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MUD: Multi-user detection. Jetmir Palushi Stevens Institute of Technology EE613 DSP for Communications. Overview. MUD in CDMA systems MUD Features Modulation and Implementation Concept Multiple Access Interference (MAI) MUD algorithms Linear Non-Linear Optimal MLSE MUD Detectors

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MUD: Multi-user detection

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Mud multi user detection l.jpg

MUD: Multi-user detection

Jetmir Palushi

Stevens Institute of Technology

EE613 DSP for Communications

Overview l.jpg


  • MUD in CDMA systems

  • MUD Features

  • Modulation and Implementation Concept

  • Multiple Access Interference (MAI)

  • MUD algorithms

    • Linear

    • Non-Linear

    • Optimal MLSE

  • MUD Detectors

    • Decorrelating

    • Minimum Mean Squared Error (MMSE)

    • Blind Adaptive MMSE

    • Multistage

    • Decision Feedback

    • Successive Interference Cancellation

  • Detector Performance

  • Limitations of MUD

  • Conclusion

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MUD in CDMA systems

  • The primary idea of Multi User Detection (MUD) techniques is to cancel the interference caused by other users. This is done by exploiting the available side information of the interfering users, rather than ignoring the presence of other users like in Single User Detection (SUD) techniques.

  • The idea of MUD was proposed by Sergio Verd´u in the early 1980’s.

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MUD in CDMA Systems

  • Multi-User Detection considers all users as signals for each other leading to joint detection

    • - Reduced interference leads to capacity increase

    • - It alleviates the near and far problems

  • System capacity is limited by interference threshold that a detector uses to make its decision

  • Multiple Access Interference increases with the number of users

  • MUD suppresses the MUI increasing the system capacity

  • Can be implemented at either base station, mobile or both

    - Size and weight requirements are not stringent for base station

    - Therefore it is currently being implemented for mobile to base station.

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MUD Features

  • Quasi-synchronous transmissions is easier than other methods

  • It has the capability to reject the interference created by the narrow band

  • Capable to achieve diversity in frequency

  • It tremendously reduces the complexity and it increases the spectral efficiency

  • Robustness to multipath fading

  • The use of modern DSP makes MC-CDMA implementation feasible and attractive

  • MC-CDMA translates the time operations to the frequency domain

  • Effect of ISI and delay spread is mitigated

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Modulation and Implementation



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Modulation and Implementation

  • Using Binary Phase Shift Keying (BPSK) technique we have:

    • The Signal for the kth user given by the formula:

    • Where

      • The i-th input symbol of the from the k-th user is x(i)

      • c(i) is the gain of channel

      • s(t) is the waveform that contains the PN sequence

      • k is the transmission delay; for synchronous CDMA, k=0 for all users

    • And the received signal is given by the formula:

    • Where

      • K is the number of users on the network at a given time t

      • z(t) is the complex White Gaussian Noise

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Modulation and Implementation

  • The Sampled output of the matched filter of kth user is given by the formula:

    • The 1st term means the desired information to be recovered

    • The 2nd term is the Multi-Access Interference (MAI)

    • And the 3rd term is the complex White Gaussian Noise

  • If we assume a two-user channel we have

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Modulation and Implementation

  • From the general equation given on the slide above we solve for user1 and user2 received signals which are y1 and y2 respectively:

  • This results on the detected symbol of k-th user:

  • Suppose the signal of user 1 is stronger than the signal of user 2 then we have the near/far problem, the MAI term rc1x1 present in the signal of user 2 is very large

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Multiple Access Interference (MAI)

  • Imperfect cross-correlation characteristics of the spreading codes

  • Multi-path fading contributes to MAI

  • Causes severe degradation in the performance of the system

  • Capacity is interference limited

  • MAI is a function of:

    • Number of Users

    • Cross-Correlation between users

    • Amplitude of Interfering Signals

  • MAI is due to the non-orthogonality between users

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MUD Algorithms

  • Linear detectors apply linear transformations to matched filter outputs to minimize MAI. Simple to implement but can get complex.

