Coded Modulation for Multiple Antennas over Fading Channels

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Coded Modulation for Multiple Antennas over
Fading Channels
Israfil Bahçeci
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Outline

• Signaling over Wireless Channels
• Fading Channels
• Diversity techniques
• Channel Coding,
• Space-time Coding for Multiple Antenna Systems
• Space-time architectures
• Turbo- and Trellis-Coded Space-Time Modulation

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Introduction
fading
multipath propagation and time variations ?
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Fading in Time, Frequency and Space
Frequency selective fading (due to delay
spread)
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Time selective fading (due to Doppler spread)
Space selective fading (due to delay spread)
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Signaling over Fading Wireless channels
diversity techniques
Frequency selective fading (due to delay
spread)
Frequency diversity
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Time diversity Channel coding and interleaving.
Antenna diversity
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Channel coding

• A sophisticated form of time diversity

• Different techniques
• linear block codes (Hamming, Hadamard, Golay,
  BCH, etc.)
• convolutional codes
• code concatenation (parallel, serial, product
  codes, etc.)
• turbo codes
• trellis coded modulation
• turbo coded modulation

Combined space and time diversity

• multiple transmit and receive antennas are used.
• robust to variations of the channel.
• high spectral efficiencies can be achieved.

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Multiple antennas at the transmitter and the
receiver
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Capacity Results for known CSI

• memoryless channel, Rayleigh flat fading

• C roughly linear with the smaller of the
  number of the
• transmitter and receiver antennas.
• i.e., if , the capacity
  increases m bits/s/Hz
• for every 3 dB increase in signal-to-noise ratio
  (SNR).

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Space-time Codes

• Combination of channel coding/modulation with
  multiple
• antennas.
• Encoder generates M elementary signals to be
  transmitted
• simultaneously.

If CSI is available

• Space-time trellis codes
• Space-time block codes
• Turbo coded modulation with antenna diversity
• Layered Space-Time Codes, i.e., BLAST

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Space-Time Trellis Codes

• Diversity order is Nr, where r is minimum rank of
  BS-S over the set of two tuples of distinct
  codewords.
• Coding gain is (?1 ?2 ?r)1/r, where ?i are
  non-zero eigenvalues of BBH.

Code construction
ML Decoding
Branch metric at time t
Viterbi algorithm is then used to find the path
with the Lowest accumulated metric.
QPSK constellation
M2, N1, R2 b/s/Hz, 4-PSK, 4-states, Diversity
order is 2.
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BLAST (Bell Labs Layered Space-Time)

• As M and N increase, complextity with ML decoding
  increase
• Suboptimal design but still achieving most of the
  capacity
• Layered space-time codes, processing higher
  dimensional signals with the use of 1-D codes.

Antennas ?
Transmission time ?
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• cancellation

• nulling

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Capacity Results for no CSI case

• Block fading channel, T coherence time of the
  channel.
• Capacity does not increase as number of transmit
  antennas increases beyond the coherence time!
• Capacity achieving signals have considerable
  structures
• Isotropically distributed random vectors x
  Diagonal random matrix
• For MN, the capacity increases by K(1-K/T)
  bits/s/Hz for every 3 dB SNR increase where K
  min(r, T/2).

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Space-Time Codes when CSI is not available

• Unitary Space-Time modulation
• Differential Space-Time Modulation schemes
• i.e., differential encoding of Group Codes
  (comprising of matrices), similar to the ordinary
  DPSK modulation for single antenna trasnmission.

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Unitary Space-Time Modulation

• Block Rayleigh fading

• Unitary space-time (UST) signals achieves
  capacity.

• Information is carried on the subspace spanned
  by orthonormal signals that are sent to transmit
  antennas.

• Large signal constellations can be generated
• systematically.

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Turbo Coded Unitary Space-Time Modulation
Block diagram of turbo coded modulation
Block diagram of turbo code
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Decoding
Find the likelihood values for transmitted bits
and use them as if they are observations from
BPSK modulation over AWGN channel
Block diagram for decoder.
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L number of signals in the constellation
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T8, L256, M2, N1, R 7/8 b/s/Hz
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T5, L 32, 1024, M2, N1, R 1 b/s/Hz
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Trellis Coded Unitary Space-Time Modulation
8-state encoder and L 8 USTM and uncoded L 4
USTM schemes
0,1,7 denote the UST signals
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Optimal Decoding
where is the received signal.

• can be implemented using Viterbi algorithm

Code Design

• Given the constellations

• Set Partitioning (similar to Ungerboeck Rules)
• small ? larger separation between signal
  pairs and
• where s.t. are
  singular values of
• Parallel transitions should be assigned to
  members of the lowest level partition.
• Adjacent transitions should be assigned the
  next available partition.

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• example, L 8 USTM

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M2, N1, R1/4 b/s/Hz. 8-state L8 USTM schemes
compared with uncoded L4 USTM.
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M2, N1, R1 b/s/Hz. 256-state L512 TCM
compared with L256 uncoded modulation.
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Conclusions

• Multiple antennas have great potential to
  provide large transmission rates, particularly
  required by multimedia applications.
• Space-time coding technology with other
  techniques such as array processing, OFDM, CDMA,
  etc. promise large performance improvement.
• Further research on space-time coding for
  various channel models needs.