PROJECT SUMMARY
Local Maximum Likelihood Multiuser Detection for CDMA
Communications
A Proposal to NSF CISE/CCR: Communications Research
Yi Sun
Department of Electrical Engineering
The City College of City University of New York
E-mail: sun@ccny.cuny.edu
Third-generation mobile radio networks have been under intense research. Code division multiple access
(CDMA) has emerged as the mainstream air interface solution for the third-generation networks. As the
demand of usable bandwidth is ever increasing, multiuser detection is a necessary means for CDMA
systems to reduce effect of multiple access interference and hence increase system capacity. The global
maximum likelihood (GML) multiuser detector achieves the minimum error probability of joint user
detection as well as optimum near-far resistance. However, the complexity of the GML detector grows
exponentially with the number of users and is infeasible for practical systems. There have been many
suboptimum multiuser detectors each achieving some performance-complexity tradeoff. However, none of
them achieves a local maximum likelihood (LML) solution with an arbitrary neighborhood size. Moreover,
most of the existing suboptimum multiuser detectors are ad hoc developed. They have low ratio of
performance to computational complexity.
In this project, we will develop local maximum likelihood detectors with an arbitrary neighborhood size.
These LML multiuser detectors can provide a broad spectrum of performance-complexity tradeoff. Their
error performance spans from that comparable to the conventional detector, MMSE receiver, MMSE-DF
receiver, superior to MMSE-DF receiver, etc., up to that of the GML detector and their computational
complexity spans from linear, quadratic, etc., up to exponential in the number of users. Furthermore, these
LML multiuser detectors achieve high ratio of performance to computational complexity as demonstrated
in preliminary simulations. Specifically, we will develop a family of linear-complexity likelihood ascent
search (LAS) multiuser detectors in some combinations of the following conditions: wireless multipath
fading channels, on-the-move (Doppler), known and unknown interference users (group blind), broadband
and multirate data, power control, adaptive modulation, turbo coded data, space-time coding, and large
systems in CDMA networks with direct sequence, frequency hopping, and multicarrier modulation.
Another family of local maximum likelihood LAS (LMLAS) multiuser detectors achieving LML
detection with an arbitrary neighborhood size will also be developed in the above various cases. The both
families of LAS and LMLAS detectors with soft intermediate decision will be investigated. We will study
strategies to determine the optimum order of bit update. Performance analysis will include the
characterization of local maximum likelihood points with an arbitrary neighborhood size, the dynamical
stability, monotonic likelihood ascent characterization, expected computational complexity, error
probability, asymptotic multiuser efficiency, near-far resistance, optimum power control, and spectral
efficiency.
The proposed investigation on LML detection will impact basic research in nonlinear signal processing
for multiuser communications, and is expected to benefit directly applications to third and fourthgeneration wireless mobile communications systems. This project will also contribute new knowledge to
theories of the fields of multiuser detection, hypothesis testing, wireless communications, image
processing, and neural networks. This project will help set up a strong program in communications in this
department and provide new research opportunities for both graduate and undergraduate students, and in
particular the minority students. The increased minority students’ research activities in modern
communications will strengthen the traditional diversity environment of this collage.
NSF CISE: Communications, (Y. Sun)
Page A-1
PROJECT DESCRIPTION
C. 1 Objectives
Wideband code division multiple access (CDMA) has emerged as the mainstream air interface solution
for the third-generation networks [1]. As the demand on usable bandwidth is ever increasing, multiuser
detection is a necessary means for CDMA systems to reduce the effect of multiple access interference and
hence increase the system capacity and alleviate the near-far problem.
Consider a K-user bit-synchronous CDMA system with spreading gain M. The received baseband
CDMA signal sampled at the rate higher than or equal to the chip rate can be written in matrix form as
y = SAb + n
(1)
where y  M is a sufficient statistic of b, S  MK is the matrix of signature waveforms which may
include multipath fading effect, A = diag(A1, …, AK) where Ak is the signal amplitude of the kth user, b 
{1, 1}K is the transmitted bit vector, and n ~ N(0, 2I) is a noise vector. When the signature waveforms
are known, the received baseband CDMA signal sampled at the output of a bank of matched filters can be
equivalently written in matrix form as
r = STy = RAb + z
(2)
where r  K is also a sufficient statistic of b, R = STS  KK is the crosscorrelation matrix of signature
waveforms, and z ~ N(0, 2R). The task of multiuser detection is to demodulate b from y or r with or
without knowing S and A. Bit-asynchronous CDMA signal with transmission of a burst data can also be
modeled as (1) and (2).
The multiuser detection problem exists in broad areas of communication systems including wireless
communication, high-speed data transmission, wireless internet, and magnetic recording. Many practical
problems in other areas also can be formulated as to solve (1), including symbol detection for multiplein/multiple-out (MIMO) channels such as OFDM [2], global positioning system [4], and image restoration
[5].
To solve problem (2), it is well-known [6] that when R, A and  are known, the (joint) optimum
demodulation selects the hypothesis maximizing the likelihood function of b or minimizing the metric
(3)
bˆ  arg min K f (r | b) , r  K
b{ 1,1}
where the metric is defined as f(r|b) = ½ bTWb  qTb with W = ARA and q = Ar. The optimum detector
in terms of the global maximum likelihood (GML) achieves the minimum error probability [7]. However,
the GML detector1 needs the comparison of 2K metric values for arbitrary signature waveforms. Its
complexity grows exponentially with the number of users and prevents implementation for a reasonable
number of users in practical systems.
There have been many suboptimum multiuser receivers each achieving some performance-complexity
tradeoff. However, none of them achieves a local maximum likelihood (LML) solution with an arbitrary
neighborhood size. Moreover, most of the existing suboptimum multiuser receivers are ad hoc developed.
They have low ratio of performance to computational complexity and are difficult to analyze. This is
particularly true for nonlinear iterative detectors. The objective of this project is to develop multiuser
detectors that provide a broad spectrum of performance-complexity tradeoff with high ratios of
performance to computational complexity. The approach is the local likelihood ascent search (LAS) [10]
and local maximum likelihood (LML) multiuser detectors [11]. As demonstrated in our preliminary study,
the error performance of these LML detectors spans from that comparable to the conventional detector,
MMSE receiver, MMSE-DF receiver, superior to MMSE-DF receiver, etc., up to that of the GML detector
and their computational complexity ranges from linear, quadratic, etc., up to exponential in the number of
users. Moreover, these LML multiuser detectors achieve high ratio of performance to computational
complexity as demonstrated in some preliminary simulations.
1
In this proposal, the optimum detector is called the GML detector in contrast with the proposed LML detectors.
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Specifically, we will develop a family of linear-complexity likelihood ascent search (LAS) multiuser
detectors [10] in some combinations of the following conditions: wireless multipath fading channels, onthe-move (Doppler), known and unknown interference users (group blind), broadband and multirate data,
power control, adaptive modulation, turbo coded data, space-time coding, and large systems in CDMA
networks with direct sequence, frequency hopping, and multicarrier modulation. Another family of local
maximum likelihood LAS (LMLAS) multiuser detectors [11] achieving LML detection with an arbitrary
neighborhood size will also be developed in the above various cases. The both families of LAS and
LMLAS detectors with soft intermediate decision will be investigated. We will study strategies to
determine the optimum order of bit update. Performance analysis will include the characterization of local
maximum likelihood points with an arbitrary neighborhood size, the dynamical stability, monotonic
likelihood ascent characterization, expected computational complexity, error probability, asymptotic
multiuser efficiency, near-far resistance, optimum power control, and spectral efficiency.
The proposed investigation on LML detection will impact basic research in nonlinear signal processing
for multiuser communications, and is expected to benefit directly applications to third and fourthgeneration wireless mobile communications systems. This project will also contribute new knowledge to
theories of the fields of multiuser detection, hypothesis testing, wireless communications, image
processing, and neural networks. This project will help set up a strong research program in
communications in this department and provide new research opportunities for both graduate and
undergraduate students, and in particular the minority students. The increased minority students’ research
activities in modern communications will strengthen the traditional diversity environment of this collage.
C. 2 Proposed Research
C. 2.1 Overview of multiuser detection
The multiuser detection of CDMA signals has received considerable attention for over a decade. A
textbook on multiuser detection was recently written by Verdú [14]. Tutorial references on multiuser
detection were presented by Verdú [15], Duel-Hallen et al. [16], and Moshavi [17] with extensive
reference lists therein.
Verdú [18][19] showed that the GML multiuser detector can achieve significant performance
improvement over the conventional detector. However, its computational complexity grows exponentially
with the number of active users. Unless the signal correlations have a special structure as was found for
nonpositive correlations by Ulukus and Yates [20], the GML detector is impractical when the number of
active users is large.
To develop low-complexity suboptimal multiuser detectors, suboptimal tree-type maximum-likelihood
sequence detectors were proposed for multiuser systems. Xie, Tushforth, and Short [21] considered the
sequential detector, and later the breadth-first algorithms [22]. Wei and Schlegel [23] used the Malgorithm tree-search scheme preceded with a decorrelating noise whitening filter. Wei et al. [24] showed
that combined with a decorrelating noise whitening matched filter, the M- and T- algorithms can provide
near optimum performance at a low level of complexity compared with the GML detector.
To develop linear suboptimum detector, Lupas and Verdú exploited a linear decorrelating detector [25]
[7], which was initially proposed in [26]. The decorrelating detector has computational complexity
significantly lower than that of the GML detector while provides substantial performance gain over the
conventional detector. The most significant advantage of the decorrelating detector is that it achieves
optimal performance of near-far resistance and needs no knowledge of interfering users’ powers.