  • Non-Linear detectors are more complex calculation wise than linear detectors due to nonlinearity, however they perform better under severe conditions

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Optimal MLSE detector

  • The Maximum-likelihood sequence estimation (MLSE) is too complex to be implemented

  • For synchronous CDMA, it searches over 2K possible combinations of the bits in vector x. Where x is given by:

  • R and W matrices are described under Decorrelating detector section and y is the received signal

  • For asynchronous CDMA it uses Viterbi algorithm with 2K-1 states which is very complicated to be implemented in practice as well

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Linear Algorithms

  • Linear mapping algorithms are applied to the outputs of the matched filters

  • Less complexity than optimal ML receiver

  • Practical Linear Algorithms:

    - Decorrelating Detector

    - Minimum-mean squared error (MMSE)

    - Blind (adaptive non-adaptive) techniques

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Matrix Filter




Decorrelating Detector

Matrix Representation:

The matrix R is of the form:

  • where y=[y1,y2,…,yK]T, R and W are KxK matrices

  • Components of R are given by cross-correlations between signature waveforms sk(t)

  • W is diagonal with component Wk,k given by the channel gain ck of the kth user

  • z is a colored Gaussian noise vector

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Decorrelating Detector

  • We can solve for x by inverting matrix R

  • The matrix representation method is analogous to zero-forcing (ZF) equalizers for ISI channels

  • Advantages:

    • Does not require knowledge of users’ powers

  • Disadvantages:

    • Noise enhancement

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Minimum Mean Squared Error (MMSE) Detector

  • Transmitted Signal can be Modeled as:

- The MMSE detector takes the background noise in to account and utilizes the knowledge of the received signal powers

-It minimizes the mean squared error between the actual data and the soft outputs of the conventional detectors

  • Then the receive Signal can be Modeled as:

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Minimum Mean Squared Error (MMSE) Detector

  • The MMSE detector output y_k is therefore:

Advantage: Better error probability performance, and no noise enhancement

Disadvantage: Requires estimation of received amplitudes, and matrix inversion

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Blind Adaptive MMSE Detector

  • Blind adaptive detector characteristics:

    - The detector doesn’t require the training sequence in order to calculate the channel impulse response

    - Requires the knowledge of the signature waveforms and timing information of the desired user

    - The limitation is that it works only for short codes

  • The major disadvantage of the adaptive MMSE detector over the “blind” adaptive MMSE is that it requires the training sequences this results on a waste of the bandwidth which is populated with signals that do not carry any communication data. Therefore for the “Blind” adaptive we have a clear benefit when it is compared to other detectors since it does not require any training sequence that’s why is called “blind”.

  • Adaptive MMSE detectors also are advantageous over other non-adaptive detectors because they can adapt to unknown and time-varying channel conditions

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Non-Linear Algorithms

  • Non-Linear Algorithms:

    Estimate the interference caused by each

    user on the others, re-spread and cancel from

    the received signal. This is done through multitude of stages.

  • Practical Non-Linear Detectors:

    - Multistage Detector

    - Decision Feedback Detector

    - Subtractive Interference cancellation

    Successive Interference Cancellation (SIC)

    Parallel Interference Cancellation (PIC)

    Selective Parallel Interference Cancellation

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Multistage Detector

The concept of the multistage detector is to make a decision in every stage as the name indicates. As shown on the diagram above the received signal is y and the detector produces the decisions x(1) x(2) up to x(n). Where:

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Decision Feedback Detector

  • As shown on the diagram there are 2 matrix transformation:

  • forward filter and feedback filter

  • Pretty much same performance as the Decorrelator detector

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Successive Interference Cancellers

  • The SIC detectors start to subtract off the strongest remaining signals in a successive fashion from the rest of the signals (See diagram to the right)

    • By canceling the strongest signal from the rest we gain most of the benefit and it is the most reliable cancellation

  • The other similar alternative is the PIC method. This starts to simultaneously subtract off all of the users’ signals from all of the others unlike the serial cancellation that starts with the strongest signal user (See diagram under Successive Interference Cancellers – PIC)

    • It works better than SIC when all of the users are received with equal strength since it is much easier to detect them and hence decreases the probability of error

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Successive Interference Cancellers- SIC

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Successive Interference Cancellers- PIC

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Successive Interference Cancellers- PIC

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Successive Interference Cancellers




The main advantages are:

1) The weakest user will see a tremendous signal gain from the MAI reduction since all of the interfering channel will add up as signals to the weakest user. Hence every user is on a win-win situation.

