Linear Multiuser Receivers in Random Environments

1. Authors: David N.C. Tse, OferZeitouni. Presented By Sai C. Chadalapaka. Linear Multiuser Receivers in Random Environments

2. Introduction Introduce receiver models Analyze the performance of Decorrelator and MMSE receiver. Antenna diversity Results Summary Outline

3. Signal to Interference Ratio is the common performance measure. • SIR performance of a linear- multiuser receiver is studied in random environments, where signals from different users arrive in “random directions”. • This occur in two cases • DS-CDMA system with random signature sequence. • System with antenna diversity where randomness is due to channel fading. • The SIR is function of spreading sequence. • Prominent linear multiuser receivers: • Decorrelator • MMSE receiver • We study the random performance of both the decorrelator and MMSE receiver. Introduction

4. In a CDMA the data is coded and transmitted using a spreading sequence. This provides additional degree of freedom or BW. • To fully utilize this, it is necessary to suppress the interference from other users at receiver. • Performance of these receivers depends on the pseudo random spreading sequence. • We assume that this random spreading sequence is known at the receivers. • In practical they are found by using methods like: • Channel measurement. • Adaptation techniques. Introduction

5. In a DS-CDMA each of users information is spread onto a much longer random spreading sequence. • y: is the received signal • b: Transmitted symbol • s: Spreading sequence • z: Random noise • The length of the signature sequence is N. It indicates the degree of freedom. • For an MMSE receiver, the SIR is • We can observe that the SIR depends on the interference power ‘T’. Design model receiver

6. For a Decorrelator, The SIR is given by: We can observe that the SIR doesn’t depend on the interference power. • This is because the decorrelator cancels the interference power at the expense of its own power. • It is observed that in a random environment the SIR of both the receivers converges to a deterministic limit. This is when we assume that the N→∞ and also number of users are assumed to be very high. • In practice since both conditions are not true, the SIR fluctuates about this limit. • Those fluctuations determine the performance measures such as probability of error and outage probability. Design model receivers

7. Calculation is simple, because it does not depend on interference power. The deterministic limit of Decorrelator is given by: The loss in SIR due to interference from other users is proportional to the number of interferers per degree of freedom. We need to find the fluctuations around this limit for a finite system to calculate performance. Then the theoretical SIR of finite system is given by: We can observe the SIR also depends on the length of the sequence N and also on the distribution of the symbols. Performance of Decorrelator

8. Simulation results of 1% outage SIR for Decorrelator (The 1% outage level is the value x, such that P(SIR<x )=0.01

9. MMSE maximizes the SIR compared to Decorrelator. We assume that the users have equal transmitted power which is P. We calculate the deterministic limit to be: We can observe that the signal power here is higher than the Decorrelator. This is because decorrelator removes the interference power at the expense of signal power. For a finite practical system the SIR is given by: Performance of MMSE receiver

10. MMSE receiver simulation

11. We compared the theoretical results with actual values to check the accuracy. Simulation results are obtained by averaging 10,000 independently generated samples. Users are received at equal power P. SIR is set at 20db. In the graph we plot the limiting SIR, mean SIR along with the simulation results. The graphs are plotted as a function of the system load for different sizes. Simulation

12. Linear multiuser receivers also operate in a system with multiple antennas. • Multiple antennas provide spatial diversity. • These antennas can be placed in an array near the base station or different geographical locations. • This diversity can be used to reduce multipath fading and large scale fading. Where h- fading of the ith user. • This is similar to DS-CDMA case. The spreading sequence is replaced by the multipath fading factor in the above function. • The SIR of the Decorrelator is given by: Antenna Diversity

13. MMSE receiver in a lognormal fading environment

14. For both the receivers we considered, the variance of the SIR decreases like 1/N, as the SIR distribution is Gaussian. We computed closed form solutions and observed that the relative fluctuation is large when there are many users per degree of freedom and hence SIR is low. Simulation results also show that asymptotic mean and variance are very accurate for even a moderate sized system. One remedy to offset the fluctuations is through power control. It is complicated because the user varies his power depending on his SIR requirements. So it is difficult to characterize the distribution of signal power to maintain desired SIR level. In this paper it is assumed that the performance of user is insensitive to the power variations of other users. Summary

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