IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO.

5, MAY 2007 1973

Analysis and Optimization of Interleave-Division

Multiple-Access Communication Systems
Kai Li, Xiaodong Wang, and Li Ping

Abstract— The recently proposed interleave-division multiple- a comprehensive analysis was not available. In this paper, we
access (IDMA) system is a flexible spread-spectrum air-interface focus on the analysis and optimization of such a system.
technique featuring low receiver complexity and high spectral Specifically, we first analyze the performance of the un-
efficiency. In IDMA, each user’s chip sequence is interleaved by
a distinct chip-level interleaver. The receiver employs a simple coded IDMA system employing a chip-level iterative detector.
chip-level iterative multiuser detector to decode the user’s data. We show that such a system can be viewed as the limit case
Here we focus on the analysis and optimization of such an of a randomly spread CDMA system employing repetition
IDMA system. We show that IDMA can be viewed as a limit codes and an SIC-MMSE [22] iterative receiver. A large-
case of the conventional CDMA employing repetition code and system performance analysis technique is used to gain some
random spreading. Two analytical tools, namely, the large-system
performance approximation and the EXIT chart technique are insight on the relationship between the IDMA system and the
tailored in the context of IDMA chip-level iterative detector to conventional CDMA system. As shown in [20], low rate code
facilitate the system performance analysis and optimization. The is necessary for a spectral-efficient multiple-access system.
spectral efficiencies of a low-rate coded IDMA system with equal We then analyze the spectral efficiencies of a low-rate coded
power setting in both single-cell and multi-cell scenarios are then IDMA system in both single-cell and multi-cell scenarios
analyzed, from which it is seen that the coded IDMA system
with turbo receiver is a spectral efficient multiple-access scheme. using the extrinsic information transfer (EXIT) chart technique
Finally, we consider optimal power allocation among users in [16], [17], [5]. It is shown that with the aid of capacity-
IDMA to maximize the spectral efficiency with finite-alphabet approaching low-rate codes (e.g., the turbo-Hadamard codes
constellation. The differential evolution technique for nonlinear [8]), the coded IDMA system is a spectral-efficient multiple-
optimization is adopted to solve the power profile optimization access scheme.
problem. With optimized power profiles, the low-rate coded
IDMA system can approach the optimal spectral efficiency with With binary codebooks, the capacity of a multiple-access
finite input constellations. system is bounded by 1 bit/sec/Hz with equal rate and
equal power configuration [15]. Recent results show that [1],
Index Terms— Multiple access, chip-level interleaving, iterative
multiuser detection, spectral efficiency, power allocation. with rate or power control and group stripping decoding,
the optimal spectral efficiency of a multiple-access channel
can be approached even with finite input constellations (e.g.,
I. I NTRODUCTION BPSK or QPSK constellations). In this paper, we also treat
the power allocation problem for IDMA systems. Analogous

R ECENTLY, a new technique for multiuser spread-

spectrum communications, the so-called interleave-
division multiple-access (IDMA) scheme, was introduced in
to the degree profile design for irregular LDPC codes, the
differential evolution technique [11] is utilized to solve the
power profile optimization problem. It is shown that with
[9], [4]. In this scheme, each user’s chip sequence is inter-
the optimized power profiles, a turbo-Hadamard coded IDMA
leaved by a user-specific distinct random interleaver. The re-
system can approach the optimal spectral efficiency with finite
ceiver employs a simple chip-level iterative multiuser detector
input constellations.
(MUD). Such a system is a logical development of the earlier
The reminder of this paper is organized as follows. Sec-
research on introducing chip-level interleaving as a means of
tion II describes the IDMA system and the iterative chip-
mitigating burst impulsive noise disturbances, multiple access
level multiuser detector. Section III presents the performance
interference, as well as intersymbol interference [14], [7],
analysis of the IDMA receiver in both uncoded and coded
[3], [6]. Although it was previously known via bit error rate
scenarios. Section IV describes the low-rate coded IDMA sys-
(BER) simulations that impressive performance gain in both
tem and analyzes the spectral efficiencies under equal power
uncoded and coded IDMA systems can be obtained [9], [4],
configuration for both single-cell and multi-cell scenarios. The
Manuscript received September 19, 2005; revised July 24, 2006; accepted
optimal power allocation for IDMA systems is also addressed
August 23, 2006. The associate editor coordinating the review of this paper in the same section. Section V contains the conclusions.
and approving it for publication was V. Bhargava. This work was supported
in part by the U.S. Office of Navel Research (ONR) under grant N00014-03-
1-0039, and in part by the U.S. National Science Foundation (NSF) under II. I NTERLEAVE -D IVISION M ULTIPLE -ACCESS S YSTEMS
grant CCR-0207550.
K. Li and X. Wang are with the Department of Electrical Engi- We consider a spread-spectrum communication system with
neering, Columbia University, New York, NY 10027. (e-mail: {likai, K users. As shown in Fig. 1.(a), at the transmitter end, the
wangx,}@ee.columbia.edu). n-th information bit (or the code bit in the coded case) of
L. Ping is with the Department of Electronic Engineering, City University
of Hong Kong. (e-mail: eeliping@cityu.edu.hk). the k-th user dk,n ∈ {+1, −1}, n = 1, 2, ..., N , in the input
Digital Object Identifier 10.1109/TWC.2007.05735. data stream dk is spread by a length-S spreading sequence
1536-1276/07$25.00 
c 2007 IEEE
1974 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 2007

Transmitter
A1, j h1, j
tive chip-by-chip receiver consists of a soft-input soft-output
d1 {c1, j} {x1, j} (SISO) chip demodulator and a bank of K single-user SISO
Spread 1
. .
decoder working in a turbo manner. The chip demodulator
.
.
.
.
Ak, j hk, j .
performs a chip-by-chip demodulation based on the channel
.
dk {ck, j} {xk, j} .
Spread k .
.
input and the prior information provided by the decoders.
. .
. .
AK, j hk, j
.
Concentrating on the k-th user, (1) can be rewritten as rj =
 
. .
dK {cK, j} {xK, j}
Spread Ak,j hk,j xk,j + ζk,j with ζk,j = k =k Ak hk ,j xk ,j + nj
being the sum of the multiuser interference and the additive
Multiuser Receiver noise with respect to this user. Each xk,j is a random variable
{
with mean x̄k,j and variance σx2k,j (initialized to 0 and 1
dem(c1, j)} -1
{ dem(x1, j)}
^
d1 SISO 1 respectively) which are related to the a priori information of
rep-dec { rep(c1, j)} { rep(x1, j)} xk,j . With perfect channel state information (CSI) known at
1
. . the receiver, from (1), we have
. .
. .
{ dem(ck, j)} { dem(xk, j)} K

