A Simple Transmit Diversity Scheme for Wireless

Communication

Author: Siavash M. Alamouti

Sujeet Patole

Dec 16, 2013

The Wireless Channel

TX

↵0

e j✓0

↵1e j✓

1

↵N e j✓

N

RX

Figure 1 : Wireless channel

• Multipath: EM waves propagate through di↵erent path before reachingreceiver.• Gains in each path are independent of each other.

• Receiver collects the superposition of multi paths ! CLT

E↵ective Complex Gain = ↵e j✓=NX

n=1

↵n

cos ✓n

+ jNX

n=1

↵n

sin ✓n

⇠ CN (0,�2)

↵ ⇠ Rayleigh, ✓ ⇠ U[�⇡,⇡] (1)

• LOS!Rician Fading

Multipath Fading

• For a Gaussian channel with no fading, using BPSK modulation with

SNR �, Pe

is Q(p2�). Note that (Q(x) 1

2

e�x

2

2 )

• Performance Degradation in the presence of Multipath Fading

s

h = ↵e j✓ n

r = hs + n

Figure 2 : Multipath channel

r = hs + n = ↵e j✓s + n (2)

• SNR at the receiver � = |h|2Eb

N

0

is RV with exponential distribution.

P̄e

=

ZQ(

p2�)f (�)d� ⇡ 1

4�̄(3)

• BER improvement costs power: to improve BER from 10�3 to 10�2, 1-2dB higher SNR is required in AWGN case while 10dB higher SNR isrequired in multi-path case.

Multipath Fading Mitigation

Using Diversity Schemes

•Transmitter Power Control! Predistort signal! Dynamic

Range, Radiated Power limitations, CSI at the transmitter

requires receiver feedback!Throughput considerations.

•Time Diversity: Same signal at di↵erent times separated by at

least coherence time ! Length of the codeword to average

out slow fading ! Delays

•Frequency Diversity: Same signal over frequencies separated

by at least coherence BW ! BW consumption

•Space Diversity: Same signal sent over two di↵erent

uncorrelated paths received using Multiple antennas !Techniques and implementation Issues

Maximal Receiver Ratio Combining (MRRC)

• At two receiving antenna under flat fading (h0

= ↵0

e j✓0 , h1

= ↵1

e j✓1)received signal is given by:

r0

= h0

s0

+ n0

, r1

= h1

s0

+ n1

(4)

Detector

h⇤1n

1

n0

h0

= ↵0

e j✓0

h1

= ↵1

e j✓1

h⇤0

r1

s̃0

r0s

0

ML

• At the receiver optimum performance is obtained using ML detection.Assuming CSI at the RX, ML detection corresponds to:

R = [r0

r1

]T maxs

i

P

✓R

H, si

◆(5)

• For Gaussian distributed noise n1

and n2

, eq. [5] corresponds to: signal si

over sk

i↵:d2(r

0

, h0

si

) + d2(r1

, h1

si

) d2(r0

, h0

sk

) + d2(r1

, h1

sk

) 8i 6= k (6)

• This performance can achieved using MRC. (SNR is maximized isobtained using optimum weights.)

s̃0

= h⇤0

r0

+ h⇤1

r1

(7)

s̃0

= (↵2

0

+ ↵2

1

)s0

+ h⇤0

n0

+ h⇤1

n1

(8)

MRRC

• SNR at the combiner output is:

SNR⌃

=(↵2

0

+ ↵2

1

)Es

N0

= sum of individual SNR (9)

• For an independent fading on each path distribution of SNR is improved.SNR

⌃

= SNR0

+ SNR1

) PSNR

⌃

(SNR)= PSNR0

(SNR) ⇤ PSNR1

(SNR)

P̄e

=

ZPe

(SNR⌃

)PSNR

⌃

(SNR) d(SNR) (10)

• Diversity order of number of receiving antennas is obtained.• With CSI at RX, ML detection can be used.

d2(s̃0

, (↵2

0

+ ↵2

1

)si

) d2(s̃0

, (↵2

0

+ ↵2

1

)sk

) 8i 6= k (11)• Multiple antenna at the Receiver ! Space in User terminals, size, cost

Various Space Diversity Schemes

Modulator

Encoder

Channel

S to P

D

g(t)

g(t)

Modulator

Figure 3 : Delay diversity

• Using Multiple antennas at the transmitter! Economical• Simulcasting: Delay diversity scheme [Wittneben, 1991]

[Wittneben, 1993][Seshadri, 1993][Winters, 1994]• Same signal is delayed and transmitted through multiple antennas.

