the CSI on the Design of a Multi-Antenna Transmitter with ML Detection Antonio Pascual Iserte Dpt. Signal Theory and Communications Technical University of Catalonia (UPC)

NEWCOM – SWP2 MEETING 2 Outline Introduction Classical Solutions ML Detection: Signal model Different degrees of CSI at the transmitter: No CSI Perfect CSI Statistical CSI Imperfect CSI Some Conclusions

NEWCOM – SWP2 MEETING 3 Introduction Transmission through MIMO channels: –Problem: design of the transmitter and the receiver –The adopted figure of merit or cost function depends of the detection strategy at the receiver –The design strategy depends on the quantity and the quality of the CSI available at the transmitter

NEWCOM – SWP2 MEETING 4 Classical Solutions Classical designs: –They are based on the use of linear transmitters and receivers mean square error signal to noise ratio … –Adopted figures of merit: mean square error (MSE), signal to noise ratio (SNR), … B AHAH s linear transmitter linear receiver

NEWCOM – SWP2 MEETING 5 Maximum Likelihood Detection Optimum receiver: –It is based on the application of the ML detector –Signal model: for a linear transmitter –Received signal: –Optimum ML detection: BnBn ML s

NEWCOM – SWP2 MEETING 6 Transmitter architecture: Temporal processing and modulation construction: Power allocation: Spatial processing: Transmitter Architecture they depend on the available CSI Modified signal model: n s streams n M spatial modes n T antennas

NEWCOM – SWP2 MEETING 7 Pairwise Error Probability Pairwise Error Probability (PEP): –Probability of deciding in favor of s b when the vector s a has been actually transmitted: –If there is only one error in the s-th stream and the symbols are BPSK v n,s : s-th column of V n H

NEWCOM – SWP2 MEETING 8 Objective: –Design of the transmitter subject to a power constraint in order to minimize the worst PEP Impact of the CSI: –The design depends on the available CSI at the transmitter: –Possible cases: No CSI Perfect CSI Statistical CSI Imperfect CSI Transmitter Design

NEWCOM – SWP2 MEETING 9 No CSI Situation: –There is no CSI at the transmitter –The minimization of the maximum PEP implies that the PEP is equal for all the possible positions of error: for BPSK streams The matrices V n H can be based on OSTBC or FFT-like matrices

NEWCOM – SWP2 MEETING 10 Perfect CSI (I) Situation: –There is a perfect CSI at the transmitter –The minimization of the worst PEP implies the maximization of the minimum distance at the receiver: –A closed-form solution exists for the case of 2 QPSK streams (n s =2)

NEWCOM – SWP2 MEETING 11 –Transmission through the two maximum eigenvectors of the MIMO channel (n M =2) –The configuration depends on the eigenvalues-ratio Perfect CSI (II) N = 1 channel access

NEWCOM – SWP2 MEETING 12 Perfect CSI (III) Constellations: 1 mode2 modes

NEWCOM – SWP2 MEETING 13 Statistical CSI (I) Situation: –Only the channel statistics are known –Channel model: are i.i.d. with Gaussian distribution: –Transmitter design: power allocation mean value: LOS covariance

NEWCOM – SWP2 MEETING 14 Statistical CSI (II) –Design objective: minimization of the mean PEP averaged over the channel statistics –Solution: optimum power allocation:

NEWCOM – SWP2 MEETING 15 Imperfect CSI (I) Situation: –Only a channel estimate, which can be noise or imperfect, is available –Possible solutions: Bayesian designsBayesian designs: the error is modelled statistically Maximin designsMaximin designs: the error is assumed to belong to an uncertainty region R, and the worst system performance for any possible error is optimized –Maximin approach: Transmission through the estimated eigenvectors Optimization of the power allocation among the estimated eigenmodes Combination with OSTBC

NEWCOM – SWP2 MEETING 16 Imperfect CSI (II) –Solution: it can be calculated numerically using convex optimization procedures

NEWCOM – SWP2 MEETING 17 Some Simulations (I) Comparison between: - Optimum linear transmitter-receiver with perfect CSI - Optimum linear transmitter with ML detection with optimum CSI - QPSK VBLAST - 16-QAM Alamouti

NEWCOM – SWP2 MEETING 18 Some Simulations (II) Comparison between: - Uniform power allocation (no CSI) - Optimum power allocation with statistical CSI and different levels of LOS

NEWCOM – SWP2 MEETING 19 Some Simulations (III) Robust design adaptive modulation Comparison in terms of achievable throughput (using adaptive modulation with maximum BER constraints): - Alamouti (n M =2) - Full OSTBC (n M =n T )

NEWCOM – SWP2 MEETING 20 Conclusions When using an optimum ML detector, the figure of merit should be based on the PEP, and not on the MSE The design of the transmitter depends on the available CSI and its quality: No CSINo CSI: equal error probability for all the possible positions of the error Perfect CSIPerfect CSI: the eigenmodes of the channel are used with a convenient power allocation and a new signal constellation Statistical CSIStatistical CSI: a power allocation is performed taking into account the LOS and the Rayleigh components Imperfect CSIImperfect CSI: a robust maximin power allocation is performed