However, its performance is far from the optimality due to the noise enhancement of the matrix inverse.
Xie, Short and Rushforth [27] applied the minimum mean-square error (MMSE) filter which compromises
both multiple access inference suppression and background noise suppression.
Viterbi [28] and Yoon, Kohno, and Imai [29] applied the idea of the successive interference cancellation
(SIC). The SIC detector takes a serial approach to canceling interference. Duel-Hallen [30][31] used the
decorrelating decision-feedback detector (DDFD). Klein, Kaleh, and Baier [32] proposed the zero-forcing
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decision-feedback detector. The DDFD performs linear preprocessing followed by a form of SIC
detection. Varanasi [33] developed a systematic approach to the design of decision feedback detectors.
The likelihood ascent search (LAS) detectors [8][9][10] to be developed as part of this project are mostly
comparable with the parallel interference cancellation (PIC) detector and the EM based receivers. There
has been considerable research on the multistage PIC detector since Varanasi and Aazhang [34][35]
proposed its structure. A basic one stage PIC structure was proposed by Kohno, Imai and Hatori [36]. In
the PIC detector, the multiple access inference is estimated based on the bit estimate from previous stage
and is subtracted from received signal in parallel. This process can be repeated for multiple stages. In the
early study, it was observed [34] that the performance of the PIC detector depends heavily on the initial
data estimates. It was indicated [35] that it is the effect of interference doubling from users that are
incorrectly detected at the penultimate stage, that ultimately limits the performance of the multistage
detector. A number of variations on the PIC detector have been proposed for improved performance. Patel
and Holtzman [37] indicated that soft-decision PIC is found to be superior in a well power-controlled
channel. Giallorenzi and Wilson [38] proposed the use of the already detected bits at the output of the
current stage to improve detection of the remaining bits in the same stage. Moshavi [39] considered the
linear combination of the soft-decision outputs of different stages of the PIC detector. Divsalar, Simon,
and Raphaeli [40] proposed a partial multiple access interference cancellation at each stage with the
amount of cancellation increasing for each successive stage. More studies on the PIC detector can be
found in literature such as Hegarty and Vojcic [41], Gray, Kocic, and Brady [42], Ghazi-Moghadam,
Nelson, and Kaveh [43], Shi, Du, and Driessen [44], Buehrer and Woener [45], Zhang and Brady [46],
and Beuhrer and Nicoloso [47]. The linear PIC (LPIC) detector that makes no hard decisions before the
final stage has also been studied in literature (see [48] and references therein). The main drawback of the
PIC and LPIC detectors is their instability. Verdú demonstrated [14] by a two-user channel that a limit
cycle exists in the process of the PIC detector. Our preliminary study [9][10] gave a set of conditions on
which the limit cycle exists for the PIC detector in a general CDMA system. Brown et al. [48] analyzed
the diverge error probability of the LPIC detector.
Nelson and Poor [49] developed several EM based receivers. Among them, the SAGE receiver has the
same structure as the PIC detector but sequentially updates bits. This change of update mode makes the
SAGE receiver monotonically increase likelihood and hence converge to a fixed point in a finite number
of iterations. Raphaeli [50] proposed the application of an EM based algorithms to multiuser detection.
This EM based algorithm can update any number of bits at a step. When only one bit is updated per step, it
becomes the SAGE receiver. A deterministic annealing technique is then applied to the SAGE algorithm
to produce soft and then gradually harder decision on bits. Wu and Wang [51] applied a local search
algorithm that was originally proposed for solving quadratic binary programming problem. The local
search algorithm presented in [51] employs 0/1 symbols. Actually, this algorithm is the SAGE receiver in
the version of 0/1 bits. This applicant [63] applied a sequential algorithm of a family of modified Hopfield
neural network based algorithms2 to multiuser detection. It turns out that this sequential algorithm is also
identical to the SAGE algorithm. The eliminating-highest-error and the fastest-metric-descent criteria
were proposed for adaptive choice of updated bit at each step and considerably reduce bit error rate and
the total number of iterations. It is not surprising that all these researchers independently obtained the
SAGE algorithm by application of quadratic optimization search algorithms in different areas to the
multiuser detection. The reason is that the SAGE receiver employs the smallest-neighborhood local search
(updates one bit per step), monotonically decreases metric, and achieves the local maximum likelihood
solution with neighborhood size one.
It is interesting to further view the PIC detectors, EM based receivers, and SAGE receiver in the
framework of the family of linear-complexity LAS detectors. Although there have been many studies on
the PIC detector in literature, we can apparently see the shortcomings in development of the PIC detectors
2
As will be addressed in the next subsection, this applicant developed a family of modified Hopfield neural network
based algorithms which can update any number of bits per step with guaranteed convergence. When applied to
multiuser detection, these algorithms perform likelihood ascent search and form the family of LAS detectors.
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and drawbacks of PIC detectors themselves. These drawbacks can be more easily seen in the framework
of the linear-complexity LAS detectors [9][10]. The PIC detector is fundamentally a search detector.
Given one demodulated vector at one stage, the PIC detector searches out another vector at next stage. The
PIC detector was developed mainly based on the intuition motivated by interference cancellation in
parallel rather than aiming at guaranteed likelihood ascent stage by stage. There is no indication about
whether performance is improved at each stage, probably partly due to lack of an efficient method for the
performance evaluation at every stage when the PIC detectors were developed. Nevertheless, it is the
motivation to cancel all interference in parallel simultaneously that yields a “greedy” and malfunctioned
PIC detector. Specifically, the size of search step in the PIC detector is too large, larger than the necessary
size to guarantee the likelihood ascent at every step with probability one. Thus, the PIC detector enters a
limit cycle with a nonzero probability. In addition to no guarantee of convergence, the existence of limit
cycle of the PIC detector results in other three drawbacks. It is shown [9] that once trapped into a limit
cycle, the PIC detector must decrease likelihood in some stages, which wastes computation time. On a
limit cycle, the PIC detector can only achieve a likelihood lower than an LML which can be achieved by
the SAGE receiver. Finally, there is no adequate criterion for the PIC detector to terminate its
iterations/search. In contrast, the family of the LAS detectors [8][9][10] to be studied as part of this
proposed project is developed by aiming at guaranteed likelihood ascent step by step, thus converging to a
fixed point in a finite number of search steps with probability one. It is shown [8][9][10] that in the family
of the LAS detectors there is a subfamily of wide-sense sequential LAS (WSLAS) detectors that achieve
local maximum likelihood (LML) detection with neighborhood size one. Thus, they achieve the local
minimum error probabilities with neighborhood size one. Many other good characteristics of the family of
LAS detectors are proved in [9]. The SAGE receiver is a WSLAS detector. The family of LAS detectors
also provides a framework for stability analysis of other iterative receivers. In the preliminary study [9],
we obtain a set of conditions under which the PIC detector converges to some limit cycle. The condition
under which the EM based algorithms with hard decision in [50] are stable are also obtained.
C. 2.2 Current state of research practice
A. Previous study in image restoration and neural networks
This applicant has long worked on image restoration and reconstruction, and neural networks. The
problem of image restoration [5] has the same formulation (2) and (3) as multiuser detection. In image
restoration, because of a large number of pixels and multiple intensity levels, the optimum solution in
terms of maximum likelihood requires comparison of an astronomic number of metric values, say
28256256 for an ordinary image of size 256256 and a total of 256 intensity levels. To develop low
computational complexity algorithms is an essential approach for image restoration. Motivated by parallel,
massive, efficient computation with implementation on a neural network hardware, the Hopfield neural
network (HNN) algorithms were applied to image restoration first by Zhou et al. [52]. However, their
proposed HNN algorithms need to check metric change step by step to guarantee monotonic metric
descent and thus is time-consuming. The modified Hopfield neural network (MHNN) models were
proposed by Paik and Katsaggelos [53] for gray image restoration and by Sun (this applicant) and Yu [54]
for binary image restoration and reconstruction. The essential difference between the MHNN and HNN is
that even though the crosscorrelation matrix in a quadratic optimization problem is nonnegative definite,
the MHNN guarantees stability by adding a threshold for each neuron, which is much simpler than check
of metric change step by step. Sun and Yu then proposed [55][56] the eliminating-highest-error (EHE)
criterion for MHNN. Many simulation results showed that under the EHE criterion the MHNN algorithms
can converge to much more accurate solutions in much fewer iterations in both blind [57] and non-blind
[58] situations. Sun [59][60] recently carried out a thorough comparison and analysis on various HNN
based algorithms which indicates that the EHE criterion based MHNN algorithms perform much better
than the other MHNN algorithms in all conditions. In particular, Sun [61][62] also developed a family of
MHNN algorithms in a generalized framework in which any number of neurons (or bits in terminology of
CDMA) can be updated and the network energy (or metric in terminology of CDMA) monotonically
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decreases. To CDMA multiuser detection, Sun [63][64] applied the sequential algorithm (same as the
SAGE receiver) of this family of MHNN algorithms with the EHE and FMD criteria. It was demonstrated
that the two sequential algorithms employing the EHE and FMD criteria considerably outperformed the
original sequential algorithm (i.e. the SAGE receiver). Since the multiuser detection problem is also a
quadratic optimization problem with binary support, this entire family of MHNN algorithms can be
applied to multiuser detection. When applied to CDMA multiuser detection, this family of MHNN
algorithms turn out to perform likelihood ascent search, and thus forming the family of linear-complexity
LAS detectors [8][9][10].
B. Preliminary study on the families of LAS and LMLAS detectors
This family of likelihood ascent search (LAS) detectors can be defined by the following generalized
likelihood ascent search (GLAS) detector.
GLAS detector: Given a sequence of bit index subsets L(t)  {1, ..., K} for t  0 and an initial b(0) 
{1, 1}K, the bits are updated by
if k  L(t ), bk (t )  1 and hk (t )  t k (t ),
 1,

