1780 ieee transactions on mobile computing, vol. 5, no. …jordan/papers/tmc-2006.pdf · 2013. 9....

Dynamic Resource Allocation inCDMA Systems with DeterministicCodes and Multirate Provisioning

Iordanis Koutsopoulos, Member, IEEE, Ulas C. Kozat, Member, IEEE, and

Leandros Tassiulas, Senior Member, IEEE

Abstract—Next generation wireless CDMA systems will provide high and variable data rates by using multicode structures,

controllable code spreading gains, and transmit power adaptation. We address the emerging resource allocation problem in that

context and consider maximizing the total achievable user rate while satisfying minimum rate requirements of users. We devise

symbol-synchronous and asynchronous models that capture different communication scenarios. The synchronous model holds for

down-link transmission in one cell. The asynchronous model captures up-link single-cell communication and down-link or up-link

scenarios in multicell systems. It can also account for multipath with each path corresponding to a virtual user. We propose a class of

two-stage resource allocation algorithms. First, an admissible set of codes is constructed with criteria that capture code cross-

correlation, induced interference to the system, and code rates. Next, the codes are allocated to users so as to satisfy their rate

requirements. In the synchronous case, the problem structure allows the distinction of the two stages. In the asynchronous case, this

distinction is not feasible due to different user delay profiles perceived at the receiver. Our models and numerical results indicate

interesting trends and lead to useful conclusions and design guidelines for resource allocation algorithms under the aforementioned

regimes.

Index Terms—Wireless communication, code division multiple access, resource allocation, power control, cross-layer design.

Ç

1 INTRODUCTION

THE last frontier in wireless networks is the ability toguarantee high and variable data rates to users so as to

support the novel emerging applications that involvetransfer of voice, video, or data for resource-demandingservices. The prevalent UMTS CDMA third generation (3G)standard relies on direct-sequence code division multipleaccess (DS-CDMA) for delivering wireless access to users.In DS-CDMA, user symbols are modulated by a high-ratechip sequence, the spreading code, or signature sequence.The number of chips per symbol is called spreading gain.Many users can simultaneously transmit in the same widefrequency band if codes with certain cross-correlationproperties are properly assigned to them. User quality ofservice (QoS) requirements are usually expressed in termsof achievable data rates, signal-to-interference-and-noiseratios (SINRs), or maximum bit error rate (BER) guarantees.

The extent to which QoS requirements are fulfilled in 3GCDMA systems depends on several factors. First, the natureand properties of signature sequences that emanate fromcode design or code generation mechanisms signify theirimpact on performance. Second, the machinery of resourceallocation to users is critical. The available resources are

usually the spreading codes and the transmission power.Depending on user rate requirements, code properties, userchannel qualities, and resource availability, multiple codeswith different spreading gains can be allocated to users.Codes with low spreading gain provide high data rates butthey lead to low diversity gain against channel impairmentsand cannot effectively suppress interference. A similartrade-off exists for high spreading gain codes. On the otherhand, transmission power adaptation can control andsuppress interference [2]. Finally, the type of signalprocessing at the receiver, namely, the kind of receiverfilter, is another factor that determines reception qualityand affects performance. Although 3G systems includemulticode structures, modulation, and power control, aswell as controllable spreading gains per code [3], the preciseresource allocation algorithms in the standards remainunspecified. Still, for a given code design methodology,these algorithms collectively determine the achievable ratesfor system users.

With regard to the nature of signature sequences, twoapproaches can be identified in the literature. The first oneassumes deterministic signature sequences and focuses ontheir design so as to maximize a capacity metric. The set ofWelch bound equality (WBE) codes was first identified in[4] as the sequence set that minimizes total squared cross-correlation (TSC) and achieves the Welch bound. For asingle-cell synchronous CDMA system with given spread-ing gain and equal or unequal received powers, [5] and [6],respectively, have shown that WBE sequences maximizeuser capacity, defined as the number of supportable users ata common SINR target. In [7], an iterative technique fordistributed signature sequence update of users is proposed,

1780 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 12, DECEMBER 2006

. I. Koutsopoulos and L. Tassiulas are with the Department of Computer andCommunications Engineering, University of Thessaly, Gklavani 37 & 28Octovriou—4th floor, Volos, GR 38 221, Greece.E-mail: {jordan, leandros}@uth.gr.

. U.C. Kozat is with DoCoMo Labs USA, 181 Metro Drive, Suite 300, SanJose, CA 95110. E-mail: [email protected].

Manuscript received 22 Sept. 2005; revised 9 Feb. 2006; accepted 21 Mar.2006; published online 16 Oct. 2006.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TMC-0283-0905.

1536-1233/06/$20.00 � 2006 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS

which turns out to converge to the code set with theminimum TSC. A different approach is discussed in [8] andfocuses on the assignment of orthogonal variable spreadingfactor (OVSF) codes. The objective is to minimize the cost ofcode reassignment for new admitted users, given that thetotal bandwidth demand is less than the rate of a code tree.

The second approach considers randomly generatedcodes with fixed expected cross-correlation and SINRs thatdepend only on received powers and spreading gains. Thefocus is on spreading gain and transmit power controlmethods that maximize system throughput. In [9], theauthors study spreading gain adaptation policies foroptimizing the performance of multiservice CDMA interms of number of real-time and non-real-time users.Transmit power control for multicode CDMA with a fixedspreading gain and for single-code CDMA with variablespreading gains is studied in [10]. Joint spreading gain andtransmit power control for maximum system throughput,expressed as a function of rate and amount of retransmis-sions, is considered in [11]. In [12], the authors optimizesystem throughput for different kinds of receivers byselecting the number of utilized codes and the modulationlevels of users.

With respect to the mode of signal reception, determi-nistic code models can further be classified into symbol-synchronous, such as the ones in [4], [5], [6], [7], andsymbol-asynchronous ones. In the latter, symbol epochs ofdifferent users are not aligned at the receiver and symbolsare received at different time instants depending on the userdelay profile. Such models capture the lack of coordinationof user transmissions as well as the different traversedpaths for transmitted signals to the receiver. The problem ofcode design for an asynchronous system with a given userdelay profile and matched filter receivers was studied in[13] for equal received powers and in [14] for unequalreceived powers. It was shown that the so-called asynchro-nous WBE signature sequences maximize user capacity andminimize total squared asynchronous cross-correlation(TSAC). Then, user capacity is the same as that of thesynchronous CDMA system. The recent work in [15]resolved the issue of code design for arbitrary user delayprofiles and received powers.

