Low Complexity Signal Detection Study: MATLAB Simulations and Research

2. Overview • Team Members • What is Low Complexity Signal Detection • Team Goals (Part 1 and Part 2) • Budget • Results • Project Applications • Future Plans • Conclusion

3. Team Members • Derek Bonner • MATLAB Simulations • Research • Richard Hansen • MATLAB Simulations • Website Design • Zaki Safar • MATLAB Simulations • Research

4. 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

5. 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

6. 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

7. 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)

8. Part 1 Project Goals • Simulate results in MatLab • Plot of SNR vs. Probability of error

9. Part 2 • MATLAB implementation of three multiuser detectors • Matched filter • Decorrelation • Mean Linear • Flop counts

10. Addition of Multiple Users • K users • Signature matrix • Signature length • N=15 • K=8 • R=ST*S • Ideally Identity Matrix

11. 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

12. 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);

15. Budget • No donations made • Possible expense – MATLAB, Microsoft Project • No expenditures

16. Project Applications • Examine detectors that can have more than 8 users • Tradeoff between detector systems and smart antennas • Shows need for multiuser detection algorithms

17. 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)

18. Questions?