COMMUNICATION THEORY
![]()
2.1 MULTIUSER DETECTION
Currently, there is an explosion of research activity in
the field of signal processing for wireless communication,
and in particular in the field of multiuser detection.
Multiuser detection studies the demodulation of one or more
digital signals in the presence of multiuser interference.
This technique is applicable to multiaccess techniques such
as asynchronous CDMA (where interuser interference occurs by
design) and TDMA (where interuser interference occurs due to
nonideal effects such as channel distortion and out-of-cell interference).
At the time of my Ph.D. thesis
S. Verdú, ``Optimum Multi-User Signal Detection,''
S. Verdú, ``Optimum Sequence Detection of Asynchronous Multiple-Access Communications,''
S. Verdú, ``Minimum Probability of Error for Asynchronous Gaussian Multiple Access Channels,''
S. Verdú, ``Optimum Multiuser Asymptotic Efficiency,''
S. Verdú, ``Computational Complexity of Optimum Multiuser Detection,''
S. Verdú, ``Multiple Access Channels with Point-Process Observations:
Optimum Demodulation,''
H. V. Poor, S. Verdú, ``Single-user Detectors for Multiuser Channels,''
S. Verdú, "Near-Far Resistant Receivers for DS/SSMA Communications,"
R. Lupas, S. Verdú, ``Linear Multiuser Detectors for Synchronous Code Division Multiple Access Channels,''
R. Lupas, S. Verdú, ``Near-Far Resistance of Multiuser Detectors in Asynchronous Channels,''
S. Verdú, ``Recent Progress in Multiuser Detection,''
Advances in Communications and Signal Processing,
S. Verdú, ``Multiuser Detection,''
N. Mandayam and S. Verdú,
``Analysis of an Approximate Decorrelating Detector,''
S. Verdú, ``Adaptive Multiuser Detection,''
Chapter in
Code Division Multiple Access Communications,
M. Honig, U. Madhow and S. Verdú,
``Blind Adaptive Multiuser Detection,''
H. Huang and S. Verdú,
``Linear Differentially Coherent Multiuser Detection for Multipath Channels,''
to appear in
S. Verdú, ``Demodulation in the presence of multiuser interference: progress and misconceptions,''
the conventional wisdom was that it was best to simply neglect
the presence of multiaccess interference since its statistical
properties would be similar to additive
white Gaussian noise, and therefore a single-user matched filter
should be near-optimal to combat such interference.
This conventional wisdom was proven wrong by the derivation and analysis
of the optimal multiuser detector, whose earliest reference is:
Ph.D. Thesis, Dept.
of Electrical and Computer Engineering, University of Illinois,
Aug. 1984.
Also Tech. Rep. no. T-151, Coordinated Science Laboratory, Urbana, IL.
Abstract in
IEEE Trans. Information Theory,
vol. IT-31, no. 4, p. 557, July 1985.
Available through UMI
Reference Number 8502332
A full analysis and derivation can be found in
Abs. 1983 IEEE Int. Symp. Information Theory,
St. Jovite, Canada, p. 80, Sep. 1983.
This paper showed that there is, in general, a huge gap in performance
between the performance of the conventional single-user matched filter and
the optimal attainable performance. Furthermore, the infamous near-far
problem was shown to be not an inherent flaw of CDMA but a consequence
of the inability of the single-user matched filter to exploit the
structure of the multiuser interference.
The Jan. 1996 paper introduced a new analysis technique for
the bit error rate of systems subject to interference: the approach of
indecomposable sequences. It was later used succesfully in the analysis
of single-user intersymbol interference problems (see 2.2.1).
The performance measure of asymptotic multiuser efficiency, now widely
used in the analysis of multiuser detectors was also introduced in the Jan.
1996 paper, and further studied in
IEEE Trans. Information Theory,
vol. IT-32, no. 1, p. 85-96, Jan. 1986.
The optimum K-user detector in the Jan. 1996 paper consists of a bank of matched filters followed by a dynamic programming algorithm of the forward
(Viterbi) type (for maximum-likelihood detection) or of the
backward-forward type (for minimum bit-error-rate detection) (see 4.1).
The time-complexity of this algorithm is exponential in K. This means
that with the computational power of a Pentium chip one can demodulate
9 simultaneous users transmitting at 8 kbps, but if the number of users is,
say, twice that many, optimum multiuser detection is computationally intractable.