(4)
bk (t  1)   1,
if k  L(t ), bk (t )  1 and hk (t )  t k (t ),
b (t ), otherwise,
 k
where tk(t) is the threshold of the kth bit at step t,
for k  L(t).
(5)
t k (t )  | Wkj | ,
jL ( t )
h(t) is the negative metric gradient with respect to b(t) which can be efficiently updated by
h(t  1)  h(t )  2  bk (t )Wk
(6)
kL ( t )
where L’(t)  L(t) is the subset of indices of bits that are flipped at step t and Wk is the kth column of W.
If b(t) = bf for all t  tf with some tf  0, bf is the finally demodulated vector.

The family of LAS detectors has many good properties as analyzed in the preliminary study [9][10]: One
produces a LAS detector by specifying a sequence of L(t), t  0 in the GLAS detector. Determined by L(t)
a LAS detector can update any number of bits at each step. A LAS detector monotonically increases
likelihood at every search step, and thus monotonically decreases error probability and converges to a
fixed point in a finite number of steps. Following any initial detector, a LAS detector can reduce the error
probability of the initial detector unless the initial detector is a fixed point of this LAS detector with
probability one. For an arbitrary crosscorrelation matrix, the thresholds set up in the LAS detectors are
optimum in the sense that the error probability achieves the minimum while the monotonic likelihood
increase is guaranteed. A LAS detector achieves a maximum likelihood solution of a subset of hypotheses
that it searched. The fewer the bits updated at each step (i.e. the smaller the |L(t)|), then the slower the
convergence, the fewer the fixed points, the smaller the difference between the fixed point region (i.e.
decision region) and the GML decision region, and the smaller the error probability. Among the LAS
detectors, the wide-sense sequential LAS (WSLAS) detectors converge with probability one to local
maximum likelihood (LML) points defined with neighborhood size one, and thus each achieves a local
minimum error probability with neighborhood size one. A WSLAS detector can reduce the error
probability of any detector to a local minimum if the detector does not achieve the LML detection with
probability one. When L(t) = {i | i = (t mod K) +1}, it defines the SAGE receiver which is also a WSLAS
detector. Except the GML detector (and the family of LMLAS detectors recently developed in [12]), none
of other well-known detectors are known to achieve LML detection with probability one and thus can be
improved by the WSLAS detectors. All linear detectors (including the conventional detector, decorrelating
detector, linear MMSE detector), and most nonlinear detectors including the PIC detector, SIC detector,
decorrelating decision feedback detector, MMSE-DF detector are not LML detectors and thus their error
probability can be reduced by followed WSLAS detectors [9]. It has been shown that all LAS detectors
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have linear complexity. Many simulations showed that the highest computational complexity of any LAS
detector is about 0.65K per demodulated bit with a random initial.
Another good characteristic of the LAS detectors is their high ratios of performance to complexity in fair
large systems (more than fifty users). Shown in Fig. 1 (a) are bit error rates (BER) of a group-parallel LAS
(GPLAS) detector with fixed group sizes (number of bits updated at each step) J = |L(t)| = 8, 4, 2, 1 (a
WSLAS detector is with J =1 here), the SLAS detector (which is the same as the SAGE receiver here), the
conventional detector, SIC detector, MMSE detector, MMSE-DF detector, and single user bound. The
system employs random binary spreading sequences, equal power with SNR = 9 dB, and fixed ratio of
number of users to processing gain K/M = 0.5. Shown in Fig. 1 (b) is the bit flip rate (BFR) of the LAS
0
10
0.7
GPLAS,
GPLAS,
GPLAS,
GPLAS,
J
J
J
J
=
=
=
=
8
4
2
1 (WSLAS)
SLAS
SIC
MMSE
MMSE-DF
0.65
0.6
Conventional
-1
Bit flip rate
Bit error rate
10
0.55
0.5
0.45
0.4
-2
10
0.35
GPLAS,
GPLAS,
GPLAS,
GPLAS,
SLAS
0.3
Single user
0.25
-3
10
10
50
100
150
200
250
K
Fig. 1 (a). Random binary spreading sequences; equal
power with SNR=9 dB; fixed K/M = 0.5; random initial.
0.2
10
50
100
150
J
J
J
J
=
=
=
=
8
4
2
1 (WSLAS)
200
250
K
Fig. 1 (b). BFR vs. K. Same conditions as in Fig. 1 (a).
detectors, which is defined as average percentage of bits flipped in a search. Since each bit flip needs K
additions, KBFR is the average number of additions per demodulated bit, which can be used as a
computational complexity measure. As we can see, while the other detectors keep the fixed BERs, the
LAS detectors monotonically decreases their BERs gradually close to the single user bound as the number
of users increases. For K  50, the WSLAS and SLAS detectors (both are LML detector with
neighborhood size one) have lower BERs than the MMSE-DF detector. As shown in Fig. 1 (b), all LAS
detectors have an average number of additions per demodulated bit smaller than 0.62K which is linear and
is lower than any linear receivers if spreading sequences are fixed (note that the computation for W =
ARA, q = Ar, and h(0) = Wb(0) + q for the LAS detectors can be done once and be ignored in
complexity account). For the random spreading sequences (which are similar to long spreading
sequences), the LAS detectors need to increase the linear-complexity computation for W = ARA, q = Ar,
and h(0) = Wb(0) + q. In contrast, the MMSE detector and the MMSE-DF detector need to increase the
computation of inverse of matrix of size KK which is much more complex than linear. Consequently, we
can conclude that the LAS detectors achieve much higher ratios of performance to computational
complexity than the MMSE and MMSE-DF detectors in the simulated case for the system of more than
fifty users.
Fig. 1 (a) and (b) also show that the BER of LAS detectors decreases and their computational complexity
increases as the number of bits updated in each step decreases, which provides a mechanism for the LAS
detectors to achieve a different tradeoff between performance and computational complexity.
The family of LAS detectors also provides a framework for stability analysis of other iterative receivers.
The condition under which the EM based algorithms with hard decision in [50] are stable was not
indicated in [50]. In the framework of the family of LAS detectors, the stability condition for these EM
based algorithms can easily obtained [9]. In the framework of the LAS detectors, it is also easy to see that
the well-known PIC detector is a malfunctioned parallel LAS (PLAS) detector. Specifically, the PIC
detector operates exactly the same as the parallel LAS (PLAS) detector but its threshold is that of the
SLAS detector. The thresholds set up in the PIC detector are too low, thus resulting in a nonzero
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probability region where the PIC detectors converges to a limit cycle. A set of conditions under which the
PIC detector enters a limit cycle is given in [9]. In contrast, the PLAS detector (actually all the LAS
detectors) converges to a fixed point in finite number of search steps with probability one.
Inspired by the fact that the WSLAS detectors achieve LML detection with neighborhood size one and
the GML detector achieves LML detection with neighborhood size equal to the total number of users, this
applicant [11][12][13] recently proposed a new concept – local maximum likelihood (LML) multiuser
detection with an arbitrary neighborhood size. Then a family of local-maximum-likelihood likelihoodascent-search (LMLAS) detectors was developed.
An LML detector with neighborhood size J is defined as [11]
(7)
bˆ  arg minˆ f (r | b) , r  K
bN J ( b )
where N J (bˆ )  {b {1,1}K ||| b  bˆ ||1 / 2  J } is the neighborhood of b̂ with size J and ||b  b̂ ||1 denotes
the Hamming distance between b and b̂ . When the neighborhood size is equal to one, the LML detection
is achieved by the WSLAS detectors (including the SAGE receiver). As we can see, when the
neighborhood size is equal to K, the LML detector becomes the famous GML detector (3). It is pointed
out that each LML detector achieves a local minimum error probability defined with the same
neighborhood size.
Every solution in (7) is an LML point with neighborhood size J. It is shown [11][12] that for r  K, b
 {1, 1}K is an LML point with neighborhood size J if and only if