-1
^
dk k SISO {r j}
SISO
chip r̄j = Ak,j hk,j x̄k,j ,
rep-dec { rep(ck, j)} { rep(xk, j)}
dem k=1
k
.
.
.
. K

. . AWGN
^
{ dem(cK, j)} -1
{ dem(xK, j)} and σr2j = A2k,j h2k,j σx2k,j + σch
2
. (2)
dK SISO K
k=1
rep-dec { rep(cK, j)} { rep(xK, j)}
K When K is large, with the central limit theorem, the interfer-
ence term ζk,j in (1) can be well approximated by a Gaussian
(a) random variable with mean and variance given respectively by
MMSE MUD
dk xk r
^
dk ζ̄k,j = r̄j − Ak,j hk,j x̄k,j ,
Repetition
Spread
encoder k
and σζ2k,j = σr2j − A2k,j h2k,j σx2k,j . (3)
Repetition
Decoder
Such an approximation is also utilized in [22] and the situation
(b) (c) here is essentially a special case of [22] with unit spreading
gain. Then the chip demodulator provides the extrinsic log-
Fig. 1. (a) IDMA transceiver. (b) The repeating-spreading CDMA transmitter likelihood ratios (LLRs) of {xk,j } computed based on (2) and
for user k. (c) The iterative multiuser receiver of user k for the repeating-
spreading CDMA system. (3) as
Pr (xk,j = +1|rj ) Pr (xk,j = +1)
λdem (xk,j ) = ln − ln
Pr (xk,j = −1|rj ) Pr (xk,j = −1)
sk in the form dk,n → dk,n sk . The chip sequence after  
2Ak,j hk,j rj − ζ̄k,j
spreading is then {ck,j , j = 1, 2, ..., P }, where P = N S is = , ∀k, j. (4)
the frame length of the chips. A chip-level interleaver πk of σζ2k,j
length P is then applied to produce the transmitted signals Such a chip demodulator is a soft-interference cancela-
{xk,j , j = 1, 2, ..., P }. Note that for a conventional CDMA tion/matched filter (SIC-MF) detector [5], [23]; it is also a
system, different signature sequences {sk , k = 1, 2, ..., K} special case of the SIC-MMSE detector [22] with spreading
are employed for user separation, and no chip-level interleaver gain being 1.
is employed. In IDMA, in principle, all users can share a
As shown in Fig. 1.(a), for user k, the chip demod-
single spreading sequence, i.e., sk = s, ∀k. The users are P
ulator outputs {λdem (xk,j )}j=1 are de-interleaved to form
then distinguished by their respective interleavers, πk , ∀k.
For simplicity, here we consider only a synchronous multi- {λdem (ck,j )}Pj=1 and then fed to the single-user de-spreader as
user system over a time-invariant single-path real channel. The the a priori information. Since spreading is a special repetition
generalization to the complex channel or asynchronous multi- code with the codewords multiplied by the signature chips, the
path channel is straightforward and can be found in [9], [4]. de-spreader is essentially a SISO repetition decoder. Consider
Assuming BPSK modulation, then in the single-cell scenario, only the chips related to dk,1 . Suppose that due to the inter-
the equivalent received signal at chip instant j is given by leaving, the received signal related to ck,j is rj  . Then based
on (4), the a posteriori LLR output of the repetition decoder
K
 for dk,1 can be computed from {λdem (ck,j )} as Λrep (dk,1 ) =
rj = Ak,j hk,j xk,j + nj , j = 1, 2, ..., P (1) S Pr(ck,j =+sk,j |rj  ) S
k=1 j=1 ln Pr(ck,j =−sk,j |rj  ) = j=1 sk,j λdem (ck,j ). The ex-
trinsic for the chip ck,j within dk,1 sk is then given by
where xk,j ∈ {+1, −1} and hk,j denote the chip and the chan-
λrep (ck,j ) = sk,j Λrep (dk,1 )− λdem (ck,j ). The extrinsic LLRs
nel coefficient of the k-th user at chip instant j, respectively;
{λrep (ck,j )} are then interleaved and fed back to the chip
Ak,j is the amplitude of the j-th chip of user k; and nj is
demodulator
  as the a priori information to update {x̄k,j } and
the zero-mean, additive white Gaussian noise (AWGN) with 2
2
variance σch = N0 /2. σxk,j as follows
 
Chip-level iterative receiver for uncoded IDMA: The itera- x̄k,j = tanh 12 λrep (xk,j ) , and σx2k,j = 1 − x̄2k,j , (5)
LI et al.: ANALYSIS AND OPTIMIZATION OF INTERLEAVE-DIVISION MULTIPLE-ACCESS COMMUNICATION SYSTEMS 1975

which in turn are used by the chip demodulator to refine A. Large-system Approximation and EXIT Chart
its outputs as in (2)-(4) for the next iteration. In the last
iteration, the repetition decoder produces hard decisions d̂k We consider a spread-spectrum system with a total band-
for the information bits dk based on the a posteriori LLRs width of W Hz. Assume that each user sends information
{Λrep(dk,n )} for the uncoded case. at a rate of R bits/sec, then based on Proposition 1 in [19],