The main characteristic of these approaches is theunderlying assumption that the spreading gain is fixed forcases of deterministic codes and is controllable only in casesof random codes. Furthermore, existing works focus solelyon physical layer aspects such as code design, spreadinggain control, and transmit power adaptation. However,existing multicode formats and advanced system capabil-ities for controlling the transmission mode in recentlyproposed wireless standards tend to expose the significanceof access control as well. In that context, the problem ofcode allocation to users obtains an interesting twist since itdetermines channel access for users. Since physical layerparameters can be at the disposal of the access controller,the necessary joint consideration of physical and accesslayer mechanisms becomes tractable as well. Inspired by theexistence of such functionalities, we investigate the problemof assigning deterministic variable-spreading-gain codes to

users with different rate requirements with the objective toincrease achievable system rate.

The contribution of our work to the current literature canbe summarized as follows:

1. We treat codes as deterministic known sequencesrather than adopting the overly-simplifying rando-mized models,

2. we introduce the variable-spreading-gain codestructures in the problem formulation,

3. we allow transmit power control, and4. we define symbol-synchronous and asynchronous

models that capture the impact of system parameterson the design and performance of resource alloca-tion algorithms.

We introduce a class of heuristic algorithms based onreadily measurable metrics such as code cross-correlation,induced interference, and rate contribution. We firstconsider the synchronous system that reflects the situationencountered in single-cell down-link transmission. Next,we extend our framework to asynchronous models that areapplicable to up-link single-cell or multicell scenarios and totransmission over channels with multipath. Interestingly,the problem structure suggests a different treatment for thesynchronous and asynchronous cases. While code admis-sion and allocation are distinguishable in the former case,they need to be jointly considered in the latter one.Compared to our preliminary work in [1], in this work,we introduce the dimension of transmit power control withassociated admissibility conditions and allocation metricsfor both cases above. We also present and formalize theasynchronous reception model and demonstrate how itcaptures the communication scenarios above. Further, weassess system sensitivity to asynchronism and show theeffect of power control on performance. Our approach fallssquarely within the context of cross-layer design in thesense that it studies the impact of physical layer parameters(such as code properties, transmission power, and symbolasynchronism) on access layer code allocation.

The rest of the paper is organized as follows: Sections 2and 3 treat the synchronous and asynchronous cases.Numerical results are presented in Section 4. Finally,Section 5 concludes our study.

2 THE SYMBOL-SYNCHRONOUS CASE

2.1 System Model

We consider down-link transmission in a single-cell symbol-

synchronous DS-CDMA system withM deterministic binary

antipodal codes fsigMi¼1 available at the base station (BS). The

codes are at the disposal of the BS as the outcome of a code

design algorithm or a method for code generation. Each

code si has different spreading gain Ni and the maximum

spreading gain is denoted by Nmax. Let ci denote the norm-

alized version of si, so that ci 2�� 1ffiffiffiffi

Ni

p�Ni for i ¼ 1; . . .M and

cTi ci ¼ 1, where superscript ð�ÞT denotes the transpose

operation. We assume antipodal BPSK modulation, so that

one symbol carries one bit. A code ci of spreading gain Ni is

associated with rate rðciÞ ¼ rðsiÞ ¼ 1=ðTcNiÞ bits/sec, where

KOUTSOPOULOS ET AL.: DYNAMIC RESOURCE ALLOCATION IN CDMA SYSTEMS WITH DETERMINISTIC CODES AND MULTIRATE... 1781

Tc is the (common for all codes) chip duration. Spreading

gains are assumed to satisfy the following condition that

enables framing at any receiver: Each spreading gain is the

common multiple of all other spreading gains of lower value.

An underlying slotted frame of some duration is also

assumed. The slot duration Td is imposed by Nmax so that

Td ¼ NmaxTcL, where L is the number of symbols that are

carried by the longest code in a slot.There exist K users in the system. In the symbol-

synchronous case, we assume that the channel from the BSto user k is characterized by slow flat fading that is reflectedin link gain hk that captures path loss and shadowing. Linkgains may change between consecutive slots. Since anti-podal BPSK modulation is employed for all users, thesymbol of user k, bk satisfies bk 2 f�1; 1g. Codes are shortwith length equal to a symbol duration and they arerepeated at each symbol interval. Each user k has aminimum bit rate requirement of rmin;k bits/sec for carryingreal-time traffic. Several codes can be allocated to each userso as to satisfy rate requirements. However, the sets ofcodes of different users must be disjoint; that is, each codecan be assigned to at most one user. Let C denote the set ofM codes. Let Ck be the set of codes assigned to user k andC0 ¼

SKk¼1 Ck � C be the set of allocated codes to all users.

Assume for now that codes of spreading gain N areused. The transmitter of user k consists of jCkj conventionalDS-CDMA transmission modules, one for each codeallocated to user k. Each user symbol is transmitted byone of these modules. The signal at the input of the receiverof user k at a symbol interval is given by

yk ¼XKn¼1

Xcj2Cn

ffiffiffiffiqjp ffiffiffiffiffi

hkp

bjncj þ n; ð1Þ

where bjn is the symbol of user n that is carried bycode cj 2 Cn, qj is the transmit power assigned to thesymbol carried by code cj, and n is an N � 1 vector of whiteGaussian noise with zero mean and a correlation matrix �2I.The receiver of user k consists of a bank of jCkj matchedfilters, each of which is matched to an allocated code ci 2 Ck.In the synchronous case, all received symbol epochs arealigned at the receiver.

The signal at the output of the matched filter tocode ci 2 Ck is yik ¼ cTi yk. We can view the double summa-tion in (1) as the summation over all used system codes.From (1), we can write yik as

yik ¼ffiffiffiffiffihk

p Xcj2C0;j6¼i

ffiffiffiffiqjp

�ijbj þffiffiffiffiqip

�iibi

0@

1Aþ ni; ð2Þ

where bj is a user symbol carried by code cj 6¼ ci. The firstterm in the parentheses above is the interference at thematched filter receiver to code ci due to utilized codes otherthan ci, the second term is the useful signal carried by ci,and the last term is noise. Furthermore, �ij is the cross-correlation between codes ci and cj, defined as �ij ¼ cTi cjwith �ii ¼ 1. It should be noted that the interference termabove for code ci of user k is due to codes of all other usersand due to codes of user k other than ci.

Now, consider codes ci and cj with unequal spreading

gains Ni 6¼ Nj and denote their cross-correlation by

�ij ¼ cTi cj, with �ii ¼ 1. Let ~�ij ¼ sTi sj be the cross-correlation

of unnormalized codes si and sj, so that �ij ¼ ~�ij=ffiffiffiffiffiffiffiffiffiffiffiNiNj

p.