(8)
Ai bi  ri   Rij A j b j   0

iL
jL


for all L  {1,…,K} such that 1  |L|  J.
Given r, (8) defines a set of LML points. On the other hand, given b, (8) defines an observation region –
LML point region, which can be viewed as a decision region for the LML point b. In general, LML point
regions with different bit vectors may be overlapped. An LML point region with neighborhood size J is
specified by a total of
   hyperplanes. The value    is also the lower bound on the order of
J
K
j 1 j
J
K
j 1 j
computational complexity for an LML detector with neighborhood size J. In other words, the LML
detectors with neighborhood sizes of one, two, etc., and up to the total number of users have the orders of
computational complexity linear, quadratic, etc., and up to exponential in the number of users,
respectively. The most complex GML detector has the largest neighborhood size K. The GML point
region is specified by a total of 2K1 hyperplanes and achieves the global minimum error probability. As
the neighborhood size J decreases, the number of hyperplanes specifying an LML point region decreases,
the difference between the LML point region and the GML point region increases, the local minimum
error probability of the LML detector increases, and the lower bound of computational complexity
decreases. When the neighborhood size reaches the minimum – one, the condition (8) becomes b  [r 
(R  I)Ab]  0 where  denotes the Hadamard product, the LML point region is the simplest, and the
computational complexity is linear. The WSLAS detectors achieve this simplest LML detection.
To realize the LML detection with an arbitrary neighborhood size, we developed a family of LMLAS
detectors [11][12][13] defined by the following generalized LMLAS (GLMLAS) detector.
GLMLAS detector: Given an initial b(0)  {1, 1}K and a sequence of bit index subsets L(t)  {1, ..., K}
such that 1  |L(t)|  J for all t  0. For all t  0, repeat the following updates until termination. If


(9)
bi (t ) hi (t )  Wij b j (t )   0

iL ( t )
jL ( t )


where hi(t) is the ith component of the negative metric gradient h(t) evaluated at b(t), then the bits are
updated by
 b (t ), if k  L(t ),
(10)
bk (t  1)   k
 bk (t ), otherwise,
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and the negative metric gradient h(t) is updated by (6). If b(t) = bf for 0  t1f  t  t 2f and
 f

f
f
f
(11)
b  2  bi e i   N J (b ) \ {b }
iL ( t )

t1f t t 2f 
where NJ(bf) denotes the neighborhood of bf with neighborhood size J, then terminate with bf of the finally
demodulated bit vector.

One produces an LMLAS detector by specifying a sequence of L(t), t  0 and neighborhood size J in the
GLMLAS detector. The family of LMLAS detectors also has many proved good properties [11][12][13].
Every LMLAS detector with J is shown to be an LML detector with neighborhood size J. An LMLAS
detector increases likelihood monotonically step by step, and thus converges to an LML point in a finite
number of search steps with probability one. Each LMLAS detector achieves a local minimum error
probability with a corresponding neighborhood size. As the neighborhood size increases, the error
probability of an LMLAS detector decreases while its computational complexity increases. By adjusting
the neighborhood size, one can make a tradeoff between error performance and computational complexity.
Following any detector, an LMLAS detector can reduce the error probability of the initial detector to a
local minimum and otherwise not change it when the initial detector itself is an LML detector with the
same or greater neighborhood size with probability one. Since the LMLAS detectors increases likelihood
at each step, they also achieve high ratio of performance to computational complexity.
Fig. 2 (a) shows BER’s of the LMLAS detectors with neighborhood sizes J = 1, 2, 3, 4, 5, 6, and the
conventional, decorrelating, MMSE, and GML detectors in a simulation. The BER of the LMLAS
detector monotonically decreases with the increase of the neighborhood size. When the neighborhood size
is 6, the performance is very close to the GML detector which has a neighborhood size 10. Fig. 2 (b)

Bit error rate vs. number of users
0
10
-1
Conventional
Decorrelator
MMSE
GML
LMLAS-J
-+- GML
__
LMLAS-J
6
3
5
10
2
J=1
Addition#/user/bit
-x-o-*-+__
10
3
BER
Computational complexity vs. number of users
4
10
-2
4
10
5
6
-3
4
3
2
10
2
1
10
10
J=1
-4
10
0
1
2
3
4
5
6
K
7
8
9
10
11
Fig. 2 (a). Random binary spreading sequences with
elimination of ill-posed R; processing gain M = 11; equal
power with SNR = 11 dB; random initial.
10
1
2
3
4
5
6
K
7
8
9
10
11
Fig. 2 (b). Same Condition as in Fig. 2 (a).
shows the average number of additions per user per search. As the neighborhood size increases, the
computational complexity increases, which confirms the lower bound on the order of computational
complexity implied by (8). Similarly to Fig. 1, our other simulation results show that when the number of
users is large (e.g. greater than 50), the LMLAS detectors considerably outperform the other existing
suboptimum detectors such as MMSE-DF detector.
In summary, these two families of LAS detectors and LMLAS detectors span a broad spectrum of
performance-complexity tradeoff with high ratio of performance to computational complexity.
Local maximum likelihood (LML) points and their properties have never been studied in multiuser
detection literature (and nor well studied in other areas). Our preliminary analysis shows interesting
properties of the LML points and their relationship with the GML point. For example, consider LML
regions defined with neighborhood size one for two-user systems (if neighborhood size two is considered,
all LML points are also GML points). For the two-user system of R12 = 0.6, A1 = 1 and A2 = 0.5, Fig. 3
NSF CISE: Communications, (Y. Sun)
Page C-8
r2
r2
++
++
+
+
0
+
0
r1
r1
+

Fig. 3. LML regions of two-user system with
R12 = 0.6, A1 = 1 and A2 = 0.5.

