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Advanced Topics in Signal Processing for Wireless Communications

Narayan Mandayam WINLAB , Rutgers University www.winlab.rutgers.edu/~narayan. Advanced Topics in Signal Processing for Wireless Communications. Introduction. Wireless Data on the move is the primary driver for innovations in signal processing Examples of situations include:

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Advanced Topics in Signal Processing for Wireless Communications

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  1. Narayan Mandayam WINLAB, Rutgers University www.winlab.rutgers.edu/~narayan Advanced Topics in Signal Processing for Wireless Communications

  2. Introduction • Wireless Data on the move is the primary driver for innovations in signal processing • Examples of situations include: • Cellular like networks for wireless data (Licensed) • Wireless access to the Internet: Wireless LANs (Unlicensed) • Infostations: Intermittent pockets of high bandwidth on the move (Unlicensed) • Wireless Data Communications characterized by • Channel variations (time, frequency, space) due to mobility and propagation effects • Multiple Access Interference from known and unknown entities • Challenges in enabling wireless data communications • Mitigating or Exploiting channel variations • Mitigating Multiaccess interference

  3. Challenges in Enabling Wireless Data • Exploiting Variations: Opportunistic Communications • Opportunities for transmission arise in time, frequency and space • Examples include: • MIMO, Space-Time Coding, Scheduling, Resource Allocation • Signal Processing challenges in opportunistic transmission strategies ? • Knowledge of temporal and spatial variations of wireless channels • Higher carrier frequencies, higher mobility, great no. of unknown parameters • Mitigating Interference: Multiuser Detection • Exploit interference structure to design tailored receivers • Examples include: • Cellular 3G, Unlicensed band Wireless LANs • Signal Processing challenges in Multiuser Detection ? • Blind and Adaptive Techniques

  4. Topics Covered in this Talk • Opportunistic Communications • Pilot Assisted MIMO Channel Estimation • Multiuser Detection • Blind Interference Cancellation Techniques for CDMA Systems • Subspace Techniques • SIR Estimation in CDMA Systems

  5. Joint work with Dragan Samardzija Bell Labs, Lucent Technologies Pilot Assisted Estimation of MIMO Fading Channel Response and Achievable Data Rates

  6. Introduction • Pilot assisted MIMO estimation and its impact on achievable rates • The effects of the estimation error are evaluated for • Estimates being available at the receiver only: open loop • Estimates are fed back to the transmitter allowing water pouring optimization: closed loop • Results/Analysis may be interpreted as a study of mismatched receiver and transmitter algorithms in MIMO systems

  7. System Assumptions • Multiple-input multiple-output (MIMO) wireless systems • Frequency-flat time-varying wireless channel with additive white Gaussian noise (AWGN), i.e., Block fading channel • We consider two pilot based approaches for the estimation: • Single pilot symbol per block with variable (from data symbols) power • More than one symbol per block with same (as data symbols) power • Orthogonality between the pilots assigned to different transmit antennas • Maximum-likelihood estimate of the channel response

  8. Signal Model • MIMO communication system that consists of M transmit and N receive antennas • Received spatial vector y y(k)=H(k)x(k)+n(k) (1) where y(k)in CN, x(k)in CM, n(k)in CN, H(k) in CN x M • x is transmitted vector, n is AWGN (E [nnH] = NoINxN), and H is the MIMO channel response matrix, all corresponding to thetime instance k • hnm (k) is the n-th row and m-th column element of the H(k) • corresponds to a SISO channel response between the transmit antenna m and receive antenna n

  9. Signal Model, contd. • n-th component of the received spatial vectory(k)=[y1(k)…yN(k)]T(i.e., signal at the receive antenna n) is (2) • gm (k) is the transmitted signal from the m-th transmit antenna, i.e., x(k)=[g1(k) … gM(k)]T. • The channel response H(k) is estimated using a pilot (training) signal that is a part of the transmitted data • Pilot is sent periodically, every K symbol periods