We now proceed to the derivation of the expression for ~�2ij

when Ni 6¼ Nj. We introduce the following notation for a

code si ¼ ½si;1; . . . ; si;Ni�T of spreading gain Ni:

. sðkÞi : A new code, formed by concatenating code si to

itself k� 1 times, e.g, sð2Þi ¼ ½si si�

T , sð3Þi ¼ ½si si si�

T ,

etc.. s

ð‘;LÞi : The ‘th L-length subsequence of si, namely

sð‘;LÞi ¼ ½si;½1þð‘�1ÞL�; . . . ; si;ð‘LÞ�T , for ‘ ¼ 1; . . . ; Ni=L,

with Ni being a multiple of L, e.g., if s1 ¼½þ1þ 1� 1� 1�T and L ¼ 2, then s

ð1;2Þ1 ¼ ½þ1þ 1�T

and sð2;2Þ1 ¼ ½�1� 1�T .

Consider the following example with codes s1, s2, and s3

of spreading gain 4, 8, and 16, with s1 ¼ ½þ1� 1þ 1� 1�T ,s2 ¼ ½þ1þ 1þ 1� 1� 1� 1þ 1þ 1�T , and

s3 ¼ ½þ1þ 1� 1� 1þ 1þ 1� 1� 1

þ 1þ 1� 1� 1þ 1þ 1� 1� 1�T ;

depicted in Fig. 1. Consider the squared cross-correlation~�2

21 between s2 and s1. The matched filter to the longercode s2 at Ts2

sees two replicas of the shorter code s1 in asymbol period Ts2

. Then, ~�21 becomes the inner product ofs2 and the concatenated version of s1. Now, considersquared cross-correlation ~�2

23 between s2 and s3. Thematched filter for the shorter code s2 at Ts2

sees twosubsequences of the longer code s3, each of length 8, and theSINR requirement for s2 should be satisfied for all suchsubsequences. It is thus meaningful to consider the worst-case SINR, which occurs when the squared cross-correlationbetween s2 and one of the two subsequences is maximum.The explicit expression for the squared cross-correlation ofcodes si and sj with spreading gain ratio R ¼ Nj=Ni is

~�2ij ¼

sTi sð1=RÞj

� �2; if Ni > Nj

maxk¼1;...;R

sTi sðk;NiÞj

� �2; if Ni < Nj:

8><>: ð3Þ

The expression for the SINR at the output of the matchedfilter to code ci or si 2 Ck is

SINRiðqÞ ¼qiP

cj2C0:j 6¼iqj�

2ij þ �2

¼ qiNiPsj2C0:j6¼i

qj~�2ij

Njþ ~�2

ð4Þ

with ~�2 ¼ Ni�2=hi.

1 A remark on transmission powercontrol needs to be made here. Under the slow fadingassumption, the period of transmit power update for allcodes is one slot as in the UMTS standard. This impliesthat all L symbols carried by a code cj of spreading gainNmax in a slot are assigned transmit power qj and allLNmax=Ni symbols transmitted with a code ci of spreading


1. Note that spreading gains affect noise power in this expression; it willbe assumed that interference is the major limitation rather than noise.

gain Ni < Nmax in a slot are assigned power qi. Forinstance, in UMTS, there are 2,560 chips per slot and thespreading gain range is 4� 256 chips for the down-linkand 4� 512 chips for the up-link.

The existence of a feasible power vector, namely, a vector

that satisfies the SINR constraints above, does not depend

on noise. Hence, for the purpose of identifying a feasible

power vector, our system can be assumed interference-

limited, so that the SINR can be replaced by the SIR. The

BER at the output of each matched filter to each code should

satisfy BER � �, where � is a predefined value. The

minimum required SIR for BER � � is given by a threshold

� ¼ � lnð5�Þ=1:5 for BPSK.

2.2 The Problems of Code Admission and CodeAllocation

A code with small spreading gain leads to short symbolduration and incurs high transmission rate. If such codes areassigned to a user, the user will need fewer codes to coverhis rate requirements. This implies that more codes remainfree for assignment and, thus, user capacity is increased.However, a code with small spreading gain results in lowSIR and also induces high cross-interference to other codes,as (4) suggests. Since low-spreading-gain codes reduce userSIRs, they do not improve user capacity. A similar trade-offbetween rate provisioning and the amounts of sustainable orinduced interference exists for codes with large spreadinggain. Therefore, it is not clear which of the following optionsleads to higher total achievable rate: more codes of largespreading gain or fewer codes of small spreading gain.

Ideally, we would like to use as many codes of low

spreading gain as possible. For a set of codes with different

pairwise cross-correlations, it is important to identify these

codes that will be employed for transmission in the presence

of the conflicting situation above. The adoption of power

control on a per-code basis as another dimension toward

interference avoidance and increase of provisioned data

rates makes the problem more challenging.The procedure for employing a set of codes for

transmission consists of two stages: 1) admission of codes

in the system and 2) allocation of admitted codes to users. A

subset of used codes out of the M available ones is specified

by a binary activation vector ði1; i2; . . . ; iMÞT , where ij ¼ 1 if

code cj is selected for transmission to a user and ij ¼ 0

otherwise. Let I denote the set of all code activation vectors.

Admission of a code set corresponds to determination of an

appropriate activation vector from I . Assume that the

selected activation vector corresponds to a set S ¼fc1; . . . ; cmg of m �M used codes. Define the m�m matrix

RS with elements Rij ¼ �2ij, the squared cross-correlations

of normalized codes ci, cj 2 S, for i; j ¼ 1; . . . ;m. Define the

code transmit power vector as q ¼ ðq1; . . . ; qmÞ with qi > 0.

The set of codes S is called admissible if there exists a

transmit power vector such that SIRi � for symbols

carried by all codes ci 2 S. This condition can be written in

matrix form as

1þ ��

q RSq: ð5Þ


Fig. 1. Illustrative example for the cross-correlation between codes of different spreading gains.

Matrix RS is nonnegative. From the Perron-Frobenius

theorem, if RS is irreducible as well, it has a positive, real

eigenvalue �maxðRSÞ ¼ maxifj�ijgmi¼1, where �i, i ¼ 1; . . . ;m

are the eigenvalues of RS . The eigenvector corresponding to

�maxðRSÞ has strictly positive entries. Furthermore, the

minimum real � for which inequality �q RSq has solutions

q > 0 is �maxðRSÞ. If �maxðRSÞ � ð1þ �Þ=�, then (5) holds and

the SIR level � is achievable for all ci 2 S or, equivalently, the

code set S is admissible. The maximum common achievable

SIR for codes in S is �c ¼ 1=ð�maxðRSÞ � 1Þ.In summary, if �maxðRSÞ � ð1þ �Þ=�, then the code set S

is admissible and the transmit power vector that achieves

the maximum common SIR �c � is the eigenvector that

corresponds to �maxðRSÞ. The actual transmit power vector

is derived by appropriate scaling of that eigenvector such

that the noise power is combated and SINR constraints are

satisfied.