the bandwidth expansion factor is Ω = 2W/R. The bandwidth
Turbo multiuser detection for coded IDMA: Note that expansion Ω can be factored into a channel coding component
the above-described chip demodulator and repetition decoder with code rate Rc bits/symbol and a spreading component with
together form a multiuser detector; and it can be easily spreading gain S. Then we have Ω = S/Rc and Eb /N0 =
modified to accept the a priori information of the code 1
Rc Es /N0 = ΩEc /N0 , where Eb /N0 , Es /N0 and Ec /N0
bits from the channel decoder, with which a joint turbo denote the SNR of the information bit, code bit and chip,
detection/decoding scheme can be applied. To distinguish respectively.
from the inner iteration between the chip modulator and We consider the asymptotic analysis where both the number
the repetition decoder, we refer to the iteration between the of users K and the spreading gain S going to infinity while
multiuser detector and channel decoder as the outer iteration. 
keeping the system load β = K/S fixed. For such a large
We again focus on the chips related to dk,1 . For the inner CDMA system employing linear multiuser detectors, a fun-
iteration, the extrinsic information is given by λrep (ck,j ) = damental result, the
sk,j Λrep (dk,1 )−λdem (ck,j )+sk,j λdec (dk,1 ), where λdec (dk,1 )  Tse-Hanlyequation, is obtained in [18],
−1
is an extrinsic LLR delivered by the outer SISO channel given by γ1 = P1 σch 2
+ βEP P1P+P
P1
γ1 , where P1 and
decoder, submitted as an a priori information to the inner γ1 are respectively the code bit power and the output signal
iteration. After a given number of inner iterations between to interference and noise ratio (SINR) of the linear MMSE
the chip-level demodulator and the repetition decoder, the receiver for user 1; P denotes the power of interference from
extrinsic information λmud (dk,1 ) passed from the multiuser other users; and EP {·} denotes the expectation with respect
detector to the outer channel decoder is given by λmud (dk,1 ) = to the empirical distribution of the received powers of the
S interferers. Since the SISO IDMA chip demodulator can be
j=1 sk,j λdem (ck,j ) = Λrep (dk,1 ).
viewed as a special case of the SIC-MMSE detector, a large-
Note on computational complexity: The major computations system approximation analysis can be applied to approxi-
involved in the chip-level IDMA receiver are given by (2)-(5). mately characterize the performance of the chip demodulator.
Although (2) involves summations over all the K users, the Although such an approximation is not very accurate, it is
results are shared by all of the users, hence the related cost is still helpful in revealing the relationship between IDMA and
only two additions and two multiplications per user per chip CDMA under the framework of repeating-spreading tradeoff
per inner iteration. Several more simple operations per user which will be discussed in Section III-B.
per chip per inner iteration are required in (3)-(5). Overall, For an equal-power multiple-access system employing turbo
the normalized complexity per user per information bit per multiuser detection, the EXIT chart [16], [17] can be used
inner iteration increase linearly with the spreading length S to characterize the convergence performance of the joint
but is independent of the number of users K. For CDMA decoding scheme. For the EXIT chart analysis, we com-
system, the MAP-based detector has a complexity of O(2K ) putes the mutual information I between the BPSK mod-
per user per information bit per iteration; and SIC-MMSE ulated code bit {+1, −1} and the corresponding extrinsic
detector has a complexity of O(K) per user per information LLR λ exchanged between the detector and the decoder.
bit per iteration [22]. With the consistent Gaussian assumption on λ, i.e., λ ∼
N ( 12 σ 2 , σ 2 ), the mutual information is a function of the

III. P ERFORMANCE A NALYSIS single parameter σ, which is given by I = J(σ) = 1 −

∞ (ζ−σ 2 /2)2  
Next we first focus on the convergence property of the √ 1
2πσ2 −∞
e− 2σ2 log2 1 + e−ζ dζ. Since J(σ) is a
chip-level MUD receiver of IDMA systems. The spectral monotonically increasing function of σ, it is invertible with
efficiency analysis of the overall IDMA system will be given σ = J −1 (I).
in Section IV. In this section, two analytical tools, namely, The EXIT curve is the nonlinear transfer function
the large-system performance approximation and the Monte- Imud,out = u(Imud,in, Eb /N0 ) of the multiuser detector or
Carlo-based EXIT chart, are tailored in the context of IDMA Idec,out = v(Idec,in ) of the decoder which represents the
chip-level iterative receiver. With these tools, the IDMA mutual information transfer characteristic of the detector or
MUD receiver performance with or without outer channel the decoder. In general, the EXIT curve can be obtained by
codes can be analyzed. These tools are also employed in the Monte Carlo method with the assumption of large frame
Section IV for the spectral efficiency analysis and optimiza- size, as shown in [16], [17], [5]. Note that for short frame
tion in IDMA systems. Note that although the large-system- size, such an asymptotical analysis is not accurate and the
approximation-based method provides less accurate estimation EXIT band technique [5] can be used to reflect the effect of
about the IDMA receiver performance than the simulation- the short frame size. Also note that with more complexity than
based scheme, its low-complexity feature will be very helpful the large-system-approximation-based method, the simulation-
for the IDMA system analysis and optimization. Also, it based EXIT chart technique provides more accurate results. It
provides a clearer connection between the IDMA system and can also be employed in the analysis of system performance
CDMA system than the simulation-based method does. over ergodic fading channels.
1976 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 2007

Large System Approximation

B. Uncoded Performance 10
0

To facilitate an analysis, we consider an uncoded system

as shown in Fig. 1.(b) and (c). The information bits of a
given user are encoded by a rate-Rc repetition code with
Rc = 1/nr to form code bits which are then interleaved and Ω=256,K=128,Eb/N0=−2dB
−1
10
randomly spread with a processing gain of S = Ω/nr . At
the receiver, the extrinsic information is exchanged between finite system BER of CDMA

BER
the SIC-MMSE MUD and the single-user repetition decoders.
Ω=30,K=12,Eb/N0=4dB
With different nr and S while keeping Ω fixed, we have differ-
ent repeating/spreading scenarios. The conventional uncoded 10
−2 finite system BER of IDMA

CDMA system (nr = 1, S = Ω) and the uncoded IDMA

system (nr = Ω, S = 1) are the two extreme cases.
Ω=256,K=128,Eb/N0=6dB
Next we consider the large-system asymptotic analysis
based on the above repeating-spreading framework and the
−3
Tse-Hanly equation. For a fixed Ω, first we specify the 10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Code Rate (1/n )
degree of the repetition code nr , with which we obtain the r

corresponding spreading gain S. For a given number of users

Fig. 2. Performance of uncoded CDMA systems with different repeating-
K, the system load is β = K/S. Consider only the AWGN spreading configurations in AWGN channels.
channel, where we have hk,j = 1, ∀k, j in (1). Also assume
that Ak,j = 1, ∀k, j, and parallel iterative processing is K=12, Ω=30, equal power
0
utilized. With the total power of the spreading sequences being 10

normalized to unity, the code bit power is then Ω/nr A2k,j =

Ω/nr and the Tse-Hanly equation for the SIC-MMSE receiver
−1
10
can be written as [23]
 

 −1 1

 

2 λin

 1 + γ 1 − tanh (
nr σch
2
1 − tanh ( )
γmud = + βEλin 2
, −2
Ω mud
2 λin
)
10
2
BER

