Linear Multiuser Receivers: Effective Interference, Effective Bandwidth and User Capacity

1. Linear Multiuser Receivers: Effective Interference, Effective Bandwidth and User Capacity Paper from David N.C.Tse and Stephen V.Hanly Presented by Di Geng

2. Outline Introduction Performance Under Random Spreading Sequence User Capacity Under Power Control Multiple Classes and Effective Bandwidths Antenna Diversity Conclusions

3. Introduction Three Important linear Multiuser Receivers: Conventional matched filter, decorrelator, Minimum mean-square error(MMSE) receiver Basic spread-spectrum model Conventional CDMA is indeed the optimal approach when interference from other users is white. However, in general the multi-access interference is not white.

4. Introduction Structure of MMSE Receiver Total interference for user1 from other users and background noise: Then If Z were white, then

5. Introduction We need whiten the interference Z, and the covariance matrix of Z is where is a N-by K-1 matrix whose columns are the signature sequences of other users, and is the covariance matrix of . Is positive definite. Factorize , where is the diagonal matrix(nonnegative) eigenvalues of , and the columns of Q are the orthonormal eigenvectors of , the whitening filter is simply , applying to Y, we get

6. Introduction Thus the MMSE demodulator is and the signal-to-interference ratio for user1 is The equation above is a formula for the performance of the MMSE receiver. However, the effect of an individual interferer on the SIR for user1 cannot be seen directly from this formula.

7. Performance Under Random Spreading Sequences For a large system, as K and N approach infinite (while the ratio of K to N fixed), the SIR is deterministic and approximately satisfies Where SIR of conventional matched filter receiver for user1 under the same condition is

8. Performance Under Random Spreading Sequences SIR for the decorrelator when N approaches infinite is

9. User Capacity Under Power Control First we consider the case in which all users require same target SIR . The received power required, asymptotically as N goes to infinite, for matched filter is given by For a given constraint P on the received power, the maximum number of user supportable is then users per degree freedom The user capacity of matched filter when P approach infinite is then users/degree freedom

10. User Capacity Under Power Control For MMSE receiver, there is an optimal solution for which the received power of every user is minimized iif the SIR can be met with equal received powers for all users. The user capacity of the system under MMSE receiver with a given received power constraint P is users/degree of freedom If without received power constraint, user capacity is users/degree of freedom

11. User Capacity Under Power Control If is feasible for both types of receiver, then MMSE has less power consumption than matched filter, and also has potentially much greater user capacity. For decorrelator,with a given received power constraint , maximum number of users with SIR requirement is

12. Multiple Classes and Effective Bandwidth Suppose we have J classes with j numbers requiring a SIR of as , matched filter results generalizes to If class j has a maximum power constraint , then we have From inequity above, we denote bandwidth by

13. Multiple Classes and Effective Bandwidth Effective bandwidth for three Multiuser Receivers MMSE filter Decorrelator Matched filter

14. Multiple Classes and Effective Bandwidth User capacity region for two classes of users

15. Antenna Diversity The user capacity of antenna-array systems can also be characterized by effective bandwidth. Model for synchronous multi-access antenna-array system The optimal receiver is MMSE when a system has a large number of antenna elements and large number of users.

16. Conclusions Theeffective interference under MMSE is nonlinear, depending on received power of the user and target SIR. The effective interference for Matched filter is the received power of interferer. For demodulator, the effective interference is , independent of actual power of interferer. The effective bandwidth under matched filter, MMSE, and decorrelator are , , and , respectively. The matched filter is more efficient when SIR is small, but far less efficient when SIR is large. The optimal receiver MMSE, operates more like MF when SIR is small, much as decorrelator when SIR is large.

17. Thank you!