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Advanced Topics in Signal Processing for Wireless Communications

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Title: Advanced Topics in Signal Processing for Wireless Communications


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

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

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 n nH No
    INxN), and H is the MIMO channel response matrix,
    all corresponding to the time 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 vector
    y(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
    vector gmgm(1) gm(K)T (whose k-th component
    is gm(k) (in (2))) is
  • (3)
  • a dimA and a pimAp are amplitudes related as
    Apa A
  • d dim is the unit-variance data, and d pjm21
    is the pilot symbol
  • sdi and spim are 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)T is the data bearing
    transmitted spatial signal where
  • p(k) p1(k) pM(k)T is the pilot portion of
    the transmitted spatial signal

12
MIMO transmitter with M antennas
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
  • L1 and Ap a A, 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 gt 1 and Ap a A (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 m1,, 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 He is
    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, i1,K-LM
  • The sufficient statistic for ith signature can be
    written as
  • (12)
  • where Eni niH No INxN
  • 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,
    IT98, 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, SNR4, 12, 20dB, K10,
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, SNR4, 12, 20dB, K10,
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, SNR12dB, K40, 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, SNR12dB, K10, 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
    (j1, , 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)
  • y0 is a cut-off value that depends 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,
SNR4dB, K40, 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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