Once an admissible code set is found, the codes must be

allocated to users. Clearly, code allocation does not affect

the admissibility of the code set and, hence, the two stages

are distinguishable. A code allocation is specified by a

vector �1; . . . ; �Mð ÞT , where �j 2 f1; . . . ; Kg [ f0g denotes

the user to which code cj is assigned. Zero entries of the

vector denote codes that have not been admitted. Let L be

the set of all possible code assignments to users. We can

index assignments as ‘ ¼ 1; 2; . . . and map assignment

index ‘ to vector �1ð‘Þ; . . . ; �Mð‘Þ½ �T . The set of codes

assigned to user k with assignment ‘ is denoted by Ckð‘Þ.A code allocation that satisfies minimum rate requirements

of all users is called feasible. The overall problem is to

identify an admissible code set and a feasible code

allocation to users such that the total user rate is max-

imized. The problem is formally stated as follows:

maxI

XMj¼1ij¼1

rðcjÞ; ð6Þ

subject to the requirement for admissible code set

SIRjðqÞ �; for j ¼ 1; . . . ;M; s:t: ij 6¼ 0; ð7Þ

and the requirement for feasibility of the allocationXcj2Ckð‘Þ

rðcjÞ rmin;k; for k ¼ 1; . . . ; K: ð8Þ

Finding the appropriate admissible code set is of

exponential complexity and requires enumeration of all

possible code activation vectors. Furthermore, given an

admissible code set S, the derivation of a feasible code

allocation is nontrivial as well. The existence of a feasible

allocation is not straightforward unlessP

cj2S rðcjÞ <PKk¼1 rmin; k in which case a feasible allocation does not

exist. In order to see the inherent difficulty of the code

allocation problem, let code cj 2 S with spreading gain Nj

be an “item” of size rðcjÞ ¼ 1=ðTcNjÞ. In addition, assume

that rate requirements rmin;k of each user k for k ¼ 1; . . . ; K

are mapped to bins of these sizes.

Then, the question about existence of a feasible code

allocation can be answered in polynomial time if and only if

the decision version of the following bin packing problem

can be answered in polynomial time: “Given jSj items, each

of size rðcjÞ, can we pack the items in K bins, each of size

rmin;k?” Clearly, a feasible code allocation exists if and only

if the answer to the bin packing question is negative, so that

the code allocation covers or overcomes rate requirements.

Since the bin packing problem is NP-Hard [16], its decision

version is NP-Complete and the answer to the existence

question cannot be given in polynomial time. Due to the

difficulty of solving the code admission and allocation

problems, we resort to heuristic algorithms. The proposed

algorithms are greedy in nature and are based on readily

measurable quantities.

2.3 Proposed Heuristic Algorithms

Code admission and code allocation can take place periodi-cally with a period of the order of one or more frames.

2.3.1 Code Admission

At each step of the proposed algorithms, a code is selected

and inserted in the admitted code set based on some

criterion, subject to maintaining the admissibility of the

code set. In other words, the SIR at the output of the

matched filter to each admitted code should exceed �. Code

cross-interference should be kept to a minimum during

each stage of code admission in order to facilitate admis-

sions at future stages of the algorithm. In addition, low

spreading gain codes should be preferable since they

provide high rates. The trade-off between code rate and

induced or sustainable interference that was discussed in

the previous section should be taken into account as well.

Consider the algorithm at some stage and let S be the set of

m codes that are already admitted until then. When power

control is used, let �S be the maximum achievable common

SIR of the admitted codes. The problem is to identify the

next code si for admission. To this end, we propose three

admission criteria:Criterion 1: Minimum SIR decrease with spreading gain

consideration. For each unadmitted code si 2 C n S, we firstneed to see whether the code set S [ fsig is admissible. Forthis purpose, we consider the ðmþ 1Þ � ðmþ 1Þ matrix ofsquared cross-correlations of codes in set S [ fsig that wedenote by Ri

S . If �maxðRiSÞ � ð1þ �Þ=�, the admission of

code si results in an admissible code set. Let �SðiÞ be themaximum common achievable SIR of codes in set S [ fsigthrough power control.

For codes si 2 C n S for which �SðiÞ �, we define apreference factor as follows: The new code should incur lowinterference to other admitted codes and, hence, it shouldlead to a minimum decrease of their SIRs after admission.The SIR decrease of each code sj 2 S due to insertion ofcode si is given as �SIRi

j ¼ �S � �SðiÞ. Code si should alsoreceive low interference from other admitted codes so thatits SIR, �SðiÞ is high. Furthermore, in an effort to admitcodes that increase the aggregate system rate, this criteriongives priority to codes with low spreading gains thatprovide high rates. To capture these objectives, we define an


admission factor (AF) Ai for each code si 2 C n S withspreading gain Ni as

Ai ¼ Ni ��S � �SðiÞ�SðiÞ

; for all si 2 CnS : �SðiÞ �: ð9Þ

Criterion 2: Minimum weighted TSC of admitted codes. Thetotal squared cross-correlation of a set of codes is a metricthat reflects code cross-interference. When transmit powercontrol is present, each term in the TSC sum should beweighted by the power allocated to that code in order tocapture cross-interference. For each code si 2 C n S, weperform the admissibility test �maxðRi

SÞ � ð1þ �Þ=� thatwas stated above. If si maintains admissibility of the codeset, we define the factor

TSCi ¼Xsj2S

~�2ij

Njqij þ qii

Xsj2S

~�2ji

Ni; for all si 2 C n S : �SðiÞ �;

ð10Þ

where ðqi1; . . . ; qimÞT is the resulting code transmit power

vector after insertion of si. The first term is the interferencethat si receives from already admitted codes and the secondterm denotes induced interference from si to other admittedcodes. It can be seen that this criterion relies on a metric thatcaptures code cross-interference but not code rates.

Criterion 3: SIR Balancing for admitted codes. The thirdcriterion admits the code si that leads to the maximumcommon SIR after insertion and power control. For eachcode si 2 C n S that qualifies for admissibility, we define thepreference factor Wi ¼ 1=�SðiÞ. By attempting to minimizethe inverse of the common SIR, we encourage admission ofmore codes with high and balanced SIRs in the system.

Depending on the employed admission criterion, thealgorithm selects a code si 2 C n S with minimum Ai, TSCi,or Wi subject to maintaining an admissible code set at eachiteration. The algorithm terminates when no more codes canbe admitted, namely, when, for all codes sj 2 C n S, it is�SðjÞ < �.