(6)
from which γmud can be solved numerically given the −3
10
single user

distribution of the a priori information of the code bit, which is 2

assumed to be consistent Gaussian, i.e., λin ∼ N (2γin , 4γin ),
single user bound
where γin is the SINR of λin and is initialized to 0 for the −4
10 MF CDMA
5

first iteration. Given γmud , the output extrinsic information of MMSE CDMA
IDMA (simulation)
the repetition decoder is also assumed to have a consistent IDMA (large system)
IDMA (SNR tracking)
Gaussian distribution, i.e., λrep ∼ N (2γrep , 4γrep ), with −5
10
0 1 2 3 4 5 6 7 8 9
γrep = (nr − 1)γmud , which is then used by (6) to obtain Eb/N0 (dB)

the output SINR of the MUD for the next iteration. We

Fig. 3. BER performance of uncoded IDMA/CDMA systems in AWGN
can thus track the SINRs exchanged between the MUD and channels.
the repetition decoder. For the last iteration, the SINR of
the a posteriori LLRs of the repetition decoder is given by
γΛrep = nr γmud . With the consistent Gaussian approximation nr = 1, 2) denote the simulated BERs. As expected, for high
√
of Λrep , the BER is given by Pb = Q( γΛrep ), where Eb /N0 , the difference between the finite-system performance

x
Q(x) = √12π −∞ e−t /2 dt.
2
and the large-system analysis result becomes significant for
Based on the above technique, Fig. 2 depicts the BER small spreading values. Specifically, the gap between the
performance of the turbo SIC-MMSE receiver in different IDMA system and the conventional uncoded CDMA with
repeating-spreading CDMA configurations in an AWGN chan- linear MMSE in a finite-system is larger than that predicted
nel with sufficient iterations, Code rate 1/nr = 1 corresponds by the large-system analysis.
to the conventional fully-spread uncoded CDMA system with Fig. 3 depicts the simulated BER performance as a function
a linear MMSE multiuser detector; and 1/nr < 1 corresponds of Eb /N0 of the uncoded IDMA system and the uncoded
to the iterative SIC-MMSE receiver with the aid of repetition conventional CDMA system with linear MMSE and MF
codes. Interestingly, it is seen from the figure that a non- detectors for K = 12 and Ω = 30. It is seen that, with only
rate-1 repetition code can always improve the BER perfor- one iteration (which corresponds to a one-pass of multiuser
mance with a turbo receiver. When comparing the two curves detection and decoding), the performance of IDMA is similar
with Eb /N0 = −2dB and 6dB for Ω = 256, it is seen to that of CDMA with the MF receiver; with two chip-
that with the increasing Eb /N0 , the difference between the level iterations, the IDMA detector outperforms the linear
fully-spread configuration and the non-fully-spread systems MMSE detector of CDMA with a gain of 1.5dB at a BER of
becomes significant. In the same figure, the crosses (with 10−3 . With 5 iterations, the performance of the IDMA system
nr = Ω which corresponds to IDMA) and diamonds (with approaches the single user bound at high SNR region which
LI et al.: ANALYSIS AND OPTIMIZATION OF INTERLEAVE-DIVISION MULTIPLE-ACCESS COMMUNICATION SYSTEMS 1977

shows the effectiveness of the chip-level iterative multiuser K=12, S=8, equal power
detection scheme. Also plotted in Fig. 3 is the estimated BER 1
0.001
performance of IDMA with the large system approximation. 0.01
0.9
It is seen that the performance of the finite IDMA system is
better than that of the large system approximation with a gain 0.8
trajectory

of around 0.5dB at a BER of 10−3 .

0.7
0.1
0.6

dec,in
C. Coded Performance

,I
0.5

mud,out
Next we compare the performance of the IDMA multi-
user detector with chip-level inner iteration with that of the 0.4

I
SIC-MMSE and SIC-MF detectors [22], [5], [23] in coded
scenario. For simplicity, we consider the AWGN channel, 0.3
CC (23,35)
where we have hk,j = 1, ∀k, j, in (1). Also assume that SIC−MF (AWGN)
0.2
Ak,j = 1, ∀k, j, and parallel iterative processing is utilized. SIC−MMSE (AWGN)
IDMA, 1 inner−iter (AWGN)
We first focus on the relationship between the IDMA detector 0.1 IDMA, 5 inner−iter (AWGN)
SIC−MMSE (Rayleigh)
and the SIC-MF detector. Since the chip demodulator is a IDMA, 5 inner−iter (Rayleigh)
special case of the SIC-MMSE multiuser detector [22], [5], 0
0 0.2 0.4 0.6 0.8 1
then similar to the EXIT chart analysis of turbo multiuser I ,I
mud,in dec,out
detection [5], the extrinsic LLRs can be well approximated
by the consistent Gaussian distribution. Based on (2)-(4) and Fig. 4. The EXIT charts of convolutional coded IDMA and CDMA systems
in the limit of large frame size. K = 12, S = 8, Rc = 1/2, Eb /N0 = 4dB.
(5), the average SINR of the output extrinsic LLRs of the
chip-level demodulator (4) can be written as
 λ 
rep
−1 0
10
K=12, S=8, equal power

γdem = σch
2
+ (K − 1)Eλrep 1 − tanh2 , (7)
2
5
where the a priori information λrep is also assumed to 1
1

be a consistent Gaussian random variable, i.e., λrep ∼ −1 2 5

10

N (2γrep , 4γrep ), with γrep being the corresponding SINR. 2

And for the first iteration, we have γrep = 0. Note that similar
to the large-system approximation given in (6), (7) can also be
BER

−2
10 single user AWGN
used to estimate the BER performance with the SINR tracking 5

technique which is considered in [10]. For the uncoded IDMA,

5
the estimated BER using (7) is plotted in Fig. 3. It is seen
5
that it is close to that of large system approximation. This −3
10

