Adaptive MIMO OFDM Receivers Implementation Impairments and Complexity Issues

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Adaptive MIMO OFDM ReceiversImplementation
Impairments and Complexity Issues

• Ali H. Sayed (sayed_at_ee.ucla.edu)
• Adaptive Systems Laboratory
• Electrical Engineering Department
• UCLA

(www.ee.ucla.edu/asl)
INRS Montreal, Canada 4/15/05 Research Triangle
Park, NC 4/6/05 UT Austin 4/1/05 Texas AM
3/31/2005 Rice University 3/29/05
Royce Hall UCLA
Ack Tarighat, Younis
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Motivation

• For wireless systems
• The available bandwidth (Hz) is limited.
• The environment is hostile (fading and
  multipath).
• MIMO techniques increase system capacity
  (bits/sec/Hz) and combat fading through diversity
  (which reduces BER).
• Orthogonal Frequency Division Multiplexing (OFDM)
  helps combat multipath conditions through simple
  receiver structures it avoids the need for
  equalization.

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Practical Challenges

• Two important issues that receive less attention
  are
• Practical OFDM systems suffer from implementation
  impairments (analog imperfections)
• DSP techniques can be used to reduce cost and
  improve performance (e.g., improved BER).
• Solutions in the digital domain as opposed to the
  analog domain.
• Code structure should be exploited when combining
  OFDM with MIMO in order to maintain simple
  receiver structures
• Space-time codes are rich in structure.
• Structure can be exploited to reduce receiver
  complexity.

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IEEE Standards

• OFDM-based physical layers have already been
  chosen (or are under consideration) for several
  wireless standards
• IEEE 802.11a wireless local area network (WLAN)
  at 5GHz band 54Mbps.
• IEEE 802.11g wireless local area network (WLAN)
  at 2.4GHz band 54Mbps.
• European digital video broadcasting system
  (DVB-T).
• IEEE P802.15.3a wireless personal area network
  (WPANUWB) 480Mbps.
• IEEE 802.20 mobile broadband wireless access
  (MBWA).
• IEEE 802.16 wireless metropolitan area networks
  (WirelessMAN).

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Why OFDM?

• OFDM leads to a simple receiver structure for
  frequency-selective channels

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Challenges

• Despite its attractive structure, the deployment
  of OFDM systems faces some challenges
• Implementation impairments degrade BER
  performance.
• Multi-antenna (MIMO) architectures increase
  complexity.
• This talk describes how to address these
  challenges for MIMO OFDM receivers.

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Outline
(SISO with distortion) How to handle distortions
in the digital domain.
1.
(MIMO with coding) How to exploit code structure
to keep MIMO receiver simple.
2.
(MIMO with distortion) How to handle distortions
in the MIMO case and how to exploit code
structure.
3.
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Challenge I Implementation Impairments

• Implementation impairments arise from component
  imperfections, such as
• i) Phase noise ii) Frequency offset iii)
  Nonlinearities iv) IQ imbalances
• Such impairments are difficult to eliminate
  using analog processing they become more
  challenging at higher carrier frequencies and for
  higher bandwidths.
• Techniques can be developed in the digital domain
  to
• eliminate mismatches introduced in the analog
  domain.
• Q How should the structure of the OFDM receiver
  be adjusted?

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IQ Imbalance

• Received signal is down converted from radio
  frequency (RF) to baseband both the sine and
  cosine waveforms are required at the receiver.

• Mismatch between the I
• and Q branches, e.g., from
• 90o phase difference and
• equal amplitudes.

What one gets is not y(t) but a combination
of y(t) and y(t).
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Outline
(SISO with distortion) How to handle distortions
in the digital domain.
1.
(MIMO with coding) How to exploit code structure
to keep MIMO receiver simple.
2.
(MIMO with distortion) How to handle distortions
in the MIMO case and how to exploit code
structure.
3.
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Modeling IQ Imbalances
IQ imbalances at receiver The distorted signal
can be modeled as
The parameters and model the imbalances
in phase and amplitude (not known to the
receiver). A similar model can be used for IQ
imbalances at transmitter (during up-conversion).
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Exclude tones 1 and N/21 no information is
carried on these tones (e.g., 802.11a) relaxes
requirements on analog receive filters and DC
offset.
The input-output relation is now given by
Ideal IQ case
cross-diagonal
diagonal
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System of equations decouples into 2x2
subequations for k2,,N/2
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Data Recovery (requires knowledge of the channel
and distortion parameters)
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Recover the channel and distortion parameters
from multiple measurements
Estimation of channel and distortion parameters
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Adaptive Equalization (ideal for time varying
scenarios)
(training iterations)
Initial conditions assume ideal IQ
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Simulation Results
Without compensation
With LMS compensation
With LS compensation and ideal IQ
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Outline
(SISO with distortion) How to handle distortions
in the digital domain.
1.
(MIMO with coding) How to exploit code structure
to keep MIMO receiver simple.
2.
(MIMO with distortion) How to handle distortions
in the MIMO case and how to exploit code
structure.
3.
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Challenge II Multi-Antenna Communications

