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)