Repetition code is used. Receiver uses MLSE with the knowledge ofchannel.

Various Space Diversity Schemes

g(t)

Encoder

Channel

S to P

g(t)

Modulator

Modulator

d2

d1

Figure 4 : Space time trellis coding

• Repetition code and delay element is replaced by trellis coding[Tarokh, 1998].

• Space time trellis coding and FEC gives space as well as coding diversitygain.

• Additional processing ! Complexity increases as a function of bits/s/Hzand Diversity order

• Simple processing schemes is required.

The New Transmit Diversity Scheme

• Assuming that fading is constant over two consecutive symbols,h0

(t) = h0

(t + T ) = h0

= ↵0

e j✓0 , h1

(t) = h1

(t + T ) = h1

= ↵1

e j✓1

n1

h0

= ↵0

e j✓0

s0

r0

r1

Detector

ML

Combiner

s⇤0

h0

h1

s̃1

s̃0

-s⇤1

s1

h1

= ↵1

e j✓1

n0

Figure 5 : New transmit diversity scheme

Time Antenna 0 Antenna 1

t s0

s1

t+T -s⇤1

s0

⇤

Table 1 : Encoding sequence at the transmitter

• Received signal over two consecutive interval is:r0

= r(t) = h0

s0

+ h1

s1

+ n0

r1

= r(t + T ) = �h0

s⇤1

+ h1s⇤0

+ n1

The New Transmit Diversity Scheme

⇣r0

r⇤1

⌘=

⇣h0

h1

h⇤1

�h⇤0

⌘⇣s0

s1

⌘+

⇣n0

n⇤1

⌘

• The combiner builds following signals which are sent to ML detector

s̃0

= h⇤0

r0

+ h1

r⇤1

s̃1

= h⇤1

r0

� h0

r⇤1

(12)

• Simplifying,s̃0

= (↵2

0

+ ↵2

1

)s0

+ h⇤0

n0

+ h1

n⇤1

s̃1

= (↵2

0

+ ↵2

1

)s1

� h0

n⇤1

+ h⇤1

n0

(13)

• Comparing equation [13] with MRRC combiner output [8].• SNR of each symbol at the combiner output is sum of individual SNRs.• Hence, same diversity order as two branch MRRC can be obtained using

two transmitter antennas.

Two Branch Transmit Diversity with Two Receivers

n3

s0

r1

s⇤0

-s⇤1

s1

h1

= ↵1

e j✓1

n0

n1

h0

= ↵0

e j✓0

Combiner

h0

Detector

ML

h2

= ↵2

e j✓2

h3

= ↵3

e j✓3

r0

r2

r3

h1

h2

h3

s̃0

s̃1

n2

Figure 6 : New transmit diversity scheme

Time Antenna 0 Antenna 1

t h0

, r0

h2

, r2

t+T h1

, r1

h3

, r3

Table 2 : Channel coe�cients and receive signal definitions

Two Branch Transmit Diversity with Two Receivers and

Extension to M receivers.

• Received signals over two consecutive interval are:

r0

= h0

s0

+ h1

s1

+ n0

r1

= �h0

s1

⇤+h1s⇤0

+ n1

r2

= h2

s0

+ h3

s1

+ n2

r3

= �h2

s1

⇤+h3s⇤0

+ n3

(14)

0

@r0

r⇤1

r0

r⇤1

1

A =

0

@h0

h1

h⇤1

�h⇤0

h2

h3

h⇤3

�h⇤2

1

A⇣s0

s1

⌘+

0

@n0

n⇤1

n2

n⇤3

1

A

• Combiner produces:

s̃0

= h⇤0

r0

+ h1

r⇤1

+ h⇤2

r2

+ h3

r⇤3

s̃1

= h⇤1

r0

� h0

r⇤1

+ h⇤3

r2

� h2

r⇤3

(15)

• Simplifying,s̃0

= (↵2

0

+ ↵2

1

+ ↵2

2

+ ↵2

3

)s0

+ h⇤0

n0

+ h1

n⇤1

+ h⇤2

n2

+ h3

n⇤3

s̃1

= (↵2

0

+ ↵2

1

+ ↵2

2

++↵2

3

)s1

� h0

n⇤1

+ h⇤1

n0

� h2

n⇤3

+ h⇤3

n2

(16)• s̃

0

, s̃1

are fed to ML detector.• Eq. [16] shows diversity order equivalent to 4-branch MRRC.