Transmit power control can be optional. Due to theOðm3Þ complexity of the admissibility test with theeigenvalue criterion for an m�m matrix, power controlcould be omitted. Then, transmit powers do not appear infactors Ai, TSCi, and Wi. The expressions for the preferencefactors are then different since the SIRs in the set ofadmitted codes are not balanced anymore. These expres-sions emerge easily and can be found in our preliminarywork [1].

2.3.2 Code Allocation to Users

Different heuristics can be considered for code allocation tousers. Here, we first sort users in decreasing order of raterequirements. We allocate codes to a user until its raterequirements are satisfied or exceeded. Then the next useris considered and the procedure is repeated. For a user k,the code sj 2 S such that sj ¼ arg minsj 2 Sjrmin; k� rðsjÞj isassigned to that user. The rationale for this allocation is tocover user rate requirements as fast as possible but also tofind the code that fits best these rate requirements, so thatthe minimum rate requirement is not exceeded by a largeamount.

We note that a feasible allocation may not exist if thereare many users with high rate requirements or if the SINRrequirement � is large.

3 THE SYMBOL-ASYNCHRONOUS CASE

We now consider a symbol-asynchronous CDMA system inwhich the symbols from different transmitters are not alignedat the receiver but instead they have nonzero relative timeoffsets. This situation arises due to lack of coordination oftransmitters or due to different lengths of traversed paths ofsignals from different transmitters to the receiver. Theasynchronous model captures the following cases:

. Up-link transmission from a set of users to a centralBS with flat fading channels. The asynchronismappears at the BS receiver of each user since symbolsof this user are not aligned with the symbols of otherusers.

. Down-link transmission in a multicell network withflat fading channels. Each BS transmits to users in itscell area. The code sets employed by different BSsmay or may not be disjoint, depending on BSproximity. Asynchronism arises at the receiver ofeach user due to the differences in time offsetsamong symbols from the serving BS and symbolstransmitted from other BSs.

. Up-link transmission in a multicell network with flatfading channels. Asynchronism arises at each BSreceiver corresponding to a served user. It occursbecause of different reception times among symbolsof a specific user and symbols of users that areserved by that BS or by other BSs.

. Down-link single-cell transmission or any one of thethree aforementioned scenarios in the presence ofmultipath. For example, for the case of down-linksingle-cell transmission with multipath, asynchron-ism arises at each user receiver since the differentpaths of the multipath channel of the user which aretraversed by user symbols have different timedelays. This asynchronism affects the transmittedcodes as well.

3.1 System Model

The assumptions made in the synchronous case aboutsignal transmission and spreading gains of codes applyhere as well. However, the symbol reception model and theexpression for the cross-correlation need to be modified. Inthe sequel, we provide a generic asynchronous model thatcaptures all scenarios above. For ease of demonstration, wedescribe our model in the context of a chip-synchronoussystem, in which time offsets of symbol reception times ofusers are integer multiples of Tc. However, our model andproblem treatment can be readily extended to the chip-asynchronous case where symbol reception time offsets cantake any value between zero and the symbol duration.Then, the expressions for cross-correlation will need to bemodified (see [17, p. 785]).

For an integer d 0, let operators TdR and TdL denote theshifting of a code vector to the right and left, respectively,by d chips. For both operations, the vacated positions of


the vector are filled with zeros. Thus, for vector x ¼ðx1; . . . ; xNÞT and d 0, define TdLx ¼ ðxdþ1; . . . ; xN; 0

dÞTand TdRx ¼ ð0d; x1; . . . ; xN�dÞT , where 0d denotes d conse-cutive zeros.

We now proceed to obtaining the expression for the

cross-correlation of codes si and sj with spreading gains Ni

and Nj. Assume for now that these codes are used by users i

and j and focus on the matched filter receiver to code si. Let

dij be the relative delay offset between users j and i, given

by dij ¼ dj � di, where delays di and dj are measured with

respect to a reference point. Each user aligns its receiver to

its own symbol interval. By using the reception time at the

receiver of user i as reference, we get di ¼ 0 and the

matched filter receiver to code si simply sees the delayed

versions of other users’ symbols.

Define R ¼ Nj=Ni and consider first the case that Ni >

Nj and the receiver is at the long code si. In Fig. 2a, we

depict an illustrative case with Ni ¼ 2Nj. The matched

filter to code si sees the delayed version of two replicas of

the short code sj. If d < Nj, then d is the delay between

the nth symbol of user i and the�Ni

Njn�th symbol of user j.

The decision statistics at the matched filter receiver to

code si arise from cross-correlating code si with vectors

x1 ¼ TNi�dL

�sð1=RÞj

�and x2 ¼ TdR

�sð1=RÞj

�that emerge from

left and right shifting of the concatenated code sð1=RÞj .

Thus,

~�2ijðdÞ ¼ sTi TNi�d

L ðsð1=RÞj Þ þ TdRðsð1=RÞj Þ

� �h i2; if Ni > Nj: ð11Þ

Consider now the case where Ni < Nj and the receiver

is at the short code si (Fig. 2b). Due to delay d, the matched

filter to code si sees portions of the two subsequences sð1;2Þj

and sð2;2Þj . At time Tsi , the matched filter sees the Ni-length

sequence consisting of the last d chips of sð2;2Þj and the first

ðNi � dÞ chips of sð1;2Þj , while, at time 2Tsi , it sees the

Ni-length sequence consisting of the last d chips of sð1;2Þj

and the first ðNi � dÞ chips of sð2;2Þj . Following a similar

rationale with the one for the synchronous case, it is

meaningful to consider the worst-case SIR, which occurs

when the cross-correlation between si and one of the two

Ni-length sequences above is maximum. It is not difficult

to see that, in the general case of R > 2, the expression for

the cross-correlation for Ni < Nj is

~�2ijðdÞ ¼ max

k¼1;...;RsTi T

Nj�dL s

ðk;NiÞj

� �þ TdR s

ððkþ1Þ mod R;NiÞj

� �h in o2:

ð12Þ

The cross-correlation ~�2ijðdÞ is a periodic function of d

with a period of minfNi;Njg. Also, if d < 0, we let

d0 ¼ minfNi;Njg � jdj. Then, d0 > 0 and ~�2ijðdÞ ¼ ~�2

ijðd0Þ.Clearly, code cross-correlation depends on the relative

delays between the symbol carried by the code of interest(whose reception epoch serves as a reference) and symbolscarried by other codes. These delays in turn depend on thelocations of the specific transmitters to which the corre-sponding codes are assigned. Therefore, relative delaysaffect the SIR at the output of the matched filter to a code.Since SIRs determine code admissibility, it can be deducedthat the latter is a function of the specific code allocation totransmitters. In the case of single-cell down-link with flatfading that we studied first, all transmitters were colocatedat the BS and, thus, symbol delay offsets at a receiver didnot occur. However, in the cases of single-cell or multicellup-link and in the case of multicell down-link, transmitters(namely, users in the up-link case and BSs in the down-linkcase) are not colocated. Hence, code admissibility does notdepend only on the code set itself, but also on codeallocation to transmitters. Clearly, a certain allocation ofcodes to each transmitter constrains the selection of anadmissible code set since it imposes a certain cross-correlation regime through the user delay profile. There-fore, in the asynchronous case, the procedures of codeadmission and allocation need to be considered jointly dueto the impact of different delay profiles of users.

