1. Coded Modulation for Multiple Antennas over Fading Channels
Israfil Bahçeci

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

3. Introduction
fading
multipath propagation and time variations 

4. Fading in Time, Frequency and Space
selective fading
(due to delay
spread)
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Time selective fading
(due to Doppler spread)
Space selective fading
(due to delay spread)

5. 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

6. Combined space and time diversity
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.

7. Multiple antennas at the transmitter and the receiver

8. 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).

9. 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

10. Space-Time Trellis Codes
Diversity order is Nr, where r is minimum rank of B=S-Ŝ over the set of two tuples of distinct codewords.
Coding gain is (λ1 λ2 …λr)1/r, where λi 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
M=2, N=1, R=2 b/s/Hz,
4-PSK, 4-states, Diversity order is 2.

11. 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. 1 9 17 25 33 41 49 57 65 73 2 10 18 26 34 42 50 58 66 3 11 19 27 35 43 51 59 4 12 20 28 36 44 52 5 13 21 29 37 45 6 14 22 30 38 7 15 23 31 8 16 24
Antennas 
Transmission time 

13. cancellation
nulling

14. 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 M=N, the capacity increases by K(1-K/T) bits/s/Hz for every 3 dB SNR increase where K= min(r, T/2).

15. 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.

16. 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.

17. Turbo Coded Unitary Space-Time Modulation
Block diagram of turbo coded modulation
Block diagram of turbo code

18. 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.

19. L = number of
signals in the constellation

20. T=8, L=256, M=2, N=1, R= 7/8 b/s/Hz

21. T=5, L= 32, 1024, M=2, N=1, R= 1 b/s/Hz

22. 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

23. Optimal Decoding Code Design 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.

24. example, L = 8 USTM
0.3835 7 3
0.3786 6 2 5 1
0.3536 4
1.000
ik
i-k mod L

25. M=2, N=1, R=1/4 b/s/Hz. 8-state L=8 USTM schemes
compared with uncoded L=4 USTM.

26. M=2, N=1, R=1 b/s/Hz. 256-state L=512 TCM
compared with L=256 uncoded modulation.

27. 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.