also suggests that the difference between the results observed IDMA, 1 inner−iter (AWGN)
CDMA, SIC−MF (AWGN)
IDMA, 5 inner−iter (AWGN)
for finite and large systems in Fig. 3 might be due to the CDMA, SIC−MMSE (AWGN)
IDMA, 5 inner−iter (Rayleigh)
independency assumption between different iterations made −4
CDMA, SIC−MMSE (Rayleigh)
10
in the SINR tracking technique instead of the large-system 0 0.5 1 1.5 2 2.5 3 3.5 4
Eb/N0 (dB)
approximation.
In the case that the chip-level inner iteration number is Fig. 5. BER performance of rate-1/2 convolutional coded IDMA and CDMA
one which corresponds to a one-pass of demodulation and systems with random spreading and joint detection. K = 12, S = 8,
despreading, with the consistent Gaussian assumption, the information block length is 128, AWGN channels. The iteration number
between multiuser detector and convolutional decoder is marked in the figure.
SINR passed from the multiuser detector to the decoder is
given by γmud = Sγdem . Note that we also have γrep = γdec ,
where γdec can be obtained by Monte Carlo simulation. Recall
that here S equals to the coded bit power, then with (7), the IDMA receiver with iteration number being one is similar to
output SINR of the IDMA multiuser detector is that of the uncoded CDMA with MF receiver.
Note that since the extrinsic information from the k-th outer
γmud = Sγdem decoder is spread by sk and used by the chip-level demodula-
2  −1
σch K −1 λdec tor during each inner iteration, with increasing inner iteration
= + Eλdec 1 − tanh2
, (8) number, the correlation between the input/output extrinsic
S S 2
information of the demodulator will also increase, in which
where λdec ∼ N (2γdec, 4γdec). Since for large K and S, case an analytical transfer function of the IDMA multiuser
(K − 1)/S  2 ≈ K/S = β, with S = ΩRc , we have detector may be inaccurate. Hence, we resort to Monte Carlo-
σch    −1
γmud ≈ ΩRc + βEλdec 1 − tanh2 λdec 2 , which co- based EXIT chart analysis to compare the performance of the
incides with the large-system asymptotic output SINR of IDMA multiuser detector and the SIC-MMSE detector.
the SIC-MF detector with S = ΩRc [23]. Hence it is not Consider equal-power convolutionally coded IDMA and
surprising to find in Fig. 3 that the performance of the uncoded CDMA systems with random spreading and turbo joint decod-
1978 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 2007

ing, where K = 12, S = 8, and the generator of the rate 1/2 and the simulation-based EXIT chart technique introduced in
convolutional code is (23, 35) in octal notation. Fig. 4 shows Section III are also applied to facilitate the spectral-efficiency
the transfer characteristics of the multiuser detector using the analysis and optimization below.
IDMA, SIC-MMSE and SIC-MF schemes in AWGN channel
for Eb /N0 = 4dB. Note that to obtain the EXIT curves, A. Turbo-Hadamard Coded IDMA Systems
we use a large frame size of 65536 in the simulations. It
is seen that, as expected, with only one inner iteration, the As discussed in Section II, for IDMA systems with separate
performance of the IDMA detector is similar to that of the channel coding, spreading and joint decoding, there are two
SIC-MF detector; however, with 5 inner iterations, the IDMA iteration loops: the chip-level inner iteration between the de-
detector provides a better mutual information than the SIC- modulator and the de-spreader, and the outer iteration between
MMSE detector. Fig. 4 also shows the EXIT curve of the the multiuser detector and the channel decoder. In CDMA
(23, 35) convolutional code and the trajectories of the coded systems, spreading can be achieved by low-rate coding, which
CDMA with SIC-MMSE and IDMA with 5 inner iterations. leads to the code-spread systems [21], [2]. Inspired by this, an
The iterative decoding process is a staircase trace between the alternative coded IDMA system can be obtained from uncoded
transfer curves of the detector and the outer channel decoder. IDMA by replacing the spreader/de-spreader in Fig.1.(a) with
It is seen that the system trajectories closely follow the transfer a low-rate channel encoder/decoder. Then there is only one
curves which indicates that the EXIT chart analysis is accurate. iteration loop between the chip-level demodulator and the
Fig. 5 depicts the bit error rate (BER) performance for an channel decoder.
information block length of 128. It is seen that the convergence The turbo-Hadamard code introduced in [8] is a class
speed of the IDMA system is faster than that of the CDMA of low-rate low-complexity turbo-like parallel concatenated
system with the SIC-MMSE detector, which is consistent with codes. It is reported that the turbo-Hadamard code can achieve
the EXIT chart analysis. In summary, with only one inner performance of BER= 10−5 at Eb /N0 = −1.2dB (only about
iteration (which corresponds to a one-pass of demodulation 0.4dB away from the ultimate low-rate Shannon limit) with
and de-spreading), the performance of the IDMA detector an information block size of 65534. In the following analysis
is similar to that of the SIC-MF detector. With increasing and optimization of the code-spread IDMA systems, the turbo-
number of inner iterations, its performance can be enhanced Hadamard code is employed.
and it can outperform the SIC-MMSE detector. Note that the
performance gain comes with expense, since with increasing B. Spectral Efficiency of IDMA with Equal Power Allocation
inner iteration number, the complexity of the IDMA receiver A fundamental performance metric of a multiple-access
is also increased. For instance, the SIC-MMSE receiver has a scheme is the spectral efficiency ν, defined as the total number
complexity of O(K = 12) per user per information bit per of bits per second per unit bandwidth (bits/sec/Hz) that can
iteration for the above example; whereas the IDMA receiver be transmitted with an arbitrarily low error probability. In
with 5 inner iteration has a complexity of O(5 × S = 40) per a CDMA system, the bandwidth is roughly equal to the
user per information bit per outer iteration, which is larger reciprocal of the chip duration, hence the spectral efficiency
than that of SIC-MMSE, but still significantly less than that of can be taken as bits per chip that the system can support.
the MAP detector which is O(2K = 4096). There is a tradeoff
between the convergence speed and the overall complexity for Spectral efficiency analysis: In case that all users employ
IDMA systems, and this also reflects the flexibility of the chip- an identical coding rate Rc (bits per symbol), the spectral
level IDMA receiver. efficiency of a CDMA system is given by ν = K S Rc , with
The EXIT chart technique can be easily extended for fading Ω = S/Rc as the total bandwidth expansion factor. For turbo-
channels. Consider an ergodic Rayleigh fading channel, the Hadamard coded IDMA, S = 1 and Rc = 1/Ω. For a given
EXIT curves of the CDMA SIC-MMSE receiver and the code, we use the largest number of users K ∗ that can transmit
IDMA receiver with 5 inner iterations are plotted in Fig. 4. It their bits reliably on the channel as a measurement of the
is seen that due to the temporal diversity that can be achieved system capacity. Clearly, K ∗ is a function of the SNR (Eb /N0 )
through chip-level interleaving, the advantage of IDMA in and Ω. Then the maximum spectral efficiency is
fading channel is larger than that of non-fading case. BER
∗ K ∗ (Ω, SNR)
performance of both systems in fading channel is also plotted νIDMA (Ω, SNR) = . (9)
Ω
in Fig. 5. It is seen that the IDMA system with 5 inner
In case that all users have equal power, and parallel itera-
iterations exhibits a significant gain over the CDMA system
tive processing is employed, K ∗ (Ω, SNR) can be accurately
with SIC-MMSE, which is consistent with the EXIT chart
obtained by the EXIT chart analysis [5].
analysis.
Numerical results: Here we present some numerical results on
IV. S PECTRAL E FFICIENCY O PTIMIZATION the spectral efficiency of a turbo-Hadamard coded equal-power
Next we conside the spectral efficiency analysis and opti- IDMA system in binary input AWGN (BIAWGN) channels.
mization of coded IDMA systems. According to [20], low- Fig. 6 depicts the spectral efficiency of two IDMA systems
rate code is necessary for a spectral-efficient multiple-access with Ω = 30 and 63, where the rate 1/30 and 1/63 turbo-
system. Therefore, we will concentrate on the low-rate coded Hadamard codes with generator polynomial 1/(1 + x) are
IDMA systems which is a special case of the coded IDMA sys- used, respectively. As shown in [13], the maximum spectral
tem considered in Section III. The large-system approximation efficiency (in bits/sec/Hz) of random CDMA with optimal
LI et al.: ANALYSIS AND OPTIMIZATION OF INTERLEAVE-DIVISION MULTIPLE-ACCESS COMMUNICATION SYSTEMS 1979