  10. Signal Model, contd. • At transmitter m, the K-dimensional temporal vectorgm=[gm(1) … gm(K)]T (whose k-th component is gm(k) (in (2))) is (3) • a dim=Aanda pim=Ap are amplitudes related as Ap=aA • d dim is the unit-variance data, and |d pjm|2=1 is the pilot symbol • sdi and spimare temporal signatures, all corresponding to the m-th transmitter; • L is the number of signal dimensions allocated to the pilot, per transmit antenna • Temporal signatures are mutually orthogonal and they could be: • canonical waveform - a TDMA-like waveform • K-dimensional Walsh sequence - a CDMA-like waveform

  11. Signal Model, contd. • Rewrite spatial received signal vector as: y(k)=H(k)(d(k) + p(k))+n(k) (4) • d(k) =[d1(k) … dM(k)]Tis the data bearing transmitted spatial signal where • p(k) =[p1(k) … pM(k)]Tis the pilot portion of the transmitted spatial signal

  12. + data A sd1 TXM dd1M data A sd1 dd11 + sdK-LM A MIMO transmitter with M antennas ddK-LM M TX1 sdK-LM A ddK-LM 1 pilot Ap sp1M dp1M pilot Ap sp11 dp11 spLM Ap dpL M spL1 Ap dpL 1 Data temporal signatures reused across Txs X M • Pilots are orthogonal between the Txs

  13. Model Assumptions • Block-fading channel model with channel coherence K Tsym, hnm(k)~hnm, for k = 1,…, K, for all m and n • The elements of H are iid random variables • When applying different number of transmit antennas, the total average transmitted power must be conserved. Per pilot period it is (5) • Amount of transmitted energy that is allocated to the pilot (percentage wise) is (6)

  14. Pilot Arrangements – case 1 • Two different pilot arrangements: • L=1 and Ap= aA, single dimension taken by pilot, with different power from data symbols. The data symbol amplitude is (7) • In SISO systems applied in CDMA wireless systems (e.g., IS-95 and WCDMA) • In MIMO systems, applied in narrowband MIMO implementations [Foschini, Valenzuela, Wolniansky] • Also wideband MIMO implementation based on 3G WCDMA.

  15. Pilot Arrangements – case 2 • L > 1 and Ap= aA (a = 1), multiple signal dimensions taken by pilot, with the same power as data. The data symbol amplitude is (8) • Frequently used in SISO systems • Wire-line modems • Wireless standards (e.g., IS-136 and GSM). • Not common practice in MIMO systems.

  16. Estimation of Channel Response • Based on previously introduced assumption: • Pilot signatures maintain orthogonality • elements of H are iid • Background noise is AWGN • Sufficient to estimate hnm(for m=1,…, M, n = 1,…, N) independently • Identical to estimating a SISO channel response between the transmit antenna m and receive antenna n • The estimate of the channel response hnm

  17. Estimation of Channel Response, contd. (9) • The estimation error is (10) • corresponds to sample of a white Gaussian random process • The channel matrix H estimate is (11) • He is the estimation error matrix • Each component of the error matrix Heis independent identically distributed random variable nenm

  18. Detection and Effective Noise • The sufficient statistics are obtained at the N receive antennas by projecting the received signal vectors with the corresponding temporal signatures si, i=1,…K-LM • The sufficient statistic for ith signaturecan be written as (12) where E[niniH] = NoINxN • The effective noise vector is (13) • Covariance matrix of the effective noise vector is (14)

  19. Open Loop Capacity • Channel estimates are available to the receiver only • Under the assumptions: • Estimate of H has to be stationary and ergodic • The channel coding will span across great number of channel blocks • Effective noise is treated as independent Gaussian interference • The lower bound for the open loop ergodic capacity is (15) • (K-LM)/K because L temporal signatures per each transmit antenna allocated to the pilot

