On the Design of RAKE Receivers with Non-uniform Tap Spacing By

On the Design of RAKE Receivers with On the Design of RAKE Receivers with Non-uniform Tap Spacing Non-uniform Tap Spacing

By

K. B. Baltzis and J. N. Sahalos

RadioCommunications Lab., Department of Physics, Aristotle University of Thessaloniki, Greece.

July 2006

RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

CONTENTSCONTENTS

1. Abstract.

2. Introduction.

3. Transmitter and Channel Model.

4. Proposed Receiver Model.

5. The Maximum Power Minimum Correlation (MPMC) Criterion.

6. Numerical Examples.

7. Conclusions. RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

ABSTRACTABSTRACT

The effect of Non-Uniform tap spacing on the performance of a

RAKE receiver is studied.

A new RAKE receiver, the MPMC RAKE, is suggested.

Taps positions optimization is done according to the MPMC criterion.

MPMC criterion considers the total received signal autocorrelation

properties at the correlators outputs of the receiver.

Numerical results, comparisons and discussions are provided.


DS/SS (WCDMA) Used in 3G Communication Systems.

RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni

INTRODUCTION

RAKE diversity Used to combat Multipath Fading.

Maximal Ratio Combining, MRC

Equal Gain Combining, EGC

(Generalized) Selection Combing, (G)SC

Maximum Likelihood criterion, MLImplementation

Strategies


INTRODUCTION

Z

COMBINER

Correla torL

Correla torL -1

Correla tor1

1/W 1/W 1/Wr(t)

x L x L-1x 1

RAKE receiver model

r(t), received signal

W, signal bandwidth

L, number of branches

xi, ith-correlator output

Z, decision variable


INTRODUCTION

TAP SPACING:

Usually taken equal to chip period.

MRC is optimum under the assumption of independent

branch signals, Dong and Beaulieu, [2002].

ML criterion is optimal when tap spacing is set less

than chip duration, Kim et al., [2000].



TRANSMITTER AND CHANNEL MODEL

ASSUMPTIONSASSUMPTIONS

1. The modulation scheme is a BPSK one.

2. Signal energy per bit Eb is assumed equal for all users.

3. Channel is modeled as a WSSUS frequency-selective

Rayleigh fading one.

4. Transmitted pulses are time-limited rectangular.

5. Power Delay Profile (PDP) is uniform or exponential.


RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni


EQUIVALENT LOWPASS TRANSMITTED SIGNAL OF THE kth–USER:

/

2 k kbk cN

Es t b a h t T

N

,N

,bE

,cT

,ka

/ ,

kNb

, x

1 , 0,

0, otherwisec cT t T

h t

bit energy

processing gain

binary data sequence of the kth user

PN signature sequence of the kth user

chip duration

xthe largest integer not greater than

normalized chip waveform




TOTAL RECEIVED EQUIVALENT LOWPASS SIGNAL AT THE RECEIVER FROND END (K ACTIVE USERS):

1

0

;

K

k k k kk

r t t s t d n t

; , k t

,n t

, k

channel impulse response of the kth user’s link at delay τ and time instant t

time of arrival of the kth user’s signal

low pass equivalent process of AWGN

It is related to the PDP function g(t) with the expression: 2;kg E t

Complex zero-mean Gaussian random process

Delay depends on the time instant t: ; ; ;k k k kt t t t t



PROPOSED RECEIVER MODEL

ASSUMPTIONSASSUMPTIONS

1. Desired user channel impulse response can be estimated.

2. Amplitude, phase and timing of the desired user’s signal are

known.

3. Chip waveform shaping filters in transmitter and receiver are

known.

4. Average received signal energy is the same for all users

(power control).


Symbol denotes the convolutional operator



1

1

K

d s k nk

X t X t X t X t X t

CORRELATOR OUTPUT:

DESIRED SIGNAL COMPONENT: 1,0 02d b hhX t E b t R t

ISI COMPONENT:

MAI DUE TO THE kth USERCOMPONENENT:

AWGN COMPONENT:

00

0

2s b n hh cnn

X t E t c R t nT

2 kk b k n hh c k

n

X t E t c R t nT

1

0* *

0

1 N

n cX t n t a h t TN




02 b hhY t E t R t

1,0 ,b the first bit of the desired user data sequence

10*

0

1,

Nk k kn nn N

c b a aN

the discrete crosscorrelation function between the desired and the kth user

* ,hhR t h t h d

the autocorrelation function of the chip waveform.