2) For severe conditions if we remove the strongest user the rest of weaker users will benefit hence the signal can be recovered

3) Can recover from near-far effects

The main disadvantages are:

1) If the strongest estimate is not highly reliable it results on performance degradation

2) As the power profile changes the signals must be reordered

3) Every stage introduces a delay

  • More vulnerable to near-far issues

  • Complicated circuitry

1) Because of the parallel nature no delays/stage required!

2) Simpler than other linear detectors

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Detector Performance

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Detector Performance

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Detector Performance

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Limitations of MUD

  • Limitations with implementation

    • Sensitivity and robustness

    • Processing delay

    • Processing complexity

  • Limitations of MUD

    • System capacity improvements are not enormous and not trivial

    • Cost must be kept low in order to increase performance/cost tradeoff

    • Capacity improvements only in the uplink would be partly used in determining the overall system capacity

      • - Need to use MUD in both uplink and downlink

      • - Implementing MUD in mobiles is still a challenge

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  • MUD has many advantages over other communications techniques however they are limited by the complexity of their implementations and a simple implementation is needed. As the DSP field progresses further and more calculations can be performed with ease more of these advantages will be implemented in future work.

  • Current investigations involve implementation and robustness issues

  • MUD research is still in a phase that would not justify to make it a mandatory feature for 3G WCDMA standards

  • Currently other techniques such as smart antenna seem to be more promising

  • Though MUD has not been a mandatory feature of the wireless standards so far, the rapid advances in DSP architectures promise the evolution of MUD as integrated feature of future wireless standards to provide better capacity and data rates

  • Feasible VLSI implementations for Mobiles

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  • R. Lupas, S. Verdu, "Linear multi-user detectors for synchronous code-division multiple-access channels," IEEE Trans. Information Theory, vol. 35, no. 1, pp. 123-136, Jan. 1989.

  • R. Lupas, S. Verdu, "Near-far resistance of multi-user detectors in asynchronous channels," IEEE Trans. Comm. Vol. 38, no. 4, pp. 496-508, April 1990.

  • M. Honig, U. Madhow, S. Verdu, "Blind adaptive multi-user detection," IEEE Trans. Info. Theory, vol. 41, no. 4, pp. 944-960, July 1995.

  • H. V. Poor, S. Verdu, "Probability of error in MMSE multi-user detection," IEEE Trans. Info. Theory, vol. 43, no. 3, pp. 858-871, May 1997.

  • M. Honig, M. K. Tsatsanis, "Adaptive techniques for multi-user CDMA receivers," IEEE Signal Processing Magazine, pp. 49-61, May 2000. [Review]

  • X. Wang, H. V. Poor, "Blind multi-user detection: a subspace approach," IEEE Transactions on Information Theory, vol. 44, no. 2, pp. 677-690, March 1998.


  • X. Wang, H.V. Poor, "Space-time multi-user detection in multi-path CDMA channels," IEEE Transactions on Signal Processing, vol. 47, no. 9, September 1999.

  • H. V. Poor, S. Verdu, "Single-user detectors for multi-user channels," IEEE Trans. Comm. Vol. 36, no. 1, pp. 50-60, Jan. 1988.

  • Duel-Hallen, J. Holtzman, Z. Zvonar, "Multi-user detection for CDMA Systems," IEEE Personal Communications, pp. 46-58, April 1995. [Review]

  • Yi Wang, Zhimin Du, Lu Gao and Weiling Wu, “Performance Analysis of MMSE Multiuser Detection”, Beijing University of Posts and Telecommunications

  • Shimon Moshavi, “Multi-User Detection for DS-CDMA Communications”, Bellcore

  • Deepak Das, “Blind Adaptive Multiuser Detection for Cellular Systems Using Stochastic Approximation With Averaging”, IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 20, NO. 2, FEBRUARY 2002

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