Transcript Rake_Reception_in_UW..

Rake Reception in UWB
Systems
Aditya Kawatra
2004EE10313
UWB and Rake Reception
• Impulse radio UWB is being considered for a
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variety of applications including as a possible
physical layer for emerging wireless personal
area networks (WPANs).
UWB systems have BW utilization > 500 MHz or
fractional BW > 25%
Sub-nanosecond pulses, high data rates possible
Channel usually consists of many multi-path
reflections – empirically confirmed
UWB and Rake Reception
• To this effect, many multi-path modeling channel
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models have been proposed, e.g. SalehValenzuela double exponential ray-cluster model;
tapped delay line model; IEEE CM1, CM2 etc
UWB exhibits high resolution among the multipath arrivals due to the extremely short duration
of the pulses
To exploit this multipath diversity, rake receivers
are used (to inc. diversity order)
Rake Receiver Principles
• Basic version consists of multiple correlators
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(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 Principles
• Rake filters are mainly categorized on the number
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of rakes like A-Rake (All Rake), P-Rake (Partial
Rake) and S-Rake (Selective Rake)
Diff b/w S-Rake and P-Rake
S-Rake is sort of best fit and P-Rake is sort of first
fit.
Tradeoff between BER (SER) and Time
Complexity (hence data rate) at the receiver.
MRC Rake
• In MRC, as name suggests, the rakes are chosen
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in which the signal-to-noise ratio is maximized.
In a typical MRC S-Rake with ‘N’ fingers, the
received signal is passed through a pulse-shaping
filter. This is sampled at symbol, chip or sub-chip
rate
The delays, amplitudes and phases of (>N)
multipaths are estimated
MRC Rake
• Then, the fingers having the largest ‘N’
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amplitudes are chosen
The signals of the selected fingers are then
despreaded by correlators
Then they are weighed by their respective
estimated amplitudes and coherently added
Then a decision maker makes the bit decision
Issues with MRC Rake
• If the signals in the rakes are uncorrelated and
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have same noise power then maximum
theoretical performance is achieved
But the signals are usually correlated,
decreasing performance
If the sampling rate is sub-chip rate then
synchronization errors are removed.
However this means higher sampling rates and
thus higher time complexity
Issues with MRC Rake
• Chip and symbol rate based receivers have much
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lower complexity
However, finding the optimum sampling point is
a problem -> timing error (jitter)
MRC Rake Block Diagram
MMSE Rake
• In MMSE, attention is paid to the rake weights
• Particular case of OC Rake
• Basically, the weight vector is improved after
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each iteration
The mean square error between the expected
decision value (for each bit) and the measured
decision value is minimized.
The correlator is assumed to have perfect
knowledge of the channel delays and amplitudes
(by way of training)
MMSE Rake mathematically
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 mathematically
Let v(t) = template at correlator = q(t) [biphase mod.]
Corresponding to the lth finger and tl delay of template,
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
MMSE Rake mathematically
The Mean Square Error is given by :
MSE = E(||dk – Transpose(w)*xk||)2
The optimal vector satisfying MMSE is givn by
wo = argminw(MSE)
The Weiner solution is given by,
wo = A*M-1*h, A being a scaling constant
M is the correlation matrix of noise = E[Transpose(nk)*nk]
And E is Expectation of (Mean)
MMSE Rake mathematically
• Instead of calculating wo iteratively by this
method, the LMS (Least Mean Square) Algorithm is
Utilized
• In this after every iteration,
w(n+1) = w(n) + mu*Err*xk
where mu = small positive const.
Err = Error = (dk – dk’)
xk = Correlation vector
MMSE Rake mathematically
• The convergence and stability of this algorithm
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depends on mu. The lower it is, the slower it
converges but the stability is assured
Also, the algorithm is known to be of lower time
complexity than the previous solution
MMSE Rake Block diagram
Simulation Log
• Gaussian double derivative (with energy = 1)
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was taken as the basic pulse shape
Channel model was the Saleh-Valenzuela
channel model with minimum inter-ray spacing
equal to the symbol time to demonstrate
multipath resolution of UWB reception
Then a pulse train was convoluted with the
channel impulse response and ouput confirmed
to be multipath resolvable
Simulation Log
• Then MMSE Partial-rake was performed (by
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taking arbitrary fingers)
Using the LMS algorithm, the decision was taken
on the correlator outputs
The input size was taken to be 1000 (due to
time constraint) and BER’s analyzed
As the signal strength was increased, the BER
‘overall’ decreased
Also, on increasing the number of fingers the
BER decreased somewhat
Simulation Log
• Then, Selective Rake was taken and simulated
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the same way
It was found to give slightly lesser BER for the
same SNR compared to partial rake
Also, as the number of rakes increased the BER
correspondingly decreased
Simulation Figures
Selective Rake
BER vs SNR
Coding Gain
• Selective Rake has coding gain of 1.25 dB over
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Partial Rake for a BER of 15/1000 in our
modified example
Higher no. of bits could not be taken because of
the amt. of computing time