DESIRED USER CHANNEL IMPULSE RESPONSE:




ITS MAIN CHARACTERISTICITS MAIN CHARACTERISTICIS THE NON-UNIFORM TAPIS THE NON-UNIFORM TAPSPACINGSPACING

ITS MAIN CHARACTERISTICITS MAIN CHARACTERISTICIS THE NON-UNIFORM TAPIS THE NON-UNIFORM TAPSPACINGSPACING



x1

x2

xL-1

xL

CORRELATION COEFFICIENTS ESTIMATOR

To SUM1UNITL signals

To SUM2UNITL(L-1)/2signals

.

.

.

Block diagram of Correlation Coefficients Estimator (CCE) Unit



Block diagram of SUM1 and SUM2 Units

From CCEUnit

Input 1

Input 2

( )2

( )2

( )2

( )2

+

To DecisionUnit

Input L for SUM

1L(L-1)/2 for SUM2

.

.

.

.

.

.

.

.

.

.

.

.


THE MAXIMUM POWER MINIMUM CORRELATION (MPMC) CRITERION

DEFINITION OF MPMC CRITERIONDEFINITION OF MPMC CRITERION

Optimum receiver performance is gained Optimum receiver performance is gained

when a simultaneous maximization of the when a simultaneous maximization of the

sum of squares of average received signal sum of squares of average received signal

power in each branch and minimization of power in each branch and minimization of

the sum of squares of autocorrelation the sum of squares of autocorrelation

between each pair of branches takes placebetween each pair of branches takes place

Multi-objective optimization problem RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki


DEFINITIONS:

1 2, ,..., ,

Lr r rT T TT

1 21 1 1V ,V ,...,V ,

L1V

,2V ,i j

2V

2

1V E , 1, 2,...,i ir

X T i L

*1 2E ,X t X t

the taps settings vector

the total signal average power coefficients vector

the total signal autocorrelation coefficients matrix

It is:

the autocorrelation function of X(t) given b1,0

,

*

2

E , 1, 2,..., , V

0, otherwise

i j

i j

r rX T X T i L j i



PROBLEM:

1VEuclidean norm of

Created in CCE Unit

Calculated in SUM1 and SUM2 Units

Applied in the Decision UnitHilbert-Schmidt norm of

22V

21V

2V

1 2

1 2

2

2

2

2

maximize , ,...,find :

minimize , ,...,

L

L

r r r

r r r

T T T

T T T

1

2

VT

V



1

1

1 1

2,...,

30

2 1subject to :

2 1 2 10 , 0

2 1 2 1i

r

ri L

T g gL

i iT g g g g

L L

g

1g

the antiderivative function of g(t)

the inverse function of g(t)

Finally MPMC criterion is defined as:

1 2

1 2

2

2

2

2

maximize , ,...,find :

minimize , ,...,

L

L

r r r

r r r

T T T

T T T

1

2

VT

V


LEXICOGRAPHIC method has been adopted for the optimization

RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

NUMERICAL RESULTS

• Processing gain N = 256

• Constant tap spacing in MRC RAKE Tr = Tc

• Constant tap spacing in ML RAKE, (Kim et al.), Tr = 0.7Tc

SIMULATION CHARACTERISTICS:

MPMC 4RAKE: 40 – 50% smaller Pe compared to ML 4RAKE at Eb/N0 = 15dB

60 – 80% smaller Pe compared to ML 4RAKE at Eb/N0 = 30dB


NUMERICAL RESULTS

Uniform PDP

tmax = 2Tc

K = 10

INTERFERENCE LIMITEDSYSTEM

TAPS SETTINGS:

MPMC 3RAKE:

0.28, 0.98, 1.69 (Tc )

MPMC 4RAKE:

0.28, 0.65, 1.3, 1.7 (Tc )