Fig. 4. LML regions of two-user system with
R12 = 0.65, A1 = 0.8 and A2 = 0.8.
shows LML regions where (1,1), (1,1), (1,1), and (1, 1) are LML points, respectively. In the shaded
region, both (1,1) and (1,1) are LML points, one of which is the GML point. As divided by the line
segment in the shaded region, in the upper shaded triangle, (1,1) is the GML point, and in the lower
shaded triangle, (1,1) is the GML point. The line segment that divides the shaded region into these two
triangles is the decision boundary of the GML detector for hypotheses (1,1) and (1,1). By the GML
detector, the upper shaded triangle is assigned to hypothesis (1,1), and the lower shaded triangle is
assigned to hypothesis (1,1). All LML detectors may perform differently only inside the shaded region.
Outside the shaded region where there is only the GML point, an LML detector performs equally well as
the GML detector. Inside the shaded region, with some probability an LML detector may select a truly
LML solution instead of the GML solution and therefore performs worse than the GML detector. This
probability depends on the particular LML detector
that makes the decision. Since all four noise-free
r2
signal points are outside the shaded region in Fig. 3,
as   0, any LML detector performs asymptotically
++
equally well as the GML detector. Because the
observed noise-free signal is below r2 = 0 for (1,1),
+
and above r2 = 0 for (1, 1), it is clear that as   0,
the conventional detector is sure to make wrong
decision on user 2 and suffers from the near-far
problem. However, as we have seen, an LML
0
r1
detector does not suffer from the near-far problem in
this near-far situation.
Fig. 4 shows the LML regions of the two-user
+
system with R12 = 0.65, A1 = 0.8 and A2 = 0.8. Since