decoding is achieved when the system load β → ∞. The Spectral Efficiencies in the Single−cell Scenario in BIAWGN channel

Spectral Efficiency (bits/sec/Hz)

1
corresponding capacity is also known as the Cover-Wyner 0.8
multiple-access capacity of the conventional AWGN channel
and coincides with ∗the AWGN single-user capacity ν ∗ , im- 0.6
ν
Eb
plicitly given by 4 2ν−1
∗ = N 0
. It is seen from Fig. 6 that the 0.4
Cover−Wyner capacity of AWGN channel
low-rate coded IDMA system provides a near-capacity perfor- 0.2 Turbo−Hadamard Coded IDMA (Ω=30)
Turbo−Hadamard Coded IDMA (Ω=63)
mance (around 1.4dB away from the Cover-Wyner capacity 0
0 2 4 6 8 10 12 14 16 18
for ν = 0.5 with Ω = 63) at the low SNR region. Note that Eb/N0 (dB)
with BPSK modulation, the spectral efficiency of the equal- Spectral Efficiencies in the Multi−cell Scenario in BIAWGN channel

Spectral Efficiency (bits/sec/Hz)

1
power IDMA system with turbo detection is bounded by 1
0.8
bit/sec/Hz, which is the maximum capacity of an equal-power
CDMA system in BIAWGN channel [15]. 0.6

Now we consider a multi-cell IDMA system, in which 0.4 IDMA (no outcell interference, Ω=63)
IDMA (outcell power:−20dB, Ω=63)
the base station receives the sum of the in-cell signals and 0.2 IDMA (outcell power:−15dB, Ω=63)
the interference from neighboring cells. Similar to [23], here IDMA (outcell power:−10dB, Ω=63)
0
we treat a typical hexagonal cell structure and consider 0 2 4 6 8 10
Eb/N0 (dB)
12 14 16 18

the interference only from the first tier of the six nearest
neighboring cells. We assume that all cells have the same Fig. 6. Spectral efficiencies of turbo-Hadamard coded IDMA systems in both
number of users K. Let k = 1, ..., K, denote in-cell users, and single-cell and multi-cell scenarios. AWGN channel with BPSK modulation;
all the users in the same cell have the same power. The relative received
k = K + 1, ..., 7K, denote out-cell users. Again, assuming out-cell user power η is given in dB.
that Ak = A for k = 1, · · · , 7K, then the ζk,j in (1) be-
K 7K
comes k =1,k =k Ak hk ,j xk ,j + k =K+1 Ak hk ,j xk ,j +
nj which represents the overall distortion term respect to the Here we consider the application of the similar principle
k-th in-cell user. Since the transmitted data of the out-cells to low-rate coded IDMA systems. For simplicity, we consider
are unknown by the current cell, the mean and variance of only the equal rate, unequal power case.
{xk ,j } of the out-cell users are always assumed to be 0
and 1, respectively. With perfect CSI known at the receiver, Problem formulation: Consider a code-spread IDMA system
the total out-cell interference  is treated2 as2 additive noise with K users which are grouped into M classes. The number
with mean zero and variance 7K k =K+1 Ak hk ,j . In this way, of users in the m-th class is Km , and the class load βm =


the presence of the out-cell interference corresponds to a Km /S = Km (for low-rate coded IDMA, S = 1). Thus, the
M
degrading of the effective SNR when comparing with the total system load is β = m=1 βm users per chip. Users
single-cell scenario. With capacity-achieving low-rate turbo- in class m have the same received SNR γm . Without loss
Hadamard codes, the IDMA system is expected to perform of generality, we assume γ1 ≤ · · · ≤ γ M . The total system
well in multi-cell scenarios. spectral efficiency is then given by ν = M m=1 βm Rc = βRc ,
Fig. 6 also depicts the spectral efficiency of the turbo- where Rc is the coding
M rate. It is clear that the total received
Hadamard coded IDMA system with Ω = 63 in the multi- SNR per chip is m=1 βm γm , with which a total number of
M
cell scenario. Due to the pass loss, the relative received signal m=1 βm Rc bits are transmitted. Hence the average Eb /N0
power level of the out-cell users are set to −10dB, −15dB over the K users (denoted as the “system” Eb /N0 ) is
and −20dB, respectively. It is seen that a substantial loss is  M M
Eb  m=1 βm γm βm γm βT γ
observed when the out-cell power level is relatively high. = M = m=1 = , (10)
N0 sys 2 m=1 βm Rc 2βRc 2βRc
 
where β = [β1 , · · · , βM ]T is the class load vector, γ =
C. Optimal Power Allocation in IDMA Systems [γ1 , · · · , γM ]T is the power profile vector, and the factor 2 in
As shown in Fig. 6, with binary codebooks and equal the denominator comes from the fact that we only consider
rate equal power configuration, the IDMA system capacity is a one dimension real channel [20]. Then the optimization
bounded by 1 bit/sec/Hz which is also the maximum capacity problem is to jointly find β and γ which minimize the
of the multiple-access BIAWGN channel with equal rate equal (Eb /N0 )sys defined in (10) subject to the constraint that the
power configuration [15]. Recent result shows that, with rate target system spectral efficiency ν is met (In practice, this is
or power control along with the stripping decoding scheme, the normally evaluated in terms of the resulting BER of each user
optimal spectral efficiency can be approached even with finite being smaller than a threshold, e.g., 10−5 ) with a particular
input constellations, e.g., BPSK or QPSK [1]. Two schemes decoding scheme.
were proposed in [1]: the equal rate, unequal power scheme; To avoid solving the above joint optimization problem
and the equal power, unequal rate scheme. In both cases, which is hard to tract, we may resort to the following two
users are divided into M classes. Users in the same class simpler sub-optimal approaches: (1) fix the received power
are decoded in parallel by a bank of single-user decoders, levels γ, and consider the optimization of the class loads
while classes are stripped off in the decreasing SNR order for β; (2) fix the class loads β and optimize the power levels
equal-rate case or in the increasing rate order for equal-power γ. Note that for IDMA systems the class loads {βm =
case. Km } are discrete integers. To avoid a discrete optimization
1980 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 2007

