1. SVD methods for CDMA 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. 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

4. 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.

5. 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.

6. 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

7. 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

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

11. More users entering
Users exiting

13. 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

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

16. 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