• A second issue that OFDM systems
• need to cope with is the emergence of
• multi-antenna architectures.
• Move from SISO to MIMO systems.
• Idea Transmit the same data from multiple
  antennas (at same total power) and collect them
  through multiple antennas at the receiver.
• A useful data coding structure is Space-Time
  Coding.
• Motivation The technique improves reliability
  (due to redundancy and path diversity) and also
  increases system capacity (bits/sec/Hz).

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MIMO Channel with MrMt
Capacity increases linearly with number of
antennas. In general, capacity increases approx.
linearly with min(Mt,Mr)
However, MIMO architectures add complexity.
Space-time (Alamouti) codes provide
diversity and simplify reception.
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Input-Output Relations
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Equalization Channel Estimation
Equalization
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Data Recovery Exploiting Structure
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2x2 Alamouti matrix
(scaled multiple of identity)
(trivialized least-squares solution)
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Outline
(SISO with distortion) How to handle distortions
in the digital domain.
1.
(MIMO with coding) How to exploit code structure
to keep MIMO receiver simple.
2.
(MIMO with distortion) How to handle distortions
in the MIMO case and how to exploit code
structure.
3.
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Recall SISO Case
The input-output relation is now given by
Ideal IQ case
cross-diagonal
diagonal
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Addressing IQ imbalances
4x4
Alamouti-coded with IQ
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Cross-coupling
2x2 Alamouti submatrices
(compare with the SISO case with IQ)
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Properties of Matrices with Alamouti Sub-blocks

• Let A and B be 2x2 Alamouti matrices with
  entries
• Then

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Let A be a matrix with 2x2 Alamouti sub-blocks,
e.g.,

• Then the following useful facts hold
• The inverse of A has a similar structure.
• The Schur complement of A w.r.t. any 2Kx2K
  submatrix has same structure.
• ALDU
• D is block diagonal with 2x2 Alamouti sub-blocks
• L (U) is lower (upper) triangular with 2x2
  Alamouti sub-blocks in its lower
• (upper) triangular part and I2 along its
  diagonal.
• AQR factorization
• R is upper triangular with I2 on diagonal and 2x2
  Alamouti sub-blocks.
• Q is unitary with 2x2 Alamouti sub-blocks.

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Least-squares data recovery
2x2 Diagonal (actually scalar multiples of I)
2x2 Alamouti
2x2 Alamouti
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Therefore, the inverse
is efficiently computable by exploiting the 2x2
Alamouti structure.
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Simulation Results
Without compensation
With compensation and ideal IQ cases
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Adaptive Equalization
We seek a linear data estimator of the form
Partition the coefficient matrix as
with 2x2 Alamouti sub-blocks, so that
2x2 Alamouti sub-blocks 8 independent parameters
in total
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2x2 Alamouti sub-blocks
Reorganizing the equations
Adaptive training with iteration index i
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Block NLMS Algorithm

• Update the equalizer coefficients according to
  the rule

• Using the matrix inversion lemma

and the following property of Alamouti matrices
We conclude that
NLMS performance at LMS complexity.
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Block RLS Algorithm

• Update the equalizer coefficients according to
  the rule

• Structures of and

RLS performance at LMS complexity.
(a diagonal structure)!
Adaptive solutions compensate for both channel
distortion and imperfection distortions.
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Simulation Results
Steady-state decision-directed performance
Without compensation
With compensation and ideal IQ cases
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Extension to MIMO Systems
(extension to OSTBC as well)
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Summary

• OFDM is a widely adopted standard for wireless
• Communications (802.11a, 802.11g, WiMax).
• The deployment of OFDM systems faces some
• challenges
• Implementation impairments degrade BER
  performance.
• Multi-antenna (MIMO) architectures increase
  complexity.
• Combating distortions in the digital domain has
• several advantages over analog domain
  compensation
• in terms of overall cost and complexity.
• Exploiting code structure and distortion models
  is
• possible in order to develop efficient receivers.

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Compensation in the digital domain
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2x2
2x2
The system of equations decouples into 2x2
subequations for k2,,N/2
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Data recovery (Least-Squares post-FFT)
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OFDM pilot symbols can be used for distortion and
channel estimation.
Distortion and channel estimation (Least-squares
post-FFT)
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Pre-FFT Compensation
IQ imbalances at receiver The distorted signal
is be modeled as
IQ distortion can be removed prior to FFT via the
transformation
???
Two separate estimates
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Why Multi-Antenna Systems?