the two noise-free signal points for (1,1) and (1,1)
are inside the shaded region, as   0, an LML
detector may suffer from the interference of the true
LML point when a GML point was transmitted. Fig.
Fig. 5. LML regions of two-user system with
5 shows the LML regions of the two-user system with
R12 = 0.5, A1 = 1 and A2 = 1.
R12 = 0.5, A1 = 1 and A2 = 1. The two noise-free
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Page C-9
signal points for (1,1) and (1,1) are located at the boundary of shaded region. As   0, an LML
detector may or may not suffer from the interference of true LML point in the neighborhood of the noisefree signal points.
Although only neighborhood size one is considered here, these two-user systems suggest rich structure of
error probability of LML detectors with an arbitrary neighborhood size.
C. 2.3 Planned research
We will develop a family of linear-complexity LAS multiuser detectors in some combinations of the
following conditions: wireless multipath fading channels, on-the-move (Doppler), known and unknown
interference users (group blind), broadband and multirate data, power control, adaptive modulation, turbo
coded data, space-time coding, and large systems in CDMA networks with direct sequence, frequency
hopping, and multicarrier modulation. The family of LMLAS multiuser detectors achieving LML
detection with an arbitrary neighborhood size will also be developed in the above various cases. The both
families of LAS and LMLAS detectors with soft intermediate decision will be investigated. We will study
strategies to determine the optimum order of bit update. Performance analysis will include the
characterization of local maximum likelihood points with an arbitrary neighborhood size, the dynamical
stability, monotonic likelihood ascent characterization, expected computational complexity, error
probability, asymptotic multiuser efficiency, near-far resistance, optimum power control, and spectral
efficiency.
Although we have many research topics in the direction of this proposal, as a three-year project for one
PI and one Ph.D. student, we will focus on the following topics.
Theoretical analysis
A. Continued study on analysis of the family of LAS detectors
In the preliminary study, many good analytical characteristics have been revealed for the family of LAS
detectors. We will continue the analysis work in the following several aspects.
The two conditions for bit flip in (4) can be concisely rewritten as bk (t ) k (t )   Ak bk (t )bk   k (t ) where
k(t) is the current interference plus noise and  k (t )   jL (t ), j k | Rkj | A j . k(t) is contributed by the
interfering bits (we call them the direct interfering users in [9]) that are updated at the same step as the bit
of interest. Clearly, the direct interfering users play a more important role in the bit flip conditions than the
other interfering users, and thus play a more important role in fixed point region (decision region), error
probability, and expected computational complexity. We expect from our preliminary study that as k(t)
increases (by increasing the number of bits updated at a step), the decision region expands, error
probability increases, and computational complexity decreases. We will rigorously analyze these roles of
the direct interfering users.
For the LAS detectors, the computational complexity changes from one observation to another because
the operation of LAS detectors depends on noise samples (the same is true for other iterative algorithms).
Then the average number of additions per demodulated bit is used as a computational complexity. Since
the average number of additions per bit is equal to the bit flip rate (BFR) (defined as the ratio of average
number of bit flips to the number of users) times the number of users, the BFR can also used as a
computational complexity. It has been shown that all LAS detectors have linear complexity. Many
simulations showed that the highest BFR of a LAS detector with random initial is about 0.65. In this
project, we will rigorously analyze error probability, near-far resistance, and BFR of LAS detectors in
two-user systems. We expect this analysis to reveal some insightful characteristics of LAS detectors.
The preliminary study showed [9] that the threshold in (5) is optimum in the sense that given the number
of bits updated in a step, the threshold in (5) guarantees the achievement of minimum error probability and
monotonic likelihood increase (which guarantees convergence and wastes no computation time). It is
expected that if the threshold is lower than the optimum, a LAS detector may enter a limit cycle. We will
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Page C-10
analyze and then obtain a set of general conditions and observation region with which a limit cycle exists.
This conditions can be specified and applied to other iterative algorithms to determine existence of limit
cycle. The direct application can be to the PIC detector and the EM-based algorithm with hard decision
[50], both of which differ from the LAS detectors only by the thresholds.
The initial detector affects the error probability and computational complexity of a LAS detector. We
already knew in our preliminary study that the error probability of a LAS detector is never higher than the
error probability of the initial detector. We expect that the error probability and the computational
complexity of the LAS detector monotonically decrease as the error probability of the initial detector
decreases. We will analyze it in this project.
B. Analysis on characteristics of LML detector with an arbitrary neighborhood size
As a brand new nonlinear detector, the characteristics of LML detector with an arbitrary neighborhood
size has not been well studied yet. The following analysis will be carried out in the project.
Except the GML detector, the decision regions (LML point region) of an LML detector may be
overlapped as shown in Figs. 3-5. All LML detectors (including the GML detector) perform differently
only in this overlapped region. Hence, determination and analysis of the region of multiple LML points
are important problems and are the first steps for performance analysis of the LML detectors. For
example, by examining inequality (8) which determines the LML point region, we can see that the noisefree signal points are always inside the corresponding LML point region for any neighborhood size. This
suggests the superior asymptotic performance of the LML detectors over the conventional detectors as 
 0. In fact, the LML point region has a rich structure as shown in Figs. 3-5. In the proposed project, we
will investigate the LML point region and its properties.
We will qualitatively analyze how the neighborhood size affects the error probability. Since multiple
LML points exist in the overlapped region, we will consider an LML detector that equiprobably selects an
LML point in the overlapped region. We expect an analytical result that the error probability of the LML
detector monotonically decreases as the neighborhood size increases.
C. Performance analysis
(a) Error probability: As demonstrated by the two-user systems in Figs. 3-5, the LML region in various
conditions presents rich structure for error probability analysis. Since the LML detectors perform
differently from the GML detector only in the shaded region, the LML detectors must have a simple
expression of the error probability in terms of the error probability of the GML detector. The performance
of the GML detector is well studied by Verdú [14]. The analysis result of the GML detector can be
borrowed by the analysis of the LML detectors. In the proposed project, the general formula of error
probability of LML detectors with an arbitrary neighborhood size will be derived and its relationship with
the error probability of the GML detector will be studied. The structure of the error probability of LML
detectors will be analyzed with the help of existing analytical results of the GML detector.
(b) Asymptotic performance analysis: Asymptotic performance analysis of the LML detectors as   0
is an interesting problem in theory and application. As demonstrated by the two-use systems in Figs. 3-5,
the asymptotic performance of the LML detectors with an arbitrary neighborhood size is determined by
the location of the noise-free signal points in observation space. If all noise-free signal points are outside
the overlapped region, the performance of an LML detector is asymptotically the same as the performance
of the GML detector. If some noise-free signal points are located at the boundary of the overlapped region
and all other signal points are outside the overlapped region, the asymptotic behavior of the LML detector
will be partly like but different from that of the GML detector. If some noise-free signal points are inside
the overlapped region, the asymptotic performance of an LML detector will be dominated by the noisefree signal points that are inside the overlapped region. In the proposed project, the asymptotic
performance analysis will be carried out in a general high-dimensional case for LML detectors with an
arbitrary neighborhood size.
(c) Multiuser efficiency and near-far resistance: Multiuser efficiency and near-far resistance are two
figures of merit of a multiuser detector, which was proposed by Verdú [19]. The multiuser efficiency and
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near-far resistance of the GML detector was well studied by Verdú [19]. As demonstrated by the two-use
systems in Figs. 3-5, the LML detectors present certain near-far resistance capability. In simulations of
[12][63][64] the LML detectors with small neighborhood size in a moderate near-far situation
demonstrated certain near-far resistant capability. A careful study of multiuser efficiency and near-far
resistance for LML detector with an arbitrary neighborhood size will be performed in a general highdimensional case for various LML detectors in this project.
(d) Spectral efficiency: Verdú and Shamai [72] studied spectral efficiency of the GML detector, and
several well-known linear detectors in large systems. In the proposed project, we will investigate the
spectral efficiency of the LML detector with an arbitrary size.
D. Performance analysis in large systems
In a large CDMA system, both the number of users and spreading gain trend to infinity while keeping
their ratio a constant. The theory of large systems with random spreading sequence has been successfully
applied to the analysis of performance of several well-known linear receivers and the GML detector and
obtained fruitful results [72][73]. In the large systems, the output interference power of a linear receiver
becomes deterministic, thus making the analysis mathematically tractable. The similar observation may be
true for the LML detector. As we can see in (8), the boundary of an LML point region is determined by a
summation involved with the crosscorrelation matrix. For large systems, the boundary may present some
regularization and mathematical tractability, and thus simplifying analysis of characteristics of the LML
detectors. We will thoroughly investigate possibilities of this kind in the project.
In general, it is hard to analyze the throughput and packet delay for a random access CDMA network
with packet combining and multiuser detection. However, our preliminary study showed [74][75][76] that
the analysis becomes tractable for a large random access CDMA network with Poisson arrival, in which
both the mean of arrival and spreading gain trend to infinity while keeping their ratio a constant. We
observed that if the analysis of the LML detector for large systems is tractable, then the analysis of
throughput and packet delay for large random access CDMA network employing the LML detector as
means of multiuser detection is also tractable. We will also thoroughly investigate this issue in this
project.
E. Optimum power control
Since LML detectors asymptotically (as   0) perform equally well as the GML detector when all
noise-free signal points are outside the overlapped region, it is interesting to find the condition regarding
R and A that all noise-free signal points are outside the overlapped region. This condition is equivalent to
the condition that with probability one there is only GML point as   0. In other words, under this
condition an LML detector almost surely performs equally well as the GML detector. To find this
condition is also significant in that under it LML detectors achieve the performance of the GML detector
with as low as linear computational complexity (when neighborhood size is one) as   0. Moreover,
given R and with this condition satisfied we can achieve optimum power control (distribution of Ak) in
terms of lowest average power consumption while achieving low-complexity GML detection. In the
project, this condition will be investigated for an LML detector with an arbitrary neighborhood size.
Algorithm development and applications
F. Soft intermediate decision
In the current version, both families of LAS detectors and LMLAS detectors employ hard decisions in
each step. In some practical systems that apply coding schemes, soft decision is necessary to provide for
decoder. Raphaeli [50] demonstrated that soft and then gradually hard decision via the deterministic
annealing technique can lead the SAGE receiver to overcome local minimum and considerably decrease
bit error rate for both uncoded and coded data. The cost is the increased computational complexity. The
SAGE receiver is one of the WSLAS detector. We believe that the same deterministic annealing technique
can be successfully applied to the both families of LAS detectors and LMLAS detectors and considerably
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Page C-12
improve their performance. In the project, we will establish the two families of soft-intermediate-decision
LAS detectors and LMLAS detectors. Their performance will be investigated.
G. Blind and group-blind LML/LMLAS detectors
For multipath frequency-selective channels, received CDMA signal is bit-asynchronous and effective
signature waveforms are unknown due to distortion of time-varying channels. Development of blind lowcomplexity multiuser detectors without knowing signature waveforms is of interest in theory and practice.
In an up-link scenario, basestation knows the spreading sequences of users in its cell and their effective
signature waveforms can be estimated via subspace technique [67]. However, the basestation does not
know the spreading sequences of users in other neighbor cells. In this case, the basestation needs to
demodulate the intra-cell users with known signature waveforms and suppress the inter-cell users without
knowing their signature waveforms. This is so called group-blind multiuser detection [67]. The
decorrelating detector, the MMSE detector and the PIC detectors for group-blind multiuser detection are
developed in [67][68]. Similarly, to achieve approximately maximum likelihood solution, Raheli et al.
[69] proposed the per-survivor processing (PSP) for blind symbol detection of single-tone single-user
channels. However, the PSP is infeasible in multiuser detection because it relies on the Viterbi algorithm
which is exponentially complex.
In the proposed project, we will consider the low-complexity blind and group-blind search detectors that
monotonically increase the blind and group-blind likelihood functions by means of the families of LAS
and LMLAS detectors. Specifically, considered is the combination of a least square (LS) filter with a LAS