A note about the case of multipath is in place here.Consider, for instance, the case of single-cell down-linktransmission. Each code that is used for transmission to auser arrives to the user receiver in several replicas with eachreplica corresponding to one path of the multipath profile ofthe user. Each path has an associated path gain. A RAKEreceiver that comes after the matched filter compensates formultipath and provides diversity combining. However, ifthe branches of the RAKE receiver are not well adjusted to


Fig. 2. Illustrative example for the asynchronous cross-correlation

between codes of different spreading gains: (a) Ni > Nj, with the

receiver at the long code si. (b) Ni < Nj, with the receiver at the short

code si.

path delays, the delayed versions of a code due to multipathcreate self-interference to that code. Each code replica canthen be viewed as a virtual code that arrives at the receiverwith some time offset. This situation is captured by ourasynchronous model as well.

For the single-cell up-link case and an active set of m �M codes S ¼ fs1; . . . ; smg, denote a code allocation by

vector ð�1; . . . ; �MÞT , where �j 2 f1; . . . ; Kg [ f0g denotes

the user to which code sj is assigned. If �j ¼ 0, then sj 62 S.

The set of all allocations is again denoted by L. For a code

assignment ‘ 2 L, �jð‘Þ denotes the user to which code sj is

assigned. For ‘ 2 L, the perceived delay profile for code i is a

vector di;1ð‘Þ; . . . ; di;i�1ð‘Þ; 0; di;iþ1ð‘Þ; . . . ; di;mð‘Þ T

, where

di;jð‘Þ is the delay offset between users �jð‘Þ and �ið‘Þ with

the reference being the symbol received from code si of

user aið‘Þ. We assume a fixed, deterministic delay profile at

each receiver with delays that can be estimated by using a

sliding correlator type of approach. The SIR at the output of

the matched filter to ci or si is

SIRiðq; ‘Þ ¼qih�ið‘ÞP

cj2S:j6¼iqjh�jð‘Þ�

2ijðdi;jð‘ÞÞ

ð13Þ

or, equivalently,

SIRiðq; ‘Þ ¼qiNih�ið‘ÞP

sj2S:j 6¼iqjh�jð‘Þ

~�2ijðdi;jð‘ÞÞNj

; ð14Þ

where h�jð‘Þ is the path gain of the link between user �jð‘Þand the receiver and the dependence of cross-correlations

on delays is clear. For a multicell network, we would

further need to change the notation for code allocation in

the expression above to �kj ð‘Þ, where index k stands for the

BS. Accordingly, path gains and delays would be denoted

as hk�jð‘Þ and dki;jð‘Þ. Similar modifications in the notation

should be made for the case of multipath.For a given code allocation ‘ 2 L, a code set S is

admissible if there exists a transmit power vector q suchthat SIRiðq; ‘Þ � for all ci. A similar inequality in matrixform as the one in (5) is derived, where matrix RS nowdepends on the specific allocation ‘ and has elements

Rijð‘Þ ¼h�jð‘Þ

h�ið‘Þ�2ijðdi;jð‘ÞÞ: ð15Þ

The problem of identifying the jointly optimal codeadmission and allocation that maximizes total user rate isformulated in accordance to (6)-(8) with the additionaldependence of SIR on code allocation.

Depending on the case where the problem arises, theremay exist additional constraints in the formulation. Forinstance, in the up-link of a single cell, each code should beallocated to at most one user, while, in a multicell network,the same code can be part of the available code sets ofdifferent BSs. Then, code reuse in different cells depends onthe amount of cross-interference. The coupling of codeadmission and allocation makes the joint problem not easierthan the two separate problems. Heuristic algorithms needto be designed for this case as well.

3.1.1 Heuristic Algorithms

The criteria for the synchronous case can be extended to theasynchronous case and can lead to joint code admission andallocation algorithms. In order to keep complexity to areasonable level, reallocations for codes admitted inprevious steps of the algorithm are not considered. Atsome stage of the algorithm, there will be again a set ofadmitted codes S allocated to users. The additional degreeof freedom here is to select the user to which the admittedcode will be allocated.

For any unassigned code si2 C n S and user�i2f1; . . . ; Kg,let �Sði; �iÞ denote the maximum common SIR of codes

after admission of code si and allocation to user �i. For the

codes si for which there exists a user �i 2 f1; . . . ; Kgsuch that �Sði; �iÞ �, we define the preference factor

Ai;�i ¼ Ni �S � �Sði; �iÞ½ �=�S . This factor corresponds to the

one defined under criterion 1 for the synchronous case. For

criterion 2, the factor TSCi;�i would be the same as the one

defined in (10) except for the dependence of cross-

correlations on delay profiles based on the allocation of

the new code. These can be denoted as ~�2ijðd�i;jÞ and

~�2jiðdj;�iÞ. For criterion 3, the corresponding factor is

Wi;�i ¼ 1=�Sði; �iÞ. In each of the three cases, the algorithm

selects a code si and performs allocation to user �i such that

the factors above are minimum. For the part of code

allocation, the algorithm should consider allocations to

users �i that have not yet satisfied their rate requirements.

If all users have satisfied their requirements, the algorithm

continues by allocating codes to any user so as to maximize

total rate until no more codes can be allocated.We note that our approach can be applied in a dynamic

communication setting with changing number of users andtime-varying channel conditions, namely, path gains anddelay profiles.

4 SIMULATION RESULTS

In this section, we evaluate and compare the performance ofthe proposed algorithms for the synchronous and asyn-chronous cases with or without power control. The codealphabet size is taken to be 106 codes, 16, 30, and 60 ofwhich have spreading gain 8, 16, and 32, respectively. Weconsider the following cases for the code alphabet:

. Case A. The code alphabet consists of only 106 de-terministic codes that are chosen randomly amongpossible codes of the code alphabet.

. Case B. The alphabet consists of a mixture ofHadamard codes (orthogonal to each other) andother nonorthogonal deterministic codes that arechosen randomly among possible codes in the codealphabet. In this case, there are 8, 16, and 32 Hada-mard codes of spreading gain 8, 16, and 32,respectively.

