Space Time Block Codes Poornima Nookala

Outline Motivation Revisit MRRC Two transmit and one Receiver scheme Two Transmit and Two receiver scheme Performance of Alamouti’s Scheme Basics of STBC Design of codes Capacity of STBC Outage Capacity Applications Performance of STBC in Powerline and satellite Communication Advantages Implementation Issues

MOTIVATION Mobile units are small, hence not optimal for receiver diversity Decoding complexity limited by the Processor Need for efficient open loop system Simple encoding and decoding algorithms Limited Power Need for transmit diversity at base station

Revisit- MRRC Received Signal: Combiner: Si will be selected iff: [1]

Alamouti’s Scheme Three functions: The encoding and transmission sequence Combining sequence Maximum likelihood decision region [1]

1. Encoding : For two branch transmission scheme Alamouti’s Scheme 1. Encoding : For two branch transmission scheme Time Antenna 0 Antenna 1 t S0 S1 t+T -S1* S0* Assume fading is constant for two consecutive symbol periods Received signal is given by [1]

Alamouti’s Scheme – Combining Sequence & Maximum likelihood Detection 2. Combining Sequences (a) Solving (b) 3. Maximum likelihood detection is used to find the most probable symbols [1]

Alamouti’s scheme- 2Tx & 2 Rx Received signals Combiner Solving [1]

Alamouti’s scheme- Performance BER comparison of coherent BPSK with MRRC and STBC In Rayleigh fading [1]

STBC STBC is the generalized scheme developed by Alamouti to an arbitrary number of tx antennas Encoding is represented by matrix is linear combination of symbols (repetition code) Code Rate – If the block encodes k symbols, code rate = k/T The decoding is same as Alamouti’s scheme

STBC No coding scheme included here, contrary to Space time trellis code (STTCs) which provides both coding as well as diversity gain. Orthogonal designs are used to construct STBC satisfying: AiTAk+ AkTAi = [0], AiTAi = I

Properties of Orthogonal Designs There are two attractions in providing transmit diversity via orthogonal designs: There is no loss in bandwidth, in the sense that orthogonal designs provide maximum possible transmission rate at full diversity There is an extremely simple maximum- likelihood decoding algorithm which uses linear combination at the receiver. [2]

Higher Order STBC for complex Constellations Three Transmit antennas , Four Transmit antennas [2]

Higher order STBC Its proved that no code for more than 2 transmit antennas can achieve full rate. For more than two antennas the maximum rate that can be achieved is ¾ Alamouti’s scheme is a special form of STBC which provides full diversity and rate Quasi – Orthogonal codes – rate 1, but not orthogonal

Performance of STBC Bit error probability versus SNR for space–time block codes at 3 bits/s/Hz; one receive antenna.

Capacity of STBC The block capacity for the channel is given by The STBC capacity in bits per channel is The difference in the capacity (ie) capacity loss: Where P is the SNR [2]

Capacity Space time block codes are optimal with respect to capacity when: Code rate is one Channel rank is one [2]

Capacity difference increases in SNR and number of antennas [2]

Outage Capacity 5%-outage capacity as a function of the average SNR at the receiver (before decoding) for some uncorrelated MIMO ricean fading channels with different number of antennas, code rates (R) and ricean-K factors (K). [4]

Some Potential Applications 802.11n(hybrid scheme – STBC/SMX) UTRA (Alamouti’s scheme) Powerline Communication(PLC) Satellite communication

Performance of STBC in PLC Channel is assumed to be frequency selective, multipath fading with AWCN BER performance of PLC using BPSK

Performance of STBC in Satellite Communication Satellite channel for urban channel is modeled as combination Rayleigh and log normal process in presence of AWGN BER performance of satellite channel using BPSK modulation

Advantages of STBC Can achieve full diversity with linear processing at the receiver. Open loop transmit diversity technique Simple encoding and decoding No bandwidth expansion

Issues Sensitivity to channel estimation error Delay Effects Antenna Configurations Soft failures [1]

References [1] S. M. Alamouti, “A simple transmitter diversity scheme for wireless communications,” IEEE J. Select. Areas Commun., vol. 16, pp. 1451–1458, Oct. 1998. [2] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Trans. Inform. Theory, vol. 45, pp. 1456–1467, July 1999. [3] S. Sandhu and A. Paulraj, “Space-time block codes: A capacity perspective,” IEEE Commun. Lett., vol. 4, pp. 384–386, Dec. 2000. [4] Jes´us P´erez, Jes´us Ib´a˜nez, Luis Vielva, and Ignacio Santamar´ıa, “Closed-form Approximation for the Outage Capacity of Orthogonal STBC”, IEEE COMMUN LETTERS, VOL. 9, NO. 11, NOVEMBER 2005 [5] Anna Papaioannou, George D. Papadopoulos, and Fotini-NioviPavlidou, “Performance of Space-Time Block Coding in Powerline and Satellite Communications”, IEEE JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, 2005

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