or LMLAS detector. This combination can achieve monotonic ascent of blind/group-blind likelihood
function, which is justified as follows. Consider the blind case. Given an arbitrary SA (say SA = [I 0]T)
and an initial sequence of bit vectors B (B is a matrix of bit vectors), a LAS/LMLAS detector searches out
a new sequence of bit vectors that is guaranteed to have increased likelihood due to the likelihood ascent
property of the LAS/LMLAS detector [9][12]. The new sequence of bit vectors is used to generate a new
matrix SA by means of the LS projection. Since the noise before the matched filter bank is white
Gaussian, the LS projection is in the maximum likelihood sense. Therefore, the LS projection also
increases the likelihood. Hence, by repeating the alternate LAS/LMLAS and LS operations, a sequence of
B and a sequence of SA are generated, which monotonically increases likelihood of SAB. It is clear that
the monotonic likelihood ascent in both operations implies the convergence in a finite number of iterations
with probability one. When the noise is severe, a minimum mean square error (MMSE) filter can be used
to replace the LS filter to mitigate noise. In the group-blind case, part of SA is known and a similar
likelihood ascent search detector can be designed. Our preliminary simulations demonstrated that this
group-blind detector outperformed the decorrelating based group-blind detectors. Convergence in a finite
number of iterations was also observed in simulations. Simple analysis suggests that the LMLAS/LS
detector converges to an LML point defined by the group-blind likelihood function. The characteristics of
the LML point defined by the group-blind likelihood function will also be studied in this project.
H. Adaptive implementation in multipath fading channels
In the current version, both families of LAS detectors and LMLAS detectors are set up for Gaussian
CDMA channels. They are applicable to “one-shot” data. For multipath fading channels, bit vectors are
correlated and the “one-shot” signal model is invalid. If data block is small, an entire block of data can
also be formed similarly to the “one-shot” model but with increased matrix size. In the case of long data
stream, the LAS and the LMLAS detectors must be adaptively implemented. A consideration is to perform
LAS or LMLAS search in a moving window. After a LAS/LMLAS detector converges to a fixed point for
the data in the window, the window is moved by a bit period so that a bit period data is moved out and a
bit period data is moved in the window. The moving size can also be greater than one bit period. We will
study this adaptive implementation of both families of LAS and LMLAS detectors and investigate their
performance in multipath fading channels.
If further the channel is time-varying, joint data detection and channel estimation with a moving window
can be considered. Similarly to G, a LAS/LMLAS detector demodulates bit vectors in the window, and an
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Page C-13
adaptive filter estimates the channel parameters based on the demodulated bit vectors. In this way, the
LAS/LMLAS detector combined with the adaptive filter constructs an adaptive blind LAS/LMLAS
detector for joint bit vector detection and channel estimation. There have been many adaptive filters [70]
such as RLS algorithm which can be used in this approach. In the proposed project, the adaptive blind
LAS/LMLAS detectors will be investigated and compared with the blind and group-blind LAS/LMLAS
detectors in G. Semi-blind detectors of this kind with a few training bits will also be investigated.
I. Combination of LAS/LMLAS detectors and tree-search detectors
From (8), we can see [12] that the regions of multiple LML points are small as demonstrated by the
shaded regions in Figs. 3-5. In other words, most of the observation space yields only the GML point (i.e.,
there is no other LML point) where a low-complexity LAS/LMLAS detector can perform equally well as
the NP-hard GML detector. Thus, the GML detection can be achieved with considerably reduced
computational complexity if the GML detector operates inside the region of multiple LML points while an
LML detector (like the LAS and LMLAS detectors) operates outside the region of multiple LML points.
To further simplify computation a suboptimal tree-search detector such as M- and T-algorithms can be
used instead of the GML detector to achieve near-optimum low-complexity detection. In the proposed
project, we will find an easy way to roughly determine if an observation r is inside the region of multiple
LML points. For example, consider the LML region defined with neighborhood size one. We can set up
some thresholds for components of r based on known RA to determine the region. Preliminary study on
the combinations of LML detectors and tree-search detectors [64] demonstrated promising results.
J. Criteria for determination of more acceptable vector
Given an initial bit vector, a LAS detector or an LMLAS detector can automatically search out a new bit
vector with guaranteed increased likelihood. Repeating the search, the LAS/LMLAS detector generates a
sequence of bit vectors with monotonic likelihood ascent. In general, in a search step there exist many bit
vectors that have greater likelihood than the current bit vector. Different choice of these acceptable bit
vectors leads the search along a different trajectory to a different finally demodulated bit vector. The
eliminate-highest-error (EHE) and fastest-metric-descent (FMD) criteria [63][64] are examples of such
criteria for the choice of acceptable bit vectors. The EHE and FMD criteria were originally proposed by
this applicant in [55][56] for image restoration and then thoroughly studied in [59][60], and preliminarily
applied to CDMA multiuser detection in [63][64] for sequential LAS detectors. Simulations therein
demonstrated considerable improvement on error performance in all cases. However, its application to the
entire family of LAS detectors and the family of LMLAS detectors has not been studied yet. In this
project, the EHE and FMD criteria will be thoroughly analyzed in the framework of CDMA multiuser
detection. Its application to the family of LAS detectors and the family of LMLAS detectors will be
studied. Other similar criteria will also be developed and studied. It is possible to develop a criterion
jointly with optimum power control in E. The criterion of demodulating bits according to the order of
users’ powers and order of SNR which are used in the decision-driven detectors [14] will also be studied
as comparison.
K. Other implementation problems
In the current version, the both families of LAS and LMLAS detectors are designed for symbol of 1’s.
Raphaeli [50] demonstrated a set of EM based algorithms that employ QPSK symbols. The SAGE
algorithm with the QPSK symbols is in this set. The SAGE algorithm is also a LAS detector. In this
project, we will investigate the extension of the both families of LAS and LMLAS detectors from the
symbol of 1’s to QPSK and other modulation symbols.
In the current version, the family of LMLAS detectors is not optimized in terms of minimization of
computational complexity though they achieve the LML detection with an arbitrary neighborhood size.
This is why in Fig. 2 (b) the LMLAS detector with neighborhood size six is more complex than the GML
detector which was optimized in computational complexity. This also suggests the potential to reduce the
computational complexity of the LMLAS detectors. In this project, we will study the other search rules so
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that the ratio of performance to computational complexity is higher than the current version of the
LMLAS detectors.
The applications of the families of LAS and LMLAS detectors to OFDM, multicarrier CDMA,
frequency-hop CDMA, broadband and multirate data, and space-time coded or turbo coded data will also
be investigated.
C. 3 Impacts and Contributions in Research and Education
The LML detectors investigated in this project provide a new means of multiuser detection for CDMA
network to increase usable bandwidth and network throughput. The proposed investigation will impact
basic research in signal processing for multiuser communications, and is expected to benefit directly
applications to fourth-generation wireless mobile communications systems. This project will contribute
new knowledge and method to applications to broad areas of wireless communication networks, highspeed data transmission, wireless internet service, digital television, magnetic recording, global
positioning systems, and image processing, and to theories of the fields of multiuser detection, hypothesis
testing, wireless communications, neural networks, and image processing.
The area of communications in the PI’s Department of Electrical Engineering at the City Collage of New
York is currently relatively weak. Only the PI is in the area of physical layer communications. Several
communication related courses such as Spread Spectrum and Information Theory and Coding have not
been offered for long since a senior faculty member was retired. Several other modern communication
courses such as Digital Communications at both undergraduate and graduate levels, and Statistical Signal
Estimation and Detection at graduate level have not been included in the curriculum (the faculty meeting
of this department just approved PI’s proposal to open Digital Communications I, and II at graduate level
in next year). On the other hand, several surveys showed significant student demand on opening
communication courses. This department has decided to develop a strong communication program. The
hiring process for a new faculty member in telecommunications has been activated. Currently this PI
works on a research project in the Collaborative Technology Alliances (CTA) program supported by ARL.
This PI directs three Ph.D. students in addition to about five MS projects and reports and five
undergraduate students in independent study yearly. The City College of New York is a minority college.
Each year several minority students (most are MS and undergraduate students) participated in the research
with the PI through assigning them projects and independent study. The support of this proposed project
will help set up a strong program in communications in this department and provide new research
opportunities for both graduate and undergraduate students, and in particular the minority students. The
increased minority students’ research activities in modern communications will strengthen the traditional
diversity environment of this collage.
NSF CISE: Communications, (Y. Sun)
Page C-15
REFERENCES CITED
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Allerton Conf. Communication, Control and Computing, Monticello, IL, Oct. 1995, pp. 1063-1072.
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communications,” IEEE Trans. Commun., vol. 44, pp. 538-541, May 1996.
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CDMA using an improved Gaussian approximation,” IEEE Trans. Commun., vol. 44, pp. 1308-1321, Oct.
1996.
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[46] X. Zhang and D. Brady, “Asymptotic multiuser efficiency for decision-directed multiuser detection,”
IEEE Trans. Inform. Theory, vol. 44, pp. 502-515, Mar. 1998.
[47] R. M. Beuhrer and S. P. Nicoloso, “ Comments on ‘partial parallel interference cancellation for
CDMA’,” IEEE Trans. Commun., vol. 47, no. 5, pp. 658-661, May 1999.
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2001.
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approach,” IEEE Trans. on Commun., vol. 44, no. 12, pp. 1700-1710, Dec. 1996.
[50] D. Raphaeli, “Suboptimal maximum-likelihood multiuser detection of synchronous CDMA on
frequency-selective multipath channels,” IEEE Trans. on Commun., vol. 48, no. 5, pp. 875-885, May
2000.
[51] B. Wu and Q. Wang, “New suboptimal multiuser detectors for Synchronous CDMA systems,” IEEE
Trans. on Commun., vol. 44, no. 7, pp. 782-785, July 1996.
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1992, vol. 3, pp. 1412-1414.
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image restoration," In Proc. Int. Symp. on Inform. Theory Applicat., ICCS/ISITA'92, Singapore, Nov. 1620, 1992, vol. 3, pp. 1409-1411.
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bilevel image restoration," Pattern Recognition Letters, vol. 14, no. 6, pp. 471-474, June 1993.
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IEEE Int. Conf. on Neural Networks, ICNN'93, San Francisco, CA, Mar. 28-Apr. 1, 1993, pp. 1656-1661.
[58] Y. Sun, J.-G. Li and S.-Y. Yu, “Improvement on performance of modified Hopfield neural network
for image restoration,” IEEE Trans. on Image Processing, vol. 4, no. 5, pp. 688-692, May 1995.
[59] Y. Sun, "Hopfield neural network based algorithms for image restoration and reconstruction - Part I:
algorithms and simulations," IEEE Trans. on Signal Processing, vol. 48, no. 7, pp. 2105-2118, July 2000.
[60] Y. Sun, "Hopfield neural network based algorithms for image restoration and reconstruction - Part II:
performance analysis," IEEE Trans. on Signal Processing, vol. 48, no. 7, pp. 2119-2131, July 2000.
[61] Y. Sun, "A generalized updating rule for modified Hopfield neural network," in Proc. IEEE Int. Conf.
on Neural Networks, ICNN’97, Houston, Texas, June 9-12, 1997, pp. 1227-1230.
[62] Y. Sun, "A generalized updating rule for modified Hopfield neural network for quadratic
optimization," Neurocomputing, 19 (1998), pp. 133-143.
[63] Y. Sun, "Eliminating-highest-error and fastest-metric-descent criteria and iterative algorithms for bitsynchronous CDMA multiuser detection," in Proc. IEEE Int. Conf. on Commun., ICC'98, Atlanta,
Georgia, June 7-11, 1998, pp. 1576-1580.
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bit-synchronous CDMA multiuser detection," in Proc. IEEE Int. Conf. on Commun., ICC'98, Atlanta,
Georgia, June 7-11, 1998, pp. 390-394.
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Areas Commun., vol. 17, pp. 1971-1984, Nov. 1999.
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[68] A. Høst-Madsen and K.-S. Cho, “MMSE/PIC multi-user detection for SD/CDMA systems with interand intra-interference,” IEEE Trans. Commun., vol. 47, pp. 291-299, Feb. 1999.
[69] R. Raheli, A. Polydoros, and C.-K. Tzou, “Per-survivor processing: a general approach to MLSE in
uncertain environments, ” IEEE Trans. On Commun., vol. 43, no. 2/3/4/, Feb./Mar./Apr. 1995.
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Trans. on Inform. Theory, vol. 45, No. 2, pp. 622-640, March 1999.
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bandwidth and user capacity,” IEEE Trans. on Inform. Theory, vol. 45, no. 2, pp. 641-657, March 1999.
[74] X. Cai, Y. Sun, and A. N. Akansu, "Asymptotic performance of DS-CDMA random access systems
with packet combining in fading channels," submitted to IEEE J. on Select. Area in Commun. (revised).
[75] Y. Sun, and X. Cai, "Multiuser detection for packet-switched CDMA networks with retransmission
diversity," submitted to IEEE Trans. on Signal Processing.
[76] X. Cai, Y. Sun, and A. N. Akansu, “Performance of slotted CDMA random access systems with
packet combining in fading channels,” in Proc. 34th Annual Conference on Information Science and
Systems, CISS'2001, The Johns Hopkins University, Baltimore, Maryland, March 21-23, 2001.
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Biographical Sketch

