rake reception in uwb systems aditya kawatra 2004ee10313

Rake Reception in UWB Rake Reception in UWB SystemsSystems

Aditya KawatraAditya Kawatra

2004EE103132004EE10313

UWB and Rake ReceptionUWB and Rake Reception

• Impulse radio UWB is being considered for a variety of applications including as a possible physical layer for emerging wireless personal area networks (WPANs).

• UWB systems have BW utilization > 500 UWB systems have BW utilization > 500 MHz or fractional BW > 25%MHz or fractional BW > 25%

• Sub-nanosecond pulses, high data rates Sub-nanosecond pulses, high data rates possiblepossible

• Channel usually consists of many multi-Channel usually consists of many multi-path reflections – empirically confirmedpath reflections – empirically confirmed

UWB and Rake ReceptionUWB and Rake Reception• To this effect, many multi-path modeling To this effect, many multi-path modeling

channel models have been proposed, e.g. channel models have been proposed, e.g. Saleh-Valenzuela double exponential ray-Saleh-Valenzuela double exponential ray-cluster model; tapped delay line model; cluster model; tapped delay line model; IEEE CM1, CM2 etcIEEE CM1, CM2 etc

• UWB exhibits high resolution among the UWB exhibits high resolution among the multi-path arrivals due to the extremely multi-path arrivals due to the extremely short duration of the pulsesshort duration of the pulses

• To exploit this multipath diversity, rake To exploit this multipath diversity, rake receivers are used (to inc. diversity order)receivers are used (to inc. diversity order)

Rake Receiver PrinciplesRake Receiver Principles

• Basic version consists of multiple correlators (fingers) where each of the fingers can detect/extract the signal from one of the multipath components provided by the channel.

• The outputs of the fingers are appropriately weighted which can be determined by a few procedures

• A few of them are MRC (Maximal Ratio Combining), MMSE (Minimal Mean Squared Error), OC (Optimal Combining) etc.

Rake Receiver PrinciplesRake Receiver Principles• Rake filters are mainly categorized on the Rake filters are mainly categorized on the

number of rakes like A-Rake (All Rake), P-number of rakes like A-Rake (All Rake), P-Rake (Partial Rake) and S-Rake (Selective Rake (Partial Rake) and S-Rake (Selective Rake)Rake)

• Diff b/w S-Rake and P-RakeDiff b/w S-Rake and P-Rake

• S-Rake is sort of best fit and P-Rake is sort S-Rake is sort of best fit and P-Rake is sort of first fit.of first fit.

• Tradeoff between BER (SER) and Time Tradeoff between BER (SER) and Time Complexity (hence data rate) at the Complexity (hence data rate) at the receiver.receiver.

MRC RakeMRC Rake

• In MRC, as name suggests, the rakes are In MRC, as name suggests, the rakes are chosen in which the signal-to-noise ratio is chosen in which the signal-to-noise ratio is maximized.maximized.

• In a typical MRC S-Rake with ‘N’ fingers, the In a typical MRC S-Rake with ‘N’ fingers, the received signal is passed through a pulse-received signal is passed through a pulse-shaping filter. This is sampled at symbol, shaping filter. This is sampled at symbol, chip or sub-chip ratechip or sub-chip rate

• The delays, amplitudes and phases of (>N) The delays, amplitudes and phases of (>N) multipaths are estimatedmultipaths are estimated

MRC RakeMRC Rake

• Then, the fingers having the largest ‘N’ Then, the fingers having the largest ‘N’ amplitudes are chosenamplitudes are chosen

• The signals of the selected fingers are The signals of the selected fingers are then despreaded by correlatorsthen despreaded by correlators

• Then they are weighed by their respective Then they are weighed by their respective estimated amplitudes and coherently estimated amplitudes and coherently addedadded

• Then a decision maker makes the bit Then a decision maker makes the bit decisiondecision

Issues with MRC RakeIssues with MRC Rake

• If the signals in the rakes are uncorrelated If the signals in the rakes are uncorrelated and have same noise power then and have same noise power then maximum theoretical performance is maximum theoretical performance is achievedachieved

• But the signals are usually correlated, But the signals are usually correlated, decreasing performancedecreasing performance

• If the sampling rate is sub-chip rate then If the sampling rate is sub-chip rate then synchronization errors are removed. synchronization errors are removed.

• However this means higher sampling rates However this means higher sampling rates and thus higher time complexity and thus higher time complexity

Issues with MRC RakeIssues with MRC Rake

• Chip and symbol rate based receivers Chip and symbol rate based receivers have much lower complexityhave much lower complexity

• However, finding the optimum sampling However, finding the optimum sampling point is a problem -> timing error (jitter)point is a problem -> timing error (jitter)

MRC Rake Block DiagramMRC Rake Block Diagram

MMSE RakeMMSE Rake

• In MMSE, attention is paid to the rake In MMSE, attention is paid to the rake weightsweights

• Particular case of OC RakeParticular case of OC Rake

• Basically, the weight vector is improved Basically, the weight vector is improved after each iterationafter each iteration

• The mean square error between the The mean square error between the expected decision value (for each bit) and expected decision value (for each bit) and the measured decision value is minimized.the measured decision value is minimized.

