on the design of rake receivers with non-uniform tap spacing by
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On the Design of RAKE Receivers with Non-uniform Tap Spacing By K. B. Baltzis and J. N. Sahalos. RadioCommunications Lab., Department of Physics, Aristotle University of Thessaloniki, Greece. July 2006. - PowerPoint PPT PresentationTRANSCRIPT
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.
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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].
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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 Thessaloniki
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni
TRANSMITTER AND CHANNEL MODEL
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
TRANSMITTER AND CHANNEL MODEL
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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).
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
Symbol denotes the convolutional operator
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
PROPOSED RECEIVER MODEL
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
PROPOSED RECEIVER MODEL
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:
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
PROPOSED RECEIVER MODEL
PROPOSED RECEIVER MODEL
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
PROPOSED RECEIVER MODEL
x1
x2
xL-1
xL
CORRELATION COEFFICIENTS ESTIMATOR
To SUM1UNITL signals
To SUM2UNITL(L-1)/2signals
.
.
.
Block diagram of Correlation Coefficients Estimator (CCE) Unit
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
PROPOSED RECEIVER MODEL
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
.
.
.
.
.
.
.
.
.
.
.
.
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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
THE MAXIMUM POWER MINIMUM CORRELATION (MPMC) CRITERION
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
THE MAXIMUM POWER MINIMUM CORRELATION (MPMC) CRITERION
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
THE MAXIMUM POWER MINIMUM CORRELATION (MPMC) CRITERION
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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 )
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
NUMERICAL RESULTS
OPTIMUM TAPS POSISTIONS MPMC 3RAKE
3rd tap
2nd tap
1st tap
Uniform PDP
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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.
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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)
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloni RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki
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
RadioCommunications Laboratory - Dept. of Physics - Aristotle University of Thessaloniki