Yi Sun
Department of Electrical Engineering
The City College of the City University of New York
Convent Avenue at 138th Street
New York, NY 10031
Phone: (212)650-6621; Fax: (212) 650-8249
E-mail: sun@ccny.cuny.edu

Education
Ph.D., EE, University of Minnesota, Minneapolis, MN, 1997
MSEE, Shanghai Jiao Tong University, Shanghai, P. R. China, 1985
BSEE, Shanghai Jiao Tong University, Shanghai, P. R. China, 1982

Professional Experience
Assistant Professor, City College of City University of New York, New York, NY, Sept. 1998 Postdoctoral Research Associate, University of Connecticut, Storrs, CT, Oct. 1997-Aug. 1998
Postdoctoral Research Fellow, University of Utah, Salt Lake City, Utah, March-Sept. 1997
Research intern, Northern Telecom, Eagan, MN, summer 1996 - Jan. 1997
Research intern, ADC Telecommunications, Minnetonka, MN, summer 1995
Research and Teaching Assistants, University of Minnesota, Minneapolis, MN, 1993 - 1996
Visiting Scientist, Concordia University, Montreal, Canada, summer 1993
Lecturer, Shanghai Jiao Tong University, Shanghai, P. R. China, 1985-1993

Publications Related to Proposed Project
[1] Y. Sun, “Local maximum likelihood multiuser detection,” in Proc. 34th Annual Conference
on Information Science and Systems, CISS'2001, pp. 7-12, The Johns Hopkins University,
Baltimore, Maryland, March 21-23, 2001.
[2] Y. Sun, “A family of linear complexity likelihood ascent search multiuser detectors for
CDMA communications,” in Proc. 34th Asilomar Conference on Signals, Systems, and
Computers, vol. 2, pp. 1163 -1167, Pacific Grove, CA, Oct. 29 - Nov. 1, 2000.
[3] Y. Sun, "Hopfield neural network based algorithms for image restoration and reconstruction Part I: algorithms and simulations," IEEE Trans. on Signal Processing, vol. 48, no. 7, pp. 21052118, July 2000.
[4] Y. Sun, "Hopfield neural network based algorithms for image restoration and reconstruction Part II: performance analysis," IEEE Trans. on Signal Processing, vol. 48, no. 7, pp. 2119-2131,
July 2000.
[5] Y. Sun, "A generalized updating rule for modified Hopfield neural network for quadratic
optimization," Neurocomputing, pp.133-143, 19 (1998).

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
Other Significant Publications
[1] Y. Sun, "Bandwidth-efficient wireless OFDM," IEEE J. on Select. Area in Commun., vol. 19,
no. 11, pp. 2267-2278, Nov. 2001.
[2] Y. Sun and D. Parker, "Small vessel enhancement for MRA images using local maximum
mean processing," IEEE Trans. on Image Processing, vol. 10, no. 11, pp. 1687-1699, Nov. 2001.
[3] Y. Sun and D. Parker, "Performance analysis of maximum intensity projection algorithm for
display of MRA images," IEEE Trans. on Medical Imaging, vol. 18, no. 12, pp. 1154-1169, Dec.
1999.
[4] Y. Sun, "Stochastic iterative algorithms for signal set design for Gaussian channels and
optimality of the L2 signal set," IEEE Trans. on Information Theory, vol. 43, pp. 1574-1587,
Sept. 1997.
[5] Y. Sun, J.-G. Li and S.-Y. Yu, “Improvement on performance of modified Hopfield neural
network for image restoration,” IEEE Trans. on Image Processing, Vol. 4, No. 5, pp. 688-692,
May 1995.

List of Collaborators
Prof. Myung Lee
Prof. Terak Saadawi
Prof. Dennis Parker
City College of New York
City College of New York
University of Utah
(applicant’s postdoctoral advisor, 20 graduates, 3 postdoctors)
Prof. Lang Tong
Cornell University
(applicant’s postdoctoral advisor, 10 graduates, 4 postdoctors)
Prof. John Kieffer
University of Minnesota
(applicant’s Ph.D. advisor)
Dr. Laurie Nelson
IDA Center for Communications Research
(applicant’s Ph.D. co-advisor)

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