NUMERICAL RESULTS

MPMC RAKE: 40 – 50% increase in the number of users compared to MRC RAKE

20 – 30% increase in the number of users compared to ML RAKE

Uniform PDP

tmax = 2Tc

Pe<10-3

INTERFERENCE LIMITEDSYSTEM

max0

00

KKNEb


NUMERICAL RESULTS

OPTIMUM TAPS POSISTIONS MPMC 3RAKE

3rd tap

2nd tap

1st tap

Uniform PDP


NUMERICAL RESULTS

OPTIMUM TAPS POSITIONS

ARE NOT AFFECTED FROM THE NUMBER OF USERSOR THE VALUE OF SIGNAL TO NOISE RATIO.

EXAMPLE (MPMC 3RAKE, tmax = 2Tc):

0 dB , 30,30 , 15,10 , 5,2bE N K

31 2, , 0.25,0.94,1.65 , 0.28,0.98,1.69 , 0.27,0.97,1.68rr r

c c c

TT T

T T T

ONLY CHANNEL CHARACTERISTICSHAVE AN IMPACT ON THEM.


NUMERICAL RESULTS

Exponential PDP, tspr = Tc Exponential PDP, tspr = 2Tc

Uniform PDP, tmax = Tc

MORE SIGNIFICANT IMPOVEMENT INPERFORMANCE FOR THE CASES OF:

UNIFORM PDP

LARGER CHANNEL SPREAD


NUMERICAL RESULTS

IMPERFECT CHANNEL IMPULSE RESPONSE ESTIMATION OR / IMPERFECT CHANNEL IMPULSE RESPONSE ESTIMATION OR / AND PARTIAL KNOWLEDGE OF CHANNEL PDP DEGRADES AND PARTIAL KNOWLEDGE OF CHANNEL PDP DEGRADES

RECEIVER PERFORMANCERECEIVER PERFORMANCE

TWO CASES ARE STUDIED:

THE “OPTIMIZED TAPS” 1. IMPERFECT DESIRED USER CHANNEL IMPULSE RESPONSE ESTIMATION

THE “NON-OPTIMIZED TAPS” 1. IMPERFECT DESIRED USER CHANNEL IMPULSE RESPONSE ESTIMATION.

2. TAPS OPTIMIZATION IS DONE ACCORDING TO THE AVERAGE AND NOT THE INSTANTANEOUS PDP VALUE. TAPS POSITIONS DO NOT CHANGE.

THIS IS ALSO THE CASE BEFORE THE TAPS ACQUIRE THEIR

OPTIMIZED VALUES (TRAINING PERIOD)


NUMERICAL RESULTS

OPTIMIZED TAPS: ITS PERFORMANCE COMPENSATES FOR THE COMPLEXITY

NON-OPTIMIZED TAPS : SIMPLE – LOW COMPUTATIONAL COST

MPMC 3RAKE

Uniform PDP

K = 10

maxˆ 2 ct T

1.1. AA RAKE receiver with non-uniform taps distribution has been proposed.

2.2. DDetermination of the optimum taps positions is based on the correlation properties of the signal components in each branch.

3.3. TThe Maximum Power Minimum Correlation (MPMC) criterion has been proposed for the optimization of taps distribution (multi-objective optimization problem).

CONCLUSIONSCONCLUSIONS

RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

4.4. CComparisons with other implementations have exhibited the improved performance of the proposed receiver especially at higher values of signal to noise ratio.

5.5. OOptimum taps settings depend only on channel characteristics.

6.6. CChannel estimation errors does not affect significantly receiver performance.

RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki

CONCLUSIONSCONCLUSIONS

On the Design of RAKE Receivers with On the Design of RAKE Receivers with Non-uniform Tap Spacing Non-uniform Tap Spacing

By

K. B. Baltzis and J. N. Sahalos

RadioCommunications Lab., Department of Physics, Aristotle University of Thessaloniki, Greece.

July 2006


On the Design of RAKE Receivers with Non-uniform Tap Spacing By

Documents

Transcript of On the Design of RAKE Receivers with Non-uniform Tap Spacing By