The following performance metrics are considered:

. Total system throughput (achievable rate), normal-ized by the chip rate, which is considered to haverate of 1.


. Total residual rate for users that do not satisfy theirrate requirements. This is a measure of the efficiencyof algorithms on the feasibility of code allocation.

. Total transmission power. This is a measure ofpower efficiency in instances where this is mean-ingful, such as in up-link transmission.

System performance is measured as a function of SIRthreshold � in the range (1,12) dB. Results are averaged over50 experiments. The user rate requirements are uniformlydistributed in a rate interval, so that the maximum raterequirement can be larger than the highest code rate and theminimum rate requirement can be smaller than the lowestcode rate. For each experiment, 10 random sets of user raterequirements are used. A noise power level of 0.01 is used.

Fig. 3 shows the total normalized rate as a function of �

for a synchronous system without power control and all

admission criteria. For Case A, criteria 2 and 3 yield a similar

rate, which is larger than that of criterion 1. As � increases,

the total rate reduces and all criteria perform closer to each

other. By measuring the standard deviation of admitted

code lengths, we observed that criterion 1 admits fewer but

variable-rate codes, while criteria 2 and 3 tend to admit more

codes of similar rate, specifically low-rate ones. Therefore,

many low-rate codes turn out to provide better performance

than few high-rate ones. This implies that a user may be

forced to use several low-rate codes although a single high-

rate code suffices. If the use of multiple codes leads to high

transmitter complexity, criterion 1 may be preferable.

When Hadamard codes are used as well, criteria 2 and

3 achieve a rate of 1 by employing only orthogonal

Hadamard codes of the same length, namely, all 32 codes

of length 32 and rate 1/32 each. Code selection and

allocation is trivial: Orthogonal codes have zero cross-

correlation and are trivially admitted. However, any other

nonorthogonal code may not be admitted due to the high

cumulative interference encountered in the next step. Since

these criteria try to admit as many codes as possible without

violating �, they first admit orthogonal codes of high

spreading gain. On the other hand, criterion 1 tries to get a

high-rate code without affecting interference on itself and

other users. Its behavior as a function of � resembles that of

Case A (although it is 20 percent to 40 percent better).

Criterion 1 differs from criteria 2 and 3 when it selects a

low-rate code that is nonorthogonal to admitted ones. In

Fig. 4, we show total residual rate for the three criteria and

for 5, 10, and 20 users. For given user load in Case A,

criterion 3 has the best performance. With increasing load,

the performance difference among the criteria becomes

more evident. In Case B, the unsatisfied users for all criteria

are fewer than the ones in A. For a small number of users,

criteria 2 and 3 may even entirely satisfy user requirements.

In Fig. 5, we depict the total rate when power control is

used. Power control per code balances the SIRs of admitted

codes as discussed in Section 2.2. The admission criteria for

the synchronous and the asynchronous case are discussed in

Sections 2.3.3 and 3.1.1. Power control results in significant

performance improvement of the order of 20 to 30 percent.

Interestingly, all admission criteria provide the same total

rate which represents the performance limits of the system.The use of Hadamard codes incurs an additional

improvement of 40 to 50 percent and criteria 2 and 3perform better than criterion 1. Similar conclusions weredrawn for total residual rate performance. In Fig. 6, weshow the total transmission power required for eachcriterion. Although this metric is not crucial for the down-link case, it can indicate the amount of caused interferenceand can serve as a reference for comparison to theasynchronous case. In Case A, criterion 1 is the mostpower-efficient one since it achieves the same total rate withless power. In Case B, the amount of consumed power isdecreased and criterion 2 is power-efficient for most of thecases. The total power decreases with �, since fewer codesare admitted then.

An interesting issue is the comparison of the perfor-

mance of our algorithms with respect to other schemes that

characterize system performance. One such scheme is the


Fig. 3. Synchronous CDMA with no power control: Total normalized rate as a function of SIR threshold � for Case A (deterministic codes chosen

randomly from possible codes in the code alphabet) and Case B (mixture of Hadamard and nonorthogonal codes).

one that leads to the optimal solution. This would require

that we test admissibility and provisioned rates of all 2106

possible subsets of codes, which is an infeasible task.

Besides, the optimal allocation will never be applied in

practice due to its prohibitive complexity. Another metric

that characterizes system performance is the achievable

total rate for random code instances. We consider random

codes, since their cross-correlation properties allow us to

obtain analytic expressions on total rate.To this end, consider the down-link single-cell synchro-

nous case with no receiver noise and no power control.

Assume that codes are random, so that the chips of each

code with spreading gain Nn are independent random

variables that take values �1=ffiffiffiffiffiffiffiNn

pwith probability 1/2.

Independence is assumed among chips of the same code

and among chips of different codes. Let IE½�2nm� denote

the expected squared cross-correlation of two codes of

length Nn and Nm, respectively, with n;m ¼ 1; 2; 3, N1 ¼ 8,

N2 ¼ 16, and N3 ¼ 32 as in our experimental setup. With

the receiver at code with spreading gain Nn, we have

IE½�2nm� ¼

1

NnNmIEXNn

k¼1

XNn

‘¼1

cikci‘cjkcj‘

" #ð16Þ

or, equivalently,

IE½�2nm� ¼

1

NnNm

XNn

k¼1

XNn

‘¼1

IE½cikci‘�IE½cjkcj‘� ¼1

Nmð17Þ

due to chip independence. Let Kn be the number of codes of

spreading gain Nn, whose cross-interference can be sus-

tained for SIR �. The SIR at the receiver of a code with

spreading gain Nn is

SIRn ¼Kn�1

Nnþ

X3

m¼1;m 6¼n

Km

Nm

!�1

: ð18Þ


Fig. 4. Synchronous CDMA with no power control: Total residual rate of users as a function of SIR threshold � and 5, 10, and 20 users for Case A

(deterministic codes chosen randomly from possible codes in the code alphabet) and Case B (mixture of Hadamard and nonorthogonal codes).

Fig. 5. Synchronous CDMA with power control: Total normalized rate as a function of SIR threshold � for Case A and Case B.

From the code set admissibility condition that the SIRshould exceed �, the following inequalities should hold forthe total rate RT :

RT ¼X3

n¼1

Kn

Nn� 1

Nnþ 1

�; for n ¼ 1; 2; 3: ð19Þ

The condition for the largest spreading gain, N3, is thetightest one. Hence, the total rate is bounded above by1=N3 þ 1=�. The performance of our heuristics (H1, H2, H3)with respect to this rate bound is shown in Table 1 withpower control (PC) or without power control (NPC). Therate bound is denoted at the last column of the table. Withthe exception of criterion 1 in very low SIRs, ourdeterministic admission criteria perform much better thanthe given upper bound on total rate for random codes.