  20. Comparison to SISO Results • SISO case [see Shamai, Biglieri, Proakis, IT’98], capacity lower bound for mismatched decoding as (16) where h and are the SISO channel response and its estimate • Proposition For M = 1, N = 1 (i.e., SISO) the rate R in (17) and R* in (18) are related as (17) where is obtained using the pilot assisted estimation • Bound in (15) is an extension of the information theoretical bound in (16), capturing the more specific pilot assisted estimation scheme and generalizing it to the MIMO case

  21. Achievable open loop rates vs. power allocated to the pilot, SISO system, SNR=4, 12, 20dB, K=10, Rayleigh channel

  22. Capacity Efficiency Ratio • Evaluate performance under optimum pilot power allocation ? • For any given SNR, define the capacity efficiency ratio h as, (18) • Maximum rate R is maximized with respect to pilot power • Ergodic capacity CMxN, with the ideal knowledge of the channel response • The index M and N correspond to number of transmit and receive antennas, respectively

  23. Capacity efficiency ratio vs. channel coherence time length, SISO system, SNR=4, 12, 20dB, K=10, 20, 40, 100, Rayleigh channel • Pilot arrangement case 1 is more efficient compared to case 2

  24. Open loop rates vs. power allocated to the pilot, MIMO system, SNR=12dB, K=40, Rayleigh channel • solid line: channel response estimation • dashed line: ideal channel knowledge • Pilot arrangement case 1

  25. Capacity efficiency ratio vs. channel coherence time length, MIMO system, SNR=12dB, K=10, 20, 40, 100, Rayleigh channel • Pilot arrangement case 1 • 1x4 the most efficient • The efficiency is getting smaller as the number of TX antennas grow (for fixed number of received antennas)

  26. Closed Loop Rates: Mismatched Water Pouring • H(i-1) and H(i) correspond to the consecutive block faded channel responses • Receiver feeds back the estimate • Instead of H(i) , is used to perform the water pouring transmitter optimization for the i-th block • Singular value decomposition (SVD) is performed • For data vector d(k), at the transmitter (19) • S(i) is a diagonal matrix whose elements sjj (j=1, …, M) are determined by the water pouring algorithm per singular value of

  27. Mismatched Water Pouring, contd. • For diagonal element of (denoted as j = 1, …, M), the diagonal element of S(i) is defined as (20) • y0is a cut-off value thatdepends on the channel fading statistics • such that the average transmit power stays the same Pav [Goldsmith 93] • Water pouring optimization is on information bearing portion of the signal d(k) • Pilot p(k) is not changed • Receiver knows that the transformation in (19) is performed at the transmitter

  28. Closed Loop Achievable Rates • Receiver performs estimation resulting in • Error matrix • Effective noise and its covariance are modified resulting in (21) • Above application of the water pouring algorithm per eigen mode is suboptimal, i.e., it is mismatched ( is used instead of H(i)) • Closed loop system capacity is lower bounded as, (22) • Assumptions on estimates and effective noise same as before

  29. Ergodic capacity vs. SNR, MIMO system, ideal knowledge of the channel response, Rayleigh channel • solid line: open loop capacity • dashed: closed loop capacity • Gap between closed loop and open loop is getting smaller for • Higher SNR • Larger ratio N/M (number of RX vs. TX antennas)

  30. CDF of capacity, MIMO system, ideal knowledge of the channel response, Rayleigh channel • solid line: open loop capacity • dashed: closed loop capacity

  31. Closed-loop rates vs. correlation between successive channel responses, MIMO system, SNR=4dB, K=40, Rayleigh channel • solid line: channel response estimation • dashed: ideal channel response • In both cases delay (temporal mismatch) exists • Pilot arrangement case 1

  32. Summary of MIMO Pilot Estimation • Pilot Assisted Channel Estimation for Multiple-input multiple-output wireless systems • Open loop and closed loop ergodic capacity lower bounds are determined • Performance depends on: • Percentage of the total power allocated to the pilot • Background noise level • Channel coherence time length • Temporal correlation (for the water pouring) • First pilot-based approach is less sensitive to the fraction of power allocated to the pilot • As the number of transmit antenna increases, the capacity efficiency ratio is lowered (while keeping the same number of receive antennas)

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