problem, here we consider the second approach, in which the tion of class m passed from the decoder to the demodulator for
optimization variables {γm } are continuous. It is clear that the next iteration is given as Idem,in (m) = v(Idem,out (m)),
the received energy should be non-negative, hence we have where the mutual information transfer function of the decoder
γ ≥ 0. Then, with a given channel code C and detection Idec,out = v(Idec,in ) can again be obtained by Monte Carlo
scheme, the optimization problem we are interested in can be simulations. After a given number of iterations, as in Sec-
formulated as follows: find γ ≥ 0 for a given β with which we tion III-A, the BER performance Pb (m) can be estimated
minimize (Eb /N0 )sys , subject to the constraint that the worst by Pb (m) = Q(J −1 (IΛdec (m))/2), with Λdec denoting the
BER among the M classes is less than a specified threshold output LLR of the decoder for the information bit, and the

. Mathematically, mutual information IΛdec (m) = ϕ(Idec,in (m)), where the

   transfer function ϕ(·) depends upon the decoder which can
Eb βT γ be obtained by Monte Carlo simulations.
γ opt = arg min = arg min ,
γ ∈RM N0 sys γ ∈RM 2βRc To speed up the optimization procedure, an SINR-tracking
s.t. max Pb (m) ≤
, and γ ≥ 0, (11) method is proposed in [10] which utilizes the result of (8). As
m
can be seen in Fig. 3, since the estimated BER of this method
where maxm Pb (m) denotes the worst BER among the is worse than that of the large-system approximation method,
M class users. Note that in [10], unequal power allocation here we consider the large-system approximation scheme.
for IDMA system is also considered, whereas only parallel Extending from the Tse-Hanly equation, the output SINR of
detection scheme is included in the optimization formulation. the chip demodulator for class m is the unique solution of
In this paper we consider a broader configuration where either
γdem (m) =
the parallel turbo detection strategy or the successive group     

1 +  β
−1
λi
γi 1 − tanh2
 
(12)
M
stripping detection strategy can be utilized.
γm i Eλ i
1 + γdem (m)γi
 2
λi
i=1 γm
1 − tanh 2
2
The optimization procedure: Note that for IDMA systems,
extrinsic information is exchanged between the chip demodu- 
σi2
where λi ∼ N 2
2 , σi with σi = J −1 (Idem,in(i)). Given
lator and single-user decoders. And the optimization problem
M
considered here is similar to the one encountered in the the input mutual information {Idem,in(i)}i=1 , γdem(m) can be
irregular LDPC code design, where a powerful population- solved numerically, with which wecan obtain the output mu-

based genetic algorithm called differential evolution (DE) [11] tual information Idem,out (m) = J 2 γdem (m) . As shown
is utilized to find the degree profile of the irregular LDPC in Fig. 2 and Fig. 3, although the large system approximation
codes [12]. The essential idea behind DE is a self-organizing generally provides a pessimistic estimation on the output SINR
scheme to generate a trial parameter vector by adding the of the chip demodulator, the estimation is satisfactory and
weighted difference between two population vectors of the helpful. As we will see from the numerical results in the next
current generation to a third vector which is the target vector. If subsection, the application of large system approximation in
the trial vector has a smaller cost value than the target vector, it the power optimization problem also give a satisfactory design
survives into the next generation of the evolution. After a given results.
number of evolutions, the vector with the smallest cost value In the case that the successive group stripping detection
among the population of current generation is the optimized and the capacity approaching codes (e.g., LDPC codes, turbo
parameter vector. Note that although there is no mathematical codes and turbo-Hadamard codes) are utilized, the above
convergence proof of DE, it is believed to be a simple and optimization procedure can be further simplified. Note that,
reliable global optimization method. a key feature of the capacity-approaching codes is that they
To solve (11) for a given β, we first choose a system Eb /N0 are characterized by the rate-threshold pair (Rc , g), such that
and find a vector γ using DE that satisfies the BER constraint if the received SNR ≥ g, the BER can be made arbitrarily

. If at least one γ exists, the system Eb /N0 is reduced and small for large block size. Assuming that all users in classes
the procedure is repeated until no such a vector γ exists. The m + 1, · · · , M have been perfectly canceled, the successive
least value of system Eb /N0 for which a power profile γ decodability condition is that the output SINR of the chip
satisfies the BER constraint is the desired minimum system demodulator after only one pass for the m-th class γdem (m)
SNR and the corresponding γ is the optimized power profile. should be no less than g, for m = M, · · · , 1. Since it is a
During differential evolution, in order to obtain the BERs one-pass detection, λi in (12) is initialized to 0. With these
{Pb (m)} for a given β and γ, we resort to the following assumptions, (12) becomes
mutual information tracking method. Since the received SNR  m
−1
 γi
γm might be different for different class, for parallel turbo γdem (m) = γm 1 + βm . (13)
detection, the input/output mutual information of the chip i=1
1 + γdem (m) γγmi
demodulator for different class users at each iteration might
Again, the optimal power profile can be obtained by differ-
also be distinct, which can be denoted as Idem,in(m) and
ential evolution. Note that the performance could be further
Idem,out (m), for m = 1, · · · , M , respectively. With given
improved by taking into account the inner parallel iteration
{Idem,in(m)} and {γm }, we can obtain {Idem,out (m)} by
within the same group.
Monte Carlo simulations, which is similar to the procedure for
equal power case discussed in Section III-A. Since all the users Example 1 - Uncoded IDMA with power allocation and
employ an identical single-user decoder, the mutual informa- parallel processing: Consider an uncoded IDMA system with
LI et al.: ANALYSIS AND OPTIMIZATION OF INTERLEAVE-DIVISION MULTIPLE-ACCESS COMMUNICATION SYSTEMS 1981