Next, we study the asynchronous case with powercontrol. Although path gains appear in the SIR andadmission criteria, we assume the same gain for alltransmitter-receiver pairs so as to eliminate the dependenceon factors related to distance or fading and focus on theeffect of asynchronism on performance. There are 20 userswith delays uniformly distributed in ½0; Nmax�. Fig. 7 showsthe total rate for the asynchronous case. A direct compar-ison with the synchronous case cannot be made, since theasynchronous case involves code allocation to users aftercode admission. However, it is worth noting that the plotfor Case A has similar form with that of the synchronous

case in Fig. 5. For Case A, the asynchronous case slightlyoutperforms the synchronous one. This is not surprising,since the delays provide an additional degree of freedomand appropriate code allocation can ameliorate interference.Clearly, the delays do not have significant impact on the(anyway nonorthogonal) codes. However, this is not truefor Case B, where the delays damage the orthogonality ofHadamard codes and deteriorate performance. In Fig. 8, weshow the total required transmission power. As in thesynchronous case, criterion 1 achieves the same rate withless consumed power. This power-efficiency is important inup-link communication scenarios. For Case A and fixed �,there is less deviation in performance of all criteria than inthe synchronous case. In Case B, the lack of synchronismincreases the total power more than in Case A.

5 DISCUSSION

We considered the resource allocation problem that arisesin CDMA systems with deterministic codes and multirateprovisioning. We devised synchronous and asynchronousmodels and identified the structure of code admissionand code allocation problems. We introduced a class ofheuristics that use criteria which rely on readily measur-able quantities. The results provide useful design guide-lines about the required properties of the code alphabet,namely, the kind, number, and lengths of codes. Theyshow the rate benefit that stems from using a mixture oforthogonal and nonorthogonal codes in the code alphabet,but they also indicate system sensitivity to asynchronismin that case. Interestingly, asynchronism does not affectperformance for purely nonorthogonal code alphabet.Furthermore, results expose the significance of powercontrol in alleviating this sensitivity and reveal thebenefits of different criteria in terms of rate provisioningand power efficiency.

There exist several directions for future study. Control-lable modulation levels can be incorporated as anothermeans for multirate provisioning; however, the trade-offbetween rate and sustainable interference for different


Fig. 6. Synchronous CDMA with power control: Total transmission power as a function of SIR threshold � for Case A and Case B.

TABLE 1Performance of our Heuristics as Compared with Average

Achievable Rate without and with Power Control (PC)

modulations should be addressed. Our study can alsoinclude different signal processing at the receiver. Forinstance, for codes with equal spreading gain, the minimummean squared error (MMSE) receiver is the optimal linearmultiuser receiver in the sense of maximizing SIR. It wouldbe interesting to study issues related to different multiuserreceivers within the framework of codes of variablespreading gain. Finally, the design of deterministic codeswith variable spreading gain that optimize certain perfor-mance metrics is another important open issue.

ACKNOWLEDGMENTS

The authors would like to express their gratitude to SennurUlukus for helpful discussions. The authors also wish tothank the anonymous reviewers for comments that im-proved the presentation of the paper. The first and thirdauthors acknowledge the support of the European Commis-sion NoE NEWCOM (IST 507325). The first author alsoacknowledges Marie Curie Grant SAINT-W (IRG-017267).

Part of this paper was presented in [1] at the International

Symposium on Spread Spectrum Techniques and Applications

(ISSSTA) 2002, Prague, Czech Republic.

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Iordanis Koutsopoulos (S’99, M’03) receivedthe diploma in electrical and computer engineer-ing from the National Technical University ofAthens, Greece, in 1997 and the MS and PhDdegrees in electrical and computer engineeringfrom the University of Maryland, College Park(UMCP), in 1999 and 2002, respectively. From1997 to 2002, he was a Fulbright Fellow and aresearch assistant with the Institute for SystemsResearch (ISR) of UMCP. He has held intern-

ship positions with Hughes Network Systems, Germantown, Maryland,Hughes Research Laboratories LLC, Malibu, California, and ApertoNetworks Inc., Milpitas, California, in 1998, 1999, and 2000, respec-tively. For the summer period of 2005, he was a visiting scholar with theUniversity of Washington, Seattle. Currently, he is a lecturer at theDepartment of Computer and Telecommunications Engineering, Uni-versity of Thessaly, Greece. His research interests are in the field ofnetworking with emphasis on wireless networks cross-layer design,sensor networks, smart antennas, and wireless network security. He is amember of the IEEE.

Ulas C. Kozat received the BS degree inelectrical and electronics engineering from Bilk-ent University, Ankara, Turkey, and the MSdegree in electrical engineering from the GeorgeWashington University, Washington D.C., in1997 and 1999, respectively. He has receivedthe PhD degree in 2004 from the Department ofElectrical and Computer Engineering at Univer-sity of Maryland, College Park. He has con-ducted research under the Institute for Systems

Research (ISR) and Center for Hybrid and Satellite Networks (CSHCN)at the same university. He worked at HRL Laboratories and TelcordiaTechnologies Applied Research as a research intern. Since May 2004,he has been with DoCoMo Communication Laboratories working mainlyon media transport, cross-layering, overlay and P2P systems, advancedcoding techniques, resource allocation, system modeling, and integra-tion of heterogeneous wireless systems. He is a member of the IEEE.

Leandros Tassiulas (S’89, M’91, SM’05) wasborn in 1965, in Katerini, Greece. He receivedthe diploma in electrical engineering from theAristotelian University of Thessaloniki, Thessa-loniki, Greece, in 1987, and the MS and PhDdegrees in electrical engineering from the Uni-versity of Maryland, College Park, in 1989 and1991, respectively. He has been a professor inthe Department of Computer and Telecommu-nications Engineering, University of Thessaly,

Greece, and a research professor in the Department of Electrical andComputer Engineering and the Institute for Systems Research,University of Maryland, College Park, since 2001. He has held positionsas assistant professor at Polytechnic University, New York (1991-1995),assistant and associate professor at the University of Maryland CollegePark (1995-2001), and professor at the University of Ioannina, Greece(1999-2001). His research interests are in the field of computer andcommunication networks with an emphasis on fundamental mathema-tical models, architectures and protocols of wireless systems, sensornetworks, high-speed internet, and satellite communications. Dr.Tassiulas received a US National Science Foundation (NSF) ResearchInitiation Award in 1992, an NSF CAREER Award in 1995, an Office ofNaval Research Young Investigator Award in 1997, a BodosakiFoundation award in 1999, and the INFOCOM ’94 best paper award.He is a senior member of the IEEE.

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