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SVD methods for CDMA communications

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. Base Station. The CDMA multiuser detection problem.

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SVD methods for CDMA communications

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  1. SVD methodsforCDMA communications

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

  3. Base Station The CDMA multiuser detection problem A user is identified through a signature signal (code) S=[s1 s2... sN]t , si=1 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

  4. bK(1) b1(1) b2(1) bK(2) b1(2) b2(2) bK(n) b1(n) b2(n) ... ... ... r(n) + s11s12 …s1N sK1sK2 …sKN s21s22 …s2N s21s22 …s2N s11s12 …s1N sK1sK2 …sKN s11s12 …s1N sK1sK2 …sKN s21s22 …s2N a1 noise a2 + + aK noise + ... ... ... noise Downlink Base Station Each user knows only HIS SIGNATURE and from the received datar(n)needs to isolate HIS INFORMATION SEQUENCE.

  5. bK(1) b2(1) b1(1) b1(2) b2(2) bK(2) b2(n) bK(n) b1(n) ... ... ... s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N ... ... ... Uplink a1 r(n) a2 + noise aK The base station knows ALL SIGNATURES and from the received datar(n) needs to isolate ALL INFORMATION SEQUENCES.

  6. b2(1) b1(1) bK(1) bK(2) b2(2) b1(2) bK(n) b2(n) b1(n) ... ... ... s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N s11s12 …s1N a1 a2 R(n) ... + aK b1(n) noise S1 a1 ... ... ... ... + R(n) bK(n) aK noise SK Downlink data model We receive sequentially R(n).Using R(n), assuming knowledge of S1we need to decide whether: b1(n)=+1or –1. Detection

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

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

  9. 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

  10. More users entering Users exiting

  11. Since an ideal B can be obtained by applying SVDon an estimate of B can be obtained by applying SVDon 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.

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

  13. 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

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