Cross-Layer Optimization for Multimedia Traffic in CDMA Cellular Networks

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 4, APRIL 2008 1379

Cross-layer Optimization for Multimedia Traffic inCDMA Cellular Networks

Daniele Veronesi, Stefano Tomasin, Member, IEEE, and Nevio Benvenuto, Senior Member, IEEE

Abstract— We consider the uplink transmission of multime-dia services in a cellular network where multiple access isimplemented by code division (CDMA) and the base stationperforms successive interference cancellation (SIC) to enhanceperformance. We propose a cross-layer optimization techniquethat operates both at the physical layer, by selecting the detectionorder at the SIC receiver, and at the medium access controllayer, by selecting the power/rate for each mobile terminal.The optimization objective is the maximization of the overallweighted network throughput with the satisfaction of the qualityof service criteria for multimedia communications. The resultingproblem turns out to be NP-complete and we resort to a discretestochastic approximation (DSA) approach for its solution. Con-cerning DSA, an efficient implementation is proposed in order toreduce memory occupation and improve the convergence of thealgorithm. In a UMTS cellular environment, numerical resultsshow that the optimization provides a significant performanceadvantage over existing techniques at the cost of an increase ofcomputational complexity and memory occupation.

Index Terms— CDMA, cross-layer design and optimization,mobile multimedia technology, resource management and QoSprovisioning, wireless personal communication systems.

I. INTRODUCTION

IN THE RECENT PAST, a significant effort has beendevoted to the optimization of resource management in the

downlink of cellular communication systems, with the aim ofreaching the required quality of service (QoS) for multimediacontent distribution [1]. Most studies assume that QoS re-quirements in the uplink are less demanding, therefore leadingto asymmetric communications with an high-rate downlinkand a medium-rate uplink. However, a consensus is recentlygathering on enabling the uplink of future cellular systems tosupport high-rate differentiated traffic [2]–[6]. This will makepossible for example video streaming from the mobile terminal(MT), interactive multimedia applications and uploads of largefiles. On the other hand, due to the limited availability ofbandwidth, efficient techniques will be required at both thephysical (PHY) and medium access control (MAC) layers. Formultimedia communications with different classes of traffic,efficiency is achieved also through resource allocation (RA)

Manuscript received November 20, 2006; revised April 12, 2007 and July16, 2007; accepted November 11, 2007. The associate editor coordinating thereview of this paper and approving it for publication was Q. Zhang. This workhas been supported in part by the National Project on Fundamental Research(FIRB) “reconfigurable platforms for wide-band wireless communications."

S. Tomasin and N. Benvenuto are with the Department of Information En-gineering (DEI), University of Padova, Via Gradenigo 6/B, I–35131 Padova,Italy (e-mail: {tomasin, nevio.benvenuto}@dei.unipd.it).

D. Veronesi was with the University of Padova. He is now withMgTech S.R.L., Via Verdi 14, I–24100 Bergamo, Italy (e-mail: [email protected]).

Digital Object Identifier 10.1109/TWC.2008.060960.

that optimizes rates and transmit powers according to the QoSrequirements [4].

At PHY and MAC layers, code division multiple access(CDMA) is considered a good solution for uplink commu-nications [7], [8], