Space Time Codes

A MIMO SYSTEM

System Model

System Model Why Space Time coding ? MIMO system with NT transmit and NR receive antennas : received vector : quasi-static channel matrix : transmitted vector : white Gaussian noise vector Why Space Time coding ?

Space-Time Coding What is Space-Time coding? Coding schemes allow for the adjusting and optimization of joint encoding across space and time in order to maximize the reliability of a wireless link. Space-Time codes allow us to achieve this goal by exploiting Spatial diversity in order to provide coding and diversity gains over an uncoded wireless link

Space-Time Coding Space-Time Block Codes: Space-Time Trellis Codes: These codes are transmitted using an orthogonal block structure which enables simple decoding at the receiver. Space-Time Trellis Codes: These are convolutional codes extended to the case of multiple transmit and receive antennas.

Space-Time Coding Space-Time Block Codes achieve maximum possible diversity advantage but no coding gain and bandwidth expansion advantage: simplicity Space-Time Trellis Codes (STTC) joint design of error control coding, Modulation, transmit and receive diversity complexity coding gain, spectral efficiency, and diversity improvement

Maximizing diversity with Space-Time Codes Space–Time Trellis Codes (STTC) offer better performance at the cost of increased complexity Complex decoding (vector version of the Viterbi algorithm) —increases exponentially with the transmission rate Full diversity. Coding gain Space–Time Block Codes (STBC) Simple maximum–likelihood (ML) decoding based on linear processing Full diversity. Minimal or no coding gain

Space-Time Trellis Coding 1 2 3 Aim : To realize joint encoding, modulation and diversity across space and time . Design : 4-QAM / QPSK 4 – state 2 – Transmit antennas

Space-Time Trellis Coding Example of a 2 transmit space-time trellis code with 4 states (4-PSK constellations, spectral efficiency of 2bps/Hz) Input Bits 00 ‘0’ 01 ‘1’ 10 ‘2’ 11 ‘3’ State 0 Output for Antenna1,Antenna2 02 03 State 1 12 13 State 2 20 21 22 23 State 3 30 31 32 State # 1 2 3

Example Assume initial state : 00  state 0 Input stream : 0 3 0 1 2 0 3 2 0 1 0 0 Tx. Ant. 1 : 0 0 3 0 1 2 0 3 2 0 1 0 Tx. Ant. 2 : 0 3 0 1 2 0 3 2 0 1 0 0 Delay diversity ?

Example - Delay diversity code, QPSK modulation Example - Delay diversity code, QPSK modulation Code rate ½ , 2 Tx antennas Input x ∈ ℤ4 output antenna 1 antenna 2 D c1 c2 Encoder structure: Example: x = 1 3 2 0 1 c1 = 1 3 2 0 1 c2 = 0 1 3 2 0 1 symbol delay

Example -Space-time ring TCM code 4-state trellis, code rate ½ (and n=2) Encoder structure: c1 x D c2 + 3 1 2 3 1 1 input seq. output seq. 1 3 0 3 0 t0 t1 2 1 input St St+1 c1 c2 1 3 2 2 1 3

Example -Space-time ring TCM code 4-state trellis, code rate ½ (and n=2)

Space Time Trellis Decoding For the 2 Tx antennas system the metric is reduced to: m (rj ( l ), ci ( l ) / h ij ( l ) ) =   [ rj( l ) - {h 1j ( l ) c1( l ) + h 2j ( l ) c2( l ) } ] 2 l = 1 j = 1 L m

Space Time Trellis Decoding

Simulation Results for Trellis Codes 2 Tx, 1Rx, 4PSK codes: 2 Tx, 2Rx, 4PSK codes: Increase in number of states → increases coding gain Increase in number of receive antennas → increases diversity gain

Space-Time Block Codes

Space-Time Block Code Alamouti Codes Tx1 Tx2 -c2* c1 c1* c2 Encoding and Transmission : Decoding: Linearly combine received symbols Perform Maximum Likelihood (ML) detection Diversity order of 2NR guaranteed The received symbols :

STBC for Tx. Ant > 2

Simulation Results for Alamouti Scheme Increase in number of receive antennas → increases diversity order

Comparison of Alamouti and Trellis Space–Time Trellis codes perform better than Alamouti scheme. Alamouti code is lot simpler to decode than trellis codes

Capacity increase in MIMO

Scope of MIMO MIMO channels offer multiplexing gain, diversity gain, power gain (array gain) and a co–channel interference cancellation gain Tradeoff between diversity gain and multiplexing gain: Careful balancing between those gains is required Space-Time Coding: Space-Time block codes (STBC) and Space-Time Trellis Codes Easy to combine with error control codes MIMO systems offer a solution choice for future generation wireless networks Distributed MIMO: Cooperative wireless networks