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Impact of the CSI on the Design of a Multi-Antenna Transmitter with ML Detection

Impact of the CSI on the Design of a Multi-Antenna Transmitter with ML Detection. Antonio Pascual Iserte tonip@gps.tsc.upc.es Dpt. Signal Theory and Communications Technical University of Catalonia (UPC). Introduction Classical Solutions ML Detection: Signal model

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Impact of the CSI on the Design of a Multi-Antenna Transmitter with ML Detection

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  1. Impact of the CSI on the Design of a Multi-Antenna Transmitter with ML Detection Antonio Pascual Iserte tonip@gps.tsc.upc.es Dpt. Signal Theory and Communications Technical University of Catalonia (UPC)

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

  3. 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 Introduction

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

  5. Optimum receiver: It is based on the application of the ML detector Signal model: for a linear transmitter Received signal: Optimum ML detection: Maximum Likelihood Detection s ML Bn

  6. Transmitter architecture: Temporal processing and modulation construction: Power allocation: Spatial processing: Transmitter Architecture Modified signal model: nM spatial modes ns streams nT antennas they depend on the available CSI

  7. Pairwise Error Probability (PEP): Probability of deciding in favor of sb when the vector sa has been actually transmitted: If there is only one error in the s-th stream and the symbols are BPSK Pairwise Error Probability vn,s: s-th column of VnH

  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

  9. 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: No CSI for BPSK streams The matrices VnH can be based on OSTBC or FFT-like matrices

  10. 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 (ns=2) Perfect CSI (I)

  11. Transmission through the two maximum eigenvectors of the MIMO channel (nM=2) The configuration depends on the eigenvalues-ratio Perfect CSI (II) N = 1 channel access

  12. Constellations: Perfect CSI (III) 1 mode 2 modes

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

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

  15. Situation: Only a channel estimate, which can be noise or imperfect, is available Possible solutions: Bayesian designs: the error is modelled statistically Maximin 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 Imperfect CSI (I)

  16. Solution: it can be calculated numerically using convex optimization procedures Imperfect CSI (II)

  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

  18. Some Simulations (II) • Comparison between: • Uniform power allocation (no CSI) • Optimum power allocation with statistical CSI and different levels of LOS

  19. Some Simulations (III) • Robust design • Comparison in terms of achievable throughput (using adaptive modulation with maximum BER constraints): • Alamouti (nM=2) • Full OSTBC (nM=nT)

  20. 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 CSI: equal error probability for all the possible positions of the error Perfect CSI: the eigenmodes of the channel are used with a convenient power allocation and a new signal constellation Statistical CSI: a power allocation is performed taking into account the LOS and the Rayleigh components Imperfect CSI: a robust maximin power allocation is performed Conclusions

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