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Detecting Active Channels in a DS-CDMA Multi-user Receiver

Detecting Active Channels in a DS-CDMA Multi-user Receiver. Rob Taylor. Outline. Motivation Problem Definition Composite Hypothesis Testing New Channel Detection framework Expectation-Maximization Results. Motivation. MUD RECEIVER CONTEXT. Pilot Search. Active Channel Detect.

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Detecting Active Channels in a DS-CDMA Multi-user Receiver

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  1. Detecting Active Channels in a DS-CDMA Multi-user Receiver Rob Taylor

  2. Outline • Motivation • Problem Definition • Composite Hypothesis Testing • New Channel Detection framework • Expectation-Maximization • Results

  3. Motivation MUD RECEIVER CONTEXT Pilot Search Active Channel Detect Active channels Pre- Processing Signals + Noise Despread - Carrier offset - Baseband filter MUD Receiver • The active channel detection algorithm identifies which channels within a carrier are active. • Over/under estimating active channels will cause very poor MUD results. • Active channel detection algorithm can be made to estimate interference in a similar fashion to MUD algorithms.

  4. Problem Definition • From received baseband signal sampled at chip rate for M symbols, determine active channelindex set , bits in those channels, and channel amplitude knowing only the filtered spreading sequences, channel phase, and channel timing delay: amplitude number of carriers spread gain AWGN received signal time index Spreading sequence channel index floor operator where now the “bits” are expanded to be to allow for inactive channels. More compactly, we estimate .

  5. Composite Hypothesis Testing Problem • Since active channel detection is a two-sided parameter test: no uniformly most powerful (UMP) test exists. • Wald test, Rao test, and generalized likelihood ratio test (GLRT) give equivalent results since the system model is linear. • Bayesian detection methods require high dimensional integration. • GLRT is chosen method for computational simplicity and accuracy. CFAR threshold Matched Filter Output • The CFAR detector will use to compute • Asymptotically, GLRT is UMP among all invariant tests (Lehmann).

  6. Gaussian Noise ~ CN(0, ) Conventional Detection vs. Interference-Rejection Detection • Conventional active channel detector uses this assumption: • Active channel detection with interference estimation assumes: Gaussian Noise ~ CN(0, ) If we can estimate the interference (even partially) we can subtract it out to lower the overall interference-plus-noise power!

  7. Computing the Maximum Likelihood Estimate • The maximum likelihood estimate (MLE) for the data vector we are trying to estimate is written as: • is the optimalestimator but is NP-complete for discrete vectors. • Combinatorial optimization methods exist (Tabu search and Semi-definite Programming relaxation) but inefficient for dimensions above 100. • Expectation-Maximization (EM) framework provides an efficient iterative numerical approach to approximate the MLE by decomposing a K-dimensional optimization into K 1-D optimization problems. • EM convergence proofs exist only for continuous parameter vectors, but the EM will converge in some cases for discrete.

  8. EM approximation to the ML Detector • Instead of trying to maximize the received signal likelihood function we will recast problem into EM framework by identifying the observation equation as incomplete data and formulating a suitable complete data representation (see Feder and Weinstein). complete data incomplete data Expectation (E) Expectation-Maximization Maximization (M)

  9. false alarm rate Active Channel Detection Diagram Received signal Matched filter bank Estimate inactive channels Compute MLE for d Estimate interference plus noise power Estimate interference Compute threshold Compute Test Stastistic Declare detection

  10. Interference-Rejection GLRT • We test the performance of the Interference-Rejection GLRT with 10 carriers under near-far scenarios where the power difference between strongest and weakest user is ~15-20dB. • Here we can watch the interference being reduced within the test statistic as the EM algorithm sequentially estimates and subtracts the interference.

  11. Pd versus Capacity Setup • 8 active channels per carrier (not including pilot channel) running from 1 to 12 carriers • unequal channel powers with 13dB difference between strongest and weakest users • pre-despread SNR of weakest signal -8dB • pre-despread SNR of strongest signal +14dB • asynchronous channels • IS-95 baseband filtered spreading codes • false alarm rate=.01 Results • Near perfect bit estimation and active channel detection for up to 48 active channels across 6 carriers. • With just 5 symbols the new detector can get better performance than conventional detector using 128 symbols in low loading scenarios. Number of active users Spreading Gain

  12. Bibliography • U. Fawar and B. Aazhang, “A Multiuser Receiver for Code Division Multiple Access Communications over Multipath Channels,” IEEE Transactions on Communications, vol. 43, No. 2/3/4, Feb/Mar/April 1995. • M. Feder and E. Weinstein, “Parameter estimation of superimposed signals using the EM algorithm,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 36, pp.477-489, April 1988. • J. Fessler and A. Hero, “Space-Alternating Generalized Expectation-Maximization Algorithm,” IEEE Transactions on Signal Processing, vol. 42, No. 10, Oct. 1994. • L. Nelson and H. V. Poor, “Iterative Multiuser Receivers for CDMA Channels: An EM-Based Approach,” IEEE Transactions on Communications, Vol. 44, No. 12, Dec. 1996. • S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, 1993. • S. M. Kay, Fundamentals of Statistical Signal Processing: Detection Theory. Prentice-Hall, 1998. • E. L. Lehmann, Testing Statistical Hypotheses, J. Wiley, New York, 1959.

  13. Backup Slides

  14. Notation Definition • Rewriting the received signal model in matrix-vector form: • Normalized matched filter output: MAI

  15. Conventional GLRT • The GLRT without interference estimation has the form: where we now insert the MLE to obtain: • This leads to the following test statistic where we have moved all non-data terms over to the right hand side:

  16. Interference-Rejection GLRT • The GLRT without interference estimation has the form: where we now insert the MLE to obtain: • This leads to the following test statistic where we have moved all non-data terms over to the right hand side: where the interference for channel k and symbol m is defined as:

  17. Estimator resulting from EM (1 of 2) Incomplete Data CompleteData Relationship between observation and complete data complete data incomplete data E-step

  18. Estimator resulting from EM (2 of 2) M-step Recursive EM estimator

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