The reason for this intractability,
as proved in my thesis and published in
IEEE Trans. Communications,
vol. COM-34, no. 9, p. 890-897, Sep. 1986.
is that the optimum multiuser detection problem
(whether in the synchronous or asynchronous versions) is NP-complete, and thus it
admits a polynomial solution if and only if
a polynomial solution can be found for famous combinatorial optimization
problems such as the traveling salesman problem which are widely believed not to
be solvable in polynomial time.
My doctoral thesis also considered the analogous optimal demodulation problem for optical
communication channels, a work that was published in (see 2.3.2)
Algorithmica,
vol. 4, no. 3, p. 303-312, 1989,
NonGaussian detection problems leading to nonlinear single-user detectors
arise when the multiaccess interference is modeled with random phases and
possibly random signature sequences. Solutions are given for various asymptotic
situations (such as weak interferers, high spreading gain and high SNR) in
IEEE Trans. Information Theory,
vol. IT-32, no. 5, p. 642-651, Sep. 1986.
The large gaps in performance and complexity between optimum multiuser detection
and conventional single-user detection have spurred much work on suboptimal solutions.
The first such detector I considered was the decorrelating detector:
IEEE Trans. Communications,
vol. COM-36, no. 1, p. 50-60, Jan. 1988.
showed that this detector achieves the same near-far resistance as the
optimum detector for synchronous channels. This result plus the justification
of the decorrelating detector
as the maximum likelihood solution when the received amplitudes are unknown
were published in
U. S. Army
Research Proposal Contract DAAL03-87-K-0062, Princeton University, 1986.
That paper also considered linear multiuser detectors that
exploit knowledge of the received amplitudes to maximize
asymptotic efficiency.
The fact that linear detectors such as the decorrelator and the MMSE detector
achieve optimum near-far resistance is a central result in multiuser detection,
which does not find a counterpart in single-user digital communication.
A saddle-point justification
for the decorrelating detector was obtained in
IEEE Trans. Information Theory,
vol. IT-35, no. 1, p. 123-136, Jan. 1989.
which gives the asynchronous version of the decorrelator
as a doubly infinite impulse response filter. The one-shot decorrelating detector is due to
IEEE Trans. Communications,
vol. COM-38, no. 4, pp. 496-508, Apr. 1990.
An approximate decorrelator detector, which requires no
algebraic operations with the crosscorrelations and is particularly
simple to implement (even in systems where the signature sequence spans an arbitrary
number of symbol periods) is proposed in the tutorial
W. Porter and S. Kak, Eds.,
Lecture Notes in Control and Information Sciences,
vol. 129, p. 27-38, Springer-Verlag, Heidelberg, 1989.
Reprinted in ``Multiple Access Communications'', N. Abramson, Ed.,
IEEE Press, 1993, p. 164-175.
Such an approximation is justified by the
analysis in
Advances in Statistical Signal Processing, vol. 2: Signal Detection
pp. 369-409, JAI Press: Greenwich, CT , 1993.
A review of adaptive linear methods for multiuser detection is given in
to appear in
Wireless Personal Communications,
Special Issue on ``Interference in Mobile Wireless Systems.''
An important conceptual development in adaptive multiuser detection has been
the proof that the MMSE detector is equivalent to an orthogonally anchored detector
(linear transformation equal to the nonadaptive signature waveform of the desired user
plus an orthogonal adaptive component) chosen to minimize the output energy:
S. G. Glisic and P. A. Leppanen, Eds., pp. 97-116, Kluwer Academic, 1995.
This paper shows how to perform optimally near-far resistant multiuser demodulation
without knowledge of the signature waveforms, data sequences, timing and amplitudes of the interferers.
The principle in the July 1995 paper
is extended to the case where the desired signature waveform
is not completely known (because of multipath) in
IEEE Trans. on Information Theory,
vol. 41, no. 4, pp. 944-960, July 1995.
A retrospective of the state-of-the-art in multiuser detection with a critical
examination of some of the misconceptions that have arisen in its development
is given in:
Wireless Personal Communications,
Special Issue on ``Interference in Mobile Wireless Systems.''
Chapter in
Intelligent Methods in Signal Processing and Communications,
D. Docampo, A. Figueiras-Vidal, F. Perez-Gonzalez, Eds.,
pp. 15-44, Birkhauser, Boston: 1997.
This page maintained by Michelle
Young - Last modified 12/17/96