Overview

• 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

• 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– Ideally Identity Matrix

-1 1 1 -1 1 -1 -1 1-1 1 -1 -1 1 -1 -1 11 1 -1 1 -1 -1 -1 -11 1 1 1 -1 -1 -1 -11 -1 -1 -1 -1 -1 -1 1-1 -1 -1 -1 -1 1 1 11 -1 1 1 1 -1 -1 -1-1 1 1 1 -1 1 1 -1-1 1 1 -1 -1 1 -1 11 -1 -1 -1 -1 -1 -1 -11 1 -1 -1 -1 -1 -1 11 1 1 1 -1 1 -1 -11 -1 -1 -1 1 -1 1 -1-1 1 -1 -1 -1 1 1 -1-1 1 1 -1 -1 1 1 -1

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

• 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 DetectionX’ = 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?