Ω=8,K=8,Eb/N0=10.3dB Uncoded IDMA with Ω=8 (BIAWGN channel)

15
1
dem, Eb/N0=8dB
dem, Eb/N0=12dB
10
dem, Eb/N0=16dB
γk (dB)

rep decoder
0.8
5

0
1 2 3 4 5 6 7 8
k 0.6

rep,in
Ω=8,K=16,Eb/N0=13.55dB
15

,I
dem,out
10

I
0.4
γ (dB)
k

0.2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
k

Fig. 7. The optimized power profile for an uncoded IDMA system with
Ω = 8. The maximum iteration number is set to 20, and the BER threshold 0
0 0.2 0.4 0.6 0.8 1
is 10−4 . Parallel iterative detection. Idem,in, Irep,out

Uncoded IDMA with Ω=8 (BIAWGN channel) Fig. 9. The EXIT chart of an uncoded IDMA system with equal power
0
10
profile. Ω = 8, K = 16, and BIAWGN channel.

−1
10 Eb /N0 = 8, 12 and 16dB. It is seen that due to the multiuser
10 20
interference, there is no an open detection tunnel between
the EXIT curves of the chip demodulator and the repetition
15 decoder/de-spreader, which means that the chip-level iterative
BER

10
−2
20
detection cannot converge to the low BER region at the given
SNRs.
5
With unequal power configuration, it is seen from Fig. 8
−3
20
that, the system successfully converges and reaches the target
BER 10−4 at an SNR of around 11.8dB with 20 iterations.
10

single user bound Note that the large-system approximation result is 13.55dB.
K=8 with optimized power
K=16 with equal power This is due to the fact that, in general the large-system
K=16 with optimized power
10
−4
approximation provides a relatively pessimistic estimation on
0 2 4 6 8 10 12 14 16
Eb/N0 the BER performance. Interestingly, as shown in Fig. 8, at
the low SNR region, the BER performance with optimized
Fig. 8. The BER performance of the worst user in an uncoded IDMA system
with Ω = 8. The iteration number is marked in the figure and the length of
power profile is slightly worse than that with equal power
the information block is 4000 bits per user. configuration. The main reason is that at low SNR, even those
users with larger power cannot successfully decode, a situation
that makes the BERs of the low-power users even worse.
Ω = 8 and parallel iterative detection as described in Section Example 2 - Turbo-Hadamard coded IDMA with power allo-
II. Setting the class number M = K, and a target BER
= cation and stripping decoding: Here we use the rate-1/52.9
10−4 for 20 iterations, we obtain the optimized power profile turbo-Hadamard code which is only 0.4dB (measured at BER
γ using differential evolution with large-system approximation = 10−5 ) away from the ultimate Shannon limit with a
of the chip demodulator, which is plotted in Fig. 7 for K = 8 interleaver size of 65534. The SNR threshold of the code
and 16, respectively. For K = 8, the equal power configuration g = −15.43dB. Assuming stripping decoding and adopting
turns out to be the optimal one, whereas for K = 16, a the large-system approximation, with 4 users/class, we can
nonuniform power profile is obtained. obtain the optimized power profiles for K = 76 and 104 with
The BER performance of the worst user is given in Fig. 8 Eb /N0 = 4.8dB and 7.4dB, respectively. We simulated the
with a block size of 4000. It is seen that the power profiles above two IDMA systems with soft-stripping decoding which
obtained with the large-system approximation work very well are marked in Fig. 10. For K = 76, the simulated Eb /N0 =
in the IDMA system. For K = 16, a significant improvement 5.0dB with N = 4900 and 30 iteration for a BER less than
is observed with the optimized power profile when comparing 10−5 , which is only around 1.5dB away from the capacity. For
with the equal power configuration. The poor performance K = 104, the simulated Eb /N0 = 7.5dB with N = 4900 and
of the equal power IDMA system with K = 16 can be 30 iteration for a BER less than 10−5 , which is around 1.6dB
explained by its EXIT charts which is plotted in Fig. 9 for away from the capacity. Also plotted in the figure is the result
1982 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 2007

Equal−rate IDMA in BIAWGN channel

5 a promising and flexible air-interface technique for heavily-
Cover−Wyner capacity of AWGN channel
Turbo−Hadamard coded IDMA with unequal power (rate 1/52.9, M=K)
loaded multiple-access systems.
4.5 Turbo−Hadamard coded IDMA with equal power (rate 1/63)

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LI et al.: ANALYSIS AND OPTIMIZATION OF INTERLEAVE-DIVISION MULTIPLE-ACCESS COMMUNICATION SYSTEMS 1983

Kai Li received the B.S. degree in Electronics Li Ping (S’87-M’91) received his Ph.D. degree
and Information Science from Peking University, at Glasgow University in 1990. He lectured at
Beijing, China, in 2000, and the M.Eng. degree Department of Electronic Engineering, Melbourne
in Electrical and Computer Engineering from Na- University, from 1990 to 1992, and was a research
tional University of Singapore, Singapore, in 2002. staff at Telecom Australia Research Laboratories
He is currently pursuing the Ph.D degree in the from 1993 to 1995. He has been with the De-
Department of Electrical Engineering, Columbia partment of Electronic Engineering, City University
University, New York, NY. His research interests of Hong Kong, since January 1996 where he is
include wireless communications, signal processing, now a professor. His research interests are mixed
information theory, codes on graphs and iterative analog/digital circuits, communications systems and
algorithms. coding theory. He received a British Telecom - Royal
Society Fellowship in 1986, the IEE J. J. Thomson premium in 1993 and the
Xiaodong Wang (S’98-M’98-SM’04) received the Croucher Foundation Award in 2005.
Ph.D degree in Electrical Engineering from Prince-
ton University. He is now on the faculty of the Elec-
trical Engineering Department, Columbia Univer-
sity. Dr. Wang’s research interests fall in the general
areas of computing, signal processing and communi-
cations, and has published extensively in these areas.
Among his publications is a book entitled “Wireless
Communication Systems: Advanced Techniques for
Signal Reception”, published by Prentice Hall in
2003. His current research interests include wireless
communications, statistical signal processing, and genomic signal processing.
Dr. Wang received the 1999 NSF CAREER Award, and the 2001 IEEE
Communications Society and Information Theory Society Joint Paper Award.
He currently serves as an Associate Editor for the IEEE Transactions on
Communications, the IEEE Transactions on Wireless Communications, the
IEEE Transactions on Signal Processing, and the IEEE Transactions on
Information Theory.