The Impact of Channel Estimation Errors on Space-Time Block Codes

1
The Impact of Channel Estimation Errors on
Space-Time Block Codes

• Presentation for Virginia Tech Symposium on
  Wireless Personal Communications
• M. C. Valenti
• D. A. Baker
• Wireless Communications Research Lab
• West Virginia University

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Benefits of Space-Time Block Codes

• Space-time block coding utilizes multiple
  transmit antennas to create spatial diversity.
• This allows a system to have better performance
  in a fading environment.
• Benefits
• Good performance with minimal decoding
  complexity.
• Can achieve maximum diversity gain equivalent to
  space-time trellis codes.
• Receivers that use only linear processing.

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Diagram of Block STC Transmission
Fading ?i
Data
STC encoder
x
r
STC decoder
Modulation
AWGN n
Encoder matrix
4
Wireless Channel Model Rayleigh Fading

• The channel between the ith transmit antenna and
  the receive antenna undergoes flat-fading
• We assume quasi-static fading
• Quasi-static means that the path gains from one
  transmit antenna to the receive antenna is
  constant over a frame.

Rayleigh
Uniform
Gaussian
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Block STC decoder

• Each symbol in a block is decoded separately by
  minimizing the metric
• The decoder outputs the hard-decisions on the
  data.
• The more TXs and RXs the system has, the better
  performance the system can achieve.

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Decoding Block STC
The received signals are
In order to minimize
it is equivalent to minimize
By using
we have
and
Since x1x2 (PSK), we can get
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Simulation of STBC

• Channel fading coefficients were modeled as
  samples of Gaussian random variables with
  variance 0.5 per dimension.
• The channel was assumed to be static over the
  length of a frame, and varies from frame to
  frame.
• Noise was modeled as Gaussian with zero mean and
  variance n/(2SNR). Where n is the number of
  transmit antennas.

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STBC With Channel Estimation Errors

• The fading coefficient between the ith transmit
  antenna and the receive antenna is given as

• A channel estimate with phase error is of the
  form

• A channel estimate with gain error is of the form

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QPSK With Perfect CSI
2 TX antennas
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Simulation Results Phase Errors _at_ Low SNR

• The SNR at the receiver is fixed at 10 dB.
• This shows a rapid decline in BER performance for
  small errors in the phase of either channel
  estimate.

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Simulation Results Phase Errors _at_ Medium SNR

• The signal to noise ratio (SNR) at the receiver
  is fixed at 20dB
• Even with the increased SNR a rapid decline in
  bit error rate performance still occurs.

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Simulation Results Phase Errors _at_ High SNR

• The signal to noise ratio (SNR) at the receiver
  is now fixed at 25dB
• Increasing SNR only results in a steeper curve as
  the performance is quickly degraded.

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Simulation Results Average Phase Error Per
Channel
1
10

• As the average phase error in each channel
  approaches 0.5 radians, the performance is
  completely degraded even with increasing values
  of SNR at the receiver.

0
BER
Received SNR
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Simulation Results Gain Errors

• The SNR is fixed at 10dB.
• The curve has a valley-like shape.
• This shows that if the error in both channel
  estimates is roughly equal, then only a small
  performance penalty is incurred.
• However, if the errors in each estimate are very
  different, performance can suffer.

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Normalized Gain Error

• Since the performance of the system is not
  adversely affected by errors in the gain of the
  estimates if the estimates are the same in each
  channel, the concept of normalized gain error is
  introduced.

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Simulation Results Normalized Gain Error

• SNR fixed at 10dB.
• SNR fixed at 20dB.

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Simulation Results Normalized Gain Error

• The performance loss is negligible when the
  normalized gain error is unity.
• When the difference between the gain errors in
  the two channels is nearly double the loss
  approaches 7dB at a BER of 10-3.

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Simulation Results Combined Gain and Phase Errors

• The shape of the curves remain similar to the
  curves generated when only considering the errors
  in the gain.
• However, the curves get flattened as the average
  phase error in each channel is increased.
• The phase errors are obviously the primary source
  of performance loss.

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Pilot Sequence Estimation

• A pilot sequence is a series of symbols that are
  known to the receiver in advance.
• By comparing what was transmitted with what was
  received, the receiver can estimate the effects
  of the channel.
• However, since the AWGN noise samples at the
  receiver are not known, the channel estimates
  will be imperfect, or noisy.

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STBC Estimation Scheme How It Works

• If we have only one receive antenna then the
  received signal at time t can be expressed as
  follows

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STBC Estimation Scheme How It Works

• The received signal can also be expressed using a
  matrix of transmitted signals instead of a matrix
  of channel gains as shown in the following

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STBC Estimation Scheme How It Works

• If the receiver knows the signals that were
  transmitted then an estimate of the channel fades
  can be derived from the received signal.

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STBC Estimation Scheme How It Works

• The channel estimate can now be shown.

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QPSK Using Pilot Sequence Estimation
QPSK with running average estimation
0
10

• The equation from the previous slides was used to
  implement a pilot symbol estimation scheme.
• The frame size for each example was 60 bits.
• The channel was assumed to be quasi-static, or
  constant fading over a frame.

BER
r1/2
r3/4
r2/3
r4/5
perfect CSI
Received SNR
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Results of Pilot Estimation Simulations

• The rate 1/2 and rate 2/3 schemes perform at a
  loss of only 2dB as compared to the case of
  perfect CSI.
• The rate 3/4 and rate 4/5 schemes perform at a
  loss of approximately 3 dB as compared to the
  case of perfect CSI.

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Conclusionsand Future Work

• Conclusions
• Block space time codes are sensitive to channel
  estimation errors.
• The impact of phase and amplitude errors were
  studied separately and jointly.
• Pilot symbol techniques can be used to assist
  estimation.
• Future Work
• Other modulation types, such as QAM, FSK, and
  DPSK, will be tested.
• Correlated fading between transmit and receive
  pairs and variable fading rates should be taken
  into account.
• Turbo principles can be used to facilitate the
  implementation of iterative channel estimation
  and decoding techniques.