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=S T *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?