Authors: David N.C. Tse, Ofer Zeitouni. Presented By Sai C. Chadalapaka.

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

 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.

 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.

 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’.

 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.

 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.

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

 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:

MMSE receiver simulation

 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.

 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 i th 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:

MMSE receiver in a lognormal fading environment

 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.

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