• Channel Capacity measures the maximum
  transmission rate of information over a channel
  (bits/sec/Hz).
• For flat Gaussian MIMO channels (ergodic
  capacity)

Fact Using multiple transmit and receive
antennas increases capacity.
Data covariance matrix Noise power
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one-to-many
many-to-one
MISO Channel (Mr1)
SIMO Channel (Mt1)
Mr Number of receive antennas Mt
Number of transmit antennas
Conclusion Receive diversity is more useful.
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Why Reliability Improves?

• We are not only interested in capacity since it
  mainly provides theoretical limits on
  transmission rates.
• In practice, we are more interested
• in the BER (bit-error-rate) performance,
• i.e., in the reliability of transmissions.
• Diversity is a mechanism to increase
• transmission reliability by providing
• the receiver with multiple independent
• copies of the transmit signal. Diversity lowers
  the
• probability of errors

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Receive Transmit Diversity
Receive Diversity Diversity order is
achievable with MRC (maximal ratio
combining). Transmit Diversity Diversity order
is achievable using beamforming. Transmit
and Receive Diversity Diversity order
is achievable using beamforming at the
transmitter and MRC at the receiver (left and
right singular vectors of channel matrix).
These three formulations, require the channel to
be known. What if channel is not known?
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How to Achieve Maximal Diversity?

• Block Transmissions. Map K symbols into an Mt x N
  matrix X. Transmit the columns of X during N
  time instants from all transmit antennas. A
  maximum diversity order of can be
  achieved. Code rate RK/N.

Example
How do we design X? Minimize the pairwise error
probability
Orthogonal space-time block codes
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Alamouti Scheme (K2 N2 R1)
-

• Received SignalThe code structure still
  preserves the simplicity of the receiver!

Channel Estimation
Equalization
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Combining STBC with OFDM
Unitary DFT matrix
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Combining STBC with OFDM
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Input-Output Relations

• STBC OFDM

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Equalization Channel Estimation

• STBC OFDM

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Channel Estimation Exploiting Structure

• Consider the channel estimation problem

• Expand the received vector

• Reorder the entries of the received vector

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• Previous equation decouples to

• The frequency-selective channel estimation
  problem decouples into N independent flat channel
  estimation problems.

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Addressing IQ Imbalances Recall SISO Case
cross-diagonal
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2x2
2x2
The system of equations decouples into 2x2
subequations for k2,,N/2
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Adaptive Equalization (post-FFT)
(training)
i iteration index
Initial conditions assume ideal IQ
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• Let C be a block row vector and D be a block
  matrix with entries
• where and are 2x2 Alamouti
  matrices. Then the following facts hold
• is a scaled multiple of the identity.
• have diagonal blocks that are
  scaled multiples of the identity matrix and
  off-diagonal blocks that are 2x2 Alamouti
  matrices.

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MIMO Formulation
Analog IQ Distortion
IFFT
FFT
MIMO Data Estimation
Analog IQ Distortion
FFT
IFFT
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MIMO Formulation
Analog IQ Distortion
IFFT
FFT
MIMO Data Estimation
Analog IQ Distortion
FFT
IFFT
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MIMO Formulation
Analog IQ Distortion
IFFT
FFT
MIMO Data Estimation
Analog IQ Distortion
FFT
IFFT
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MIMO Formulation
Analog IQ Distortion
IFFT
FFT
Analog IQ Distortion
FFT
IFFT
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MIMO Formulation
Ideal system
Due to imbalances
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MIMO Formulation
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MIMO Input-Output Relation

• This result precisely describes the input-output
  relation as a function of channel and distortion
  parameters.
• This system of equations can be now used to
  apply ML or MMSE algorithms to MIMO receivers
  with compensation for IQ imbalances.

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MIMO Formulation
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Ideal versus Proposed
Channel estimation data decoding (k2)
Channel/distortion estimation data decoding
(k2)
Channel estimation data decoding (kN/2)
Channel estimation data decoding (kN/22)
Channel/distortion estimation data decoding
(kN/2)
Channel estimation data decoding (kN)
Ideal Receiver
Proposed Receiver
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MIMO with STBC
same channel matrix
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Block NLMS Algorithm

• Update the equalizer coefficients according to
  the rule

• Using the matrix inversion lemma

and the following property of Alamouti matrices
We conclude that
NLMS performance at LMS complexity.
75
Block RLS Algorithm

• Update the equalizer coefficients according to
  the rule

• Structures of and

RLS performance at LMS complexity.
(a diagonal structure)!
Adaptive solutions compensate for both channel
distortion and imperfection distortions.