Simulation Results

• Combined signal from two antennas is addition of combined signal fromsingle antenna case.

• Thus, two receiver antenna case can be extended to M receivingantennas.• Using two transmitter antennas and M receiver antennas give 2 timesMRRC diversity gain. Total diversity gain obtained is 2M.

• Uncoded coherent BPSK is used for the simulations. Total transmittedpower from two antennas is same as single antenna transmitted power inMRRC.• 3dB penalty in power as compared to MRRC.

Figure 7 : Simulation Results

Figure 8 : Simulation Results

Implementation Issues

Power Requirements: RF power handling limitation

For same total radiated power at the transmitter, 3dB penalty in errorperformance is seen. Half power transmitted from each antenna.Cheaper,smaller, more e�cient and less intermodulation distortion power amplifiers arepossible. Same performance is obtained when there is no TX power limit.

Sensitivity to Channel Estimation Error

Perfect CSI at the receiver is assumed. Pilot symbols used for estimation[Sampei , 1989][Cavers, 1991]. Quantization and interpolation errors. Pilotinsertion frequency should be greater than twice doppler shift (Throughput).

• One TX!Many RX• Many RX!One RX! M more pilots are required

Two orthogonal symbols are needed at the transmitter (Number of pilots aretwo times MRRC).

Decoding Delay

Two symbols decoding delay. Can be reduce to one symbol by using twodi↵erent frequencies (within the coherence BW) and transmitting at the sametime sending copies of same signal.

Implementation Issues

Antenna Configuations

Diversity requires to uncorrelated signal paths. Receive diversity requirements:10� at base station Rx and 3� at UT. Reciprocal channel. Same requirementsfor transmit diversity.

Soft failure

Failure of the transmitting antenna implies lost diversity gain. Same as MRRC.

Impact of interference

Half the interference power and double the number of interferes same powerand interference distribution within the system. If possible interferencecancellation may be used.

Conclusions

•The new transmit scheme with two TX and one RX antenna

provide same diversity order as one TX and two RX MRRC

scheme.

•With two TX and M RX antenna 2M diversity order is

obtained.

•Less computational complexity, no feedback from receiver.

•3 dB SNR loss.

•Twice number of pilot symbols.

References

Wittneben, A (1991)

Basestation modulation diversity for digital simulcast

IEEE Vehicular Technology Conf. , 848-853.

Wittneben, A (1993)

Basestation modulation diversity for digital simulcast

IEEE International Conf. on Communications , 1630-1634.

N. Seshadri and J. H. Winters(1993)

Two signaling schemes for improving the error performance offrequency-division-duplex (FDD) transmission systems using transmitterantenna diversity

IEEE Vehicular Technology Conf. , 508-511

J. H. Winters(1994)

The diversity gain of transmit diversity in wireless systems with Rayleighfading

ICC/SUPERCOMM , 1121-1125

References

V. Tarokh, N. Seshadri and A. R. Calderbank (1998)

Space-time codes for high data rate wireless communication

IEEE Trans. Inform. Theory , 1121-1125

J. K. Cavers (1991)

An analysis of pilot symbol assisted modulation for Rayleigh fadingchannels

IEEE Trans. Veh. Technol , Vol.40 686-693

S. Sampei and T. Sunaga(1989)

Rayleigh fading compensation method for 16 QAM in digital land mobileradio channels

IIEEE Trans. Veh. Technol , 640646

V. Tarokh, A. Naguib, N. Seshadri and A. R. Calderbank (1998)

pace- time codes for wireless communication: Combined array processingand space time coding

IEEE Trans. Inform. Theory