A Simple Transmit Diversity Technique for Wireless Communications -M. Alamouti 1998

Chou-pin Wu

09/06/2006

Abstract Using two transmit antennas and one receive antenna the

scheme provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas.

Advantage: 1. Redundancy is applied in space across multiple antennas, not in time or frequency. =>Doesn’t require any bandwidth expansion . 2. It doesn’t need any feedback from the receiver to the TX. 3. Its computation complexity is similar to MRRC. 4. Two transmit antennas and M receive antennas provides a

diversity order of 2M.

Introduction

The remote units are supposed to be small lightweight pocket communicators and provide high bit rate data services.

The communication systems are supposed to have better quality and coverage, be more power and bandwidth efficient.

The fundamental phenomenon which makes reliable wireless

transmission difficult is time-varying multipath fading .

ex: BER= 10-2 => 10-3

environment SNR increasing

AWGN 1 or 2 db

Multipath >10dB

Introduction (cont)

Transmitter power control (the most effective ) : If channel conditions are known at the transmitter ,the transmitte

r can predistort the signal in order to overcome the effect of the channel at the receiver.

Two problems: Transmitter dynamic range: a. For the transmitter to overcome a certain level of fading, it must increase its power by that same level . b. It is not practical because of radiation power limitations and the size and cost of the amplifiers. Channel information: a. The channel information has to be fed back to the transmitter.

b. throughput degradation and added complexity to both the transmitter and the receiver.

Introduction (cont)

Time and frequency diversity: time interleaving and error correction coding resulting in

large delays when the channel is slowly varying.

spread spectrum techniques are ineffective when the coherence BW of the channel is larger than the spreading BW.

Antenna diversity : a. use multiple antennas at the RX (RX diversity) and perform combining or selection and switching to improve the quality of the received signal.

b. makes the remote units larger and more expensive.

MRRC (Maximum Receive Ratio Combining)

note1

MRRC (cont)

Using Euclidean distance to detect:

chose xi if

d2(xi ,y) <= d2(xk ,y) i != k

ps. d2(x ,y) = (x - y) (x*-y*)

MRRC: SO’= (α02 + α1

2) sO + h0* n0 + h1

* n1

chose si if

d2(s0’ , (α0

2 + α12) si ) <= d2(s0

’ , (α02 + α1

2) sk )

if signals are equal constellations:

d2(s0’ , si ) <= d2(s0

’ , sk )

MRRC Note

By Schwartz’ Inequality

, if

Maximize SNR =>

0

1

qq

q

*a kb

*0 0*

*1 1

q hq h

q h

0 0

1 1

h nr h s n s

h n

2

2

q hsSNR

q n

2 22a b a b

2 22a b a b

oS q r q hs q n

The new transmit diversity scheme

encoding and transmission sequence

combining scheme

maximum likelihook decision rule

New scheme (cont)

time antenna0 antenna1

t s0 s1

t+T -s1* s0*

Combining scheme: Maximum likelihood decision rule:

chose si if

it is equal to two-branch MRRC.

Encoding and transmission sequence :

Assumption:

d2(s0’ , (α02 + α1

2) si ) <= d2(s0’ , (α0

2 + α12) sk )

*0 0 0

*0 1 1

( )

( )

r t s sr h n

r t T s s

00 0 0 0

11 1 1 1

( ) ( )

( ) ( )

i

i

h t h t T h e

h t h t T h e

*00 0 1

* *1 1 0 1

rs h hS

s h h r

*0 02 2 0 1

0 1 *1 1 1 0

( )s s h h

ns s h h

New scheme (cont)- two-branch transmit diversity with M antennas

New scheme (cont)- two-branch transmit diversity with M antennas

*0 1 0 1 0 1

*2 3 2 3 1 0

r r h h s sn

r r h h s s

RX

TX

Antenna0 Antenna1

Antenna0 h0 h2

Antenna1 h1 h3

Assumption:

Encoding and transmission sequence:

like 2-to-1 transmission diversity.

Combining scheme:

0* * *

0 0 1 2 3 1

**20 2311*

3

r

S h h h h r

rh hhhSr

0 02 2 2 20 1 2 3

1 1

( )s s

s s

* *0 1 2 3

**0 231

h h h hn

h hhh

New scheme (cont)- two-branch transmit diversity with M antennas

Maximum likelihood decision rule: chose si if

if signals are equal constellations:

The combined signals from the two RX antennas are the addition of the combined signals from each antenna ,i.e., the combining scheme is identical to a single RX antenna .

=>using two transmit and M receive antennas ,we can use the combiner

to obtain the same diversity order as 2M-branch MMRC.

d2(s0’ , (α02 + α1

2+α22 + α3

2) si ) <= d2(s0’ , (α02 + α1

2+α22

+ α32) sk )

d2(s0’ , si ) <= d2(s0’ , sk )

Error performance simulation

The total radiated power at Tx are equal. => the performance of the new scheme with two transmitters a

nd a single receiver is 3 dB worse than two-branch MRRC.

Implement issues

Power requirements:

1. the 3-dB reduction of power in each transmit chain translates to cheaper, smaller, or less linear power amplifiers.

2. to employ two half-power amplifiers rather than a single full power amplifier.

Sensitivity to Channel Estimation Errors:

1. The RX extracts the samples and interpolates them to construct an estimate of the channel for every data symbol transmitted.

2. With 2(M) TX and 1 RX antennas, however, the estimates of the 2(M) channels must be derived from a single received signal.

=>2(M) times as many pilots are needed

Implement issues (cont)

Delay effects 1.With 2-branch transmit diversity, if the transformed copies of th

e signals are transmitted at distinct intervals from all the antennas, the decoding delay is symbol 2 periods.

2. if the copies are sent at the same time and on different carrier frequencies, then the decoding delay is only one symbol period.

Antenna configurations 1. the propagation medium between the TX and TX in either dire

ction are identical. 2. to provide sufficient decorrelation between the signals transmi

tted from the two transmit antennas at base station >= 10 wavelengths.

3. the transmit antennas at the remote units must be separated by about 3 wavelengths to provide diversity at the base station.

Implement issues (cont)

Soft failure

1.one of the channel fail, and the other channel is operational, then the performance loss is on the order of the diversity gain.

2. adding reliability due to multiple TX chains. Impact on interference

1. simultaneous transmission of signals from two antennas.

=>it appears that the number of potential interferers is doubled ,however, each with half the interference power.

2. If interference has properties where interference cancellation schemes may be effectively used.

Conclusion and discussions

Using 2 TX antennas and 1 RX antenna the scheme provides the same diversity order as maximal-ratio receiver combining (MRRC) with 1 TX antenna, and 2 RX antennas.

2 TX antennas and M RX antennas provides a diversity order of 2M.

To employ two half-power amplifiers rather than a single full power amplifier.

2 times as many pilots are needed.