• The correlator is assumed to have perfect The correlator is assumed to have perfect knowledge of the channel delays and knowledge of the channel delays and amplitudes (by way of training)amplitudes (by way of training)

MMSE Rake mathematicallyMMSE Rake mathematicallyIn most general form,In most general form,

Here, p(t) ≡ basic pulse shape, Tf ≡ Average Pulse Time

Cj = Time-hopping code, Tc = Chip time and NcxTc <= Tf

Energy in q(t) is taken to be 1.

Assuming biphase modulation received signal is,

rk(t) = dk*sqrt(Eb)*q(t-k*Ts)*h(t) + n(t)Here, dk is data bit from {1,-1}, Eb is bit energy at receiver, Ts is symbol time (bit time), h(t) is channel response and n(t) is received noise

MMSE Rake mathematicallyMMSE Rake mathematically

Let v(t) = template at correlator = q(t) [biphase mod.]Let v(t) = template at correlator = q(t) [biphase mod.]

Corresponding to the lth finger and tl delay of template,Corresponding to the lth finger and tl delay of template,

Output at correlator = Output at correlator =

This is = dk*sqrt(Eb)*hl + nl,k

In vector form, xk = dk*sqrt(Eb)*h + nk

Dk’ = (Transpose(w)*xk), the measured decision value


The Mean Square Error is given by :The Mean Square Error is given by :

MSE = E(||dk – Transpose(w)*xMSE = E(||dk – Transpose(w)*xkk||)||)22

The optimal vector satisfying MMSE is givn byThe optimal vector satisfying MMSE is givn by

wwoo = argmin = argminww(MSE)(MSE)

The Weiner solution is given by,The Weiner solution is given by,

wo = A*M-wo = A*M-11**hh, A being a scaling constant, A being a scaling constant

M is the correlation matrix of noise = M is the correlation matrix of noise = E[Transpose(nE[Transpose(nkk)*n)*nkk]]

And E is Expectation of (Mean)And E is Expectation of (Mean)


• Instead of calculating wo iteratively by thisInstead of calculating wo iteratively by this

method, the LMS (Least Mean Square) method, the LMS (Least Mean Square) Algorithm is Algorithm is

UtilizedUtilized

• In this after every iteration,In this after every iteration,

w(n+1) = w(n) + mu*Err*w(n+1) = w(n) + mu*Err*xxkk

where mu = small positive const.where mu = small positive const.

Err = Error = (dErr = Error = (dkk – d – dkk’)’)

xxkk = Correlation vector= Correlation vector


• The convergence and stability of this The convergence and stability of this algorithm depends on mu. The lower it is, algorithm depends on mu. The lower it is, the slower it converges but the stability is the slower it converges but the stability is assuredassured

• Also, the algorithm is known to be of lower Also, the algorithm is known to be of lower time complexity than the previous solutiontime complexity than the previous solution

MMSE Rake Block diagramMMSE Rake Block diagram

Simulation LogSimulation Log

• Gaussian double derivative (with energy = Gaussian double derivative (with energy = 1) was taken as the basic pulse shape1) was taken as the basic pulse shape

• Channel model was the Saleh-Valenzuela Channel model was the Saleh-Valenzuela channel model with minimum inter-ray channel model with minimum inter-ray spacing equal to the symbol time to spacing equal to the symbol time to demonstrate multipath resolution of UWB demonstrate multipath resolution of UWB receptionreception

• Then a pulse train was convoluted with the Then a pulse train was convoluted with the channel impulse response and ouput channel impulse response and ouput confirmed to be multipath resolvableconfirmed to be multipath resolvable


• Then MMSE Partial-rake was performed (by Then MMSE Partial-rake was performed (by taking arbitrary fingers)taking arbitrary fingers)

• Using the LMS algorithm, the decision was Using the LMS algorithm, the decision was taken on the correlator outputstaken on the correlator outputs

• The input size was taken to be 1000 (due The input size was taken to be 1000 (due to time constraint) and BER’s analyzedto time constraint) and BER’s analyzed

• As the signal strength was increased, the As the signal strength was increased, the BER ‘overall’ decreasedBER ‘overall’ decreased

• Also, on increasing the number of fingers Also, on increasing the number of fingers the BER decreased somewhatthe BER decreased somewhat


• Then, Selective Rake was taken and Then, Selective Rake was taken and simulated the same waysimulated the same way

• It was found to give slightly lesser BER for It was found to give slightly lesser BER for the same SNR compared to partial rakethe same SNR compared to partial rake

• Also, as the number of rakes increased the Also, as the number of rakes increased the BER correspondingly decreased BER correspondingly decreased

Simulation FiguresSimulation Figures

Selective RakeSelective Rake

BER vs SNRBER vs SNR

Coding GainCoding Gain

• Selective Rake has coding gain of 1.25 dB Selective Rake has coding gain of 1.25 dB over Partial Rake for a BER of 15/1000 in over Partial Rake for a BER of 15/1000 in our modified exampleour modified example

• Higher no. of bits could not be taken Higher no. of bits could not be taken because of the amt. of computing timebecause of the amt. of computing time

rake reception in uwb systems aditya kawatra 2004ee10313

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