Coded Modulation for Multiple Antennas over Fading Channels Israfil Bahçeci

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

Introduction fading multipath propagation and time variations 

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

Signaling over Fading Wireless channels diversity techniques Frequency selective fading (due to delay spread) Frequency diversity aeimqbfjncskodhlp Time diversity: Channel coding and interleaving. Antenna diversity

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.

Multiple antennas at the transmitter and the receiver

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).

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

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.

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 

cancellation nulling

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).

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.

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.

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

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.

L = number of signals in the constellation

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

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

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

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.

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

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

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

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.