SVD methods for CDMA communications

Outline The CDMA multiuser detection problem Popular detection structures Adaptive realizations using stochastic gradient algorithms Stochastic gradient with subspace tracking (SVD) Conclusion

The CDMA multiuser detection problem A user is identified through a signature signal (code) S=[s1 s2... sN]t , si=1 Base Station To send a “1”, the user, or the base station, transmits the signature S, whereas to send a “0” they transmit - S. Several users communicate at the same time with the base station (uplink) The base station communicates with all users at the same time (downlink) CDMA: Code division multiple access

Downlink + noise r(n) Base Station s11 s12 …s1N b1(1) ... b1(2) b1(n) + a1 a2 aK ... s21 s22 …s2N b2(1) b2(2) b2(n) sK1sK2 …sKN bK(1) bK(2) bK(n) Each user knows only HIS SIGNATURE and from the received data r(n) needs to isolate HIS INFORMATION SEQUENCE.

Uplink s11 s12 …s1N b1(1) ... b1(2) b1(n) a1 s11 s12 …s1N b2(1) ... b2(2) b2(n) a2 r(n) + ... aK noise s11 s12 …s1N bK(1) ... bK(2) bK(n) The base station knows ALL SIGNATURES and from the received data r(n) needs to isolate ALL INFORMATION SEQUENCES.

Downlink data model + a1 a2 aK ... s11 s12 …s1N b2(1) b2(2) b2(n) bK(1) bK(2) bK(n) noise R(n) b1(1) b1(2) b1(n) + a1 aK ... noise R(n) b1(n) bK(n) S1 SK We receive sequentially R(n). Using R(n), assuming knowledge of S1 we need to decide whether: b1(n)=+1 or –1. Detection

Popular detection structures Optimum (minimizes the probability to make a wrong decision). Computationally expensive Requires knowledge of all signatures, user and noise powers. Linear detectors Matched Filter Detector Near-Far Problem

Minimum Mean Square Error Detector Bad Conditioning No Near-Far Problem Requires knowledge of all signatures, and signal and noise powers.

Adaptive realizations We adaptively estimate Co using stochastic gradient type algorithms. Assume at time n available an estimate C(n-1) and when the new data set R(n) arrives, we compute the estimate C(n) as follows

More users entering Users exiting

Subspace tracking In order to avoid all undesirable phenomena we only need a basis B for the subspace spanned by the signatures S1, S2,…, SK. Since an ideal B can be obtained by applying SVD on an estimate of B can be obtained by applying SVD on

We need algorithms for Tracking singular vectors for rank-1 modifications Reliable estimates of the low rank order K (number of users)

Conclusion We have presented the CDMA multiuser detection problem and the existing popular detection structures Adaptive realization based on simple stochastic gradient type algorithms we seen to have problems in performance Performance was improved significantly with the help of subspace tracking techniques