Transcript Slide 1
Overview
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Team Members
What is Low Complexity Signal Detection
Team Goals (Part 1 and Part 2)
Budget
Results
Project Applications
Future Plans
Conclusion
Team Members
• Derek Bonner
– MATLAB Simulations
– Research
• Richard Hansen
– MATLAB Simulations
– Website Design
• Zaki Safar
– MATLAB Simulations
– Research
Low Complexity Signal
Detection
• Look at current CDMA systems
• Evaluate the complexity and performance of
different signal detection methods
• Evaluate different methods of simplifying the
optimal detector
• Determine an acceptable tradeoff of
performance for low complexity
Part 1
• Divided up into three questions
• Question 1 – Proof of square root transmit
power
• Question 2 – Derivation of probability
detection error
• Question 3 – MATLAB implementation
Part 1 Project Goals
• Determine the valid
mathematical model
– Determine Signal to Noise
Ratio equations
• We call the transmitted signal x
{+1,-1}
• We call the power of he signal h
• We call the channel gain w
• We call the noise n and assume
it has a Gaussian distribution
• We call the received signal y
=> y = h*w*x + n
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Power = V^2/R
The signal can be seen as a
voltage
Assume the resistance is 1
P = (h*x)^2/1;
P = (h*w*x)^2/1;
P = (h*w)^2;
The same process can be applied
to the noise resulting in:
• SNR = (h*w)^2/sigma^2
Part 1 Project Goals
• Determine the
probability of
receiving a wrong
bit
– We can show that
the noise
distribution is
centered at h*w*x
(mean = h*w*x)
– There for we say
the probability of
error is P(X <= 0)
Part 1 Project Goals
• Simulate results in
MatLab
– Plot of SNR vs.
Probability of error
Part 2
• MATLAB implementation of three
multiuser detectors
– Matched filter
– Decorrelation
– Mean Linear
• Flop counts
Addition of Multiple Users
• K users
• Signature matrix
– Signature length
• N=15
• K=8
• R=ST*S
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– Ideally Identity Matrix
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Part 2 Project Goals
• Expansion of our mathematical
model to the Multi-User case
– We see that we can represent
the power, the channel
attenuation, the transmitted
bit, and the noise for each
user as a vector.
– We define a new parameter S
as the signature sequence of
the user (S is a vector N bits
long)
– The signal to noise ratio can
be shown to be SNR =
N*(h*w)^2/sigma^2
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z = S*h*w*x + v;
y = S.'*z;
y = R*h*w*x + n;
where R = S.'*S;
P = (R*h*w*x)^2
P = (N*h*w)^2
Same Process can be applied
to the noise
• SNR = (N*h*w)^2/sigma^2N
• SNR = N*(h*w)^2/sigma^2
Part 2 Project Goals
• Simulate and compare
different detection
processes
– Matched Filter Detection
X’ = sgn(y);
– Decorrelation Detection
X’ = sgn(R-1*y);
– Maximum Likelihood
Detection
X’ = min (y – R*h*w*x).’*R-1*(y - R*h*w*x);
Budget
• No donations made
• Possible expense – MATLAB, Microsoft
Project
• No expenditures
Project Applications
• Examine detectors that can have more
than 8 users
• Tradeoff between detector systems and
smart antennas
• Shows need for multiuser detection
algorithms
Future Design Plans
• Performance analysis of detectors (Part 2 & 3)
• Develop several low complexity sub optimal detectors
including the decision feedback detector (Part 3)
• Compare performance with the optimal detector (Part 4)
• Explore various techniques of making the optimal
detector less complex (Part 4)
• Determine algorithms to determine tradeoffs between
complexity and performance (Part 4)
Questions?