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- MRRCReceived Signal:

Si will be selected iff:

Combiner:

[1]

Alamouti’s Scheme

Three functions:

• The encoding and transmission sequence

• Combining sequence

• Maximum likelihood decision region

[1]

Alamouti’s Scheme

Time Antenna 0 Antenna 1

t S0 S1

t+T -S1* S0

*

1. Encoding : For two branch transmission scheme

Assume fading is constant for two consecutive symbol periods

Received signal is given byReceived signal is given by

[1]

Alamouti’s Scheme – Combining Sequence & Maximum likelihood Detection

2. Combining Sequences

Solving

3. Maximum likelihood detection is used to find the most probable symbols

(a)

(b)

[1]

Alamouti’s scheme- 2Tx & 2 RxReceived 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+ Ak

TAi = [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 oneChannel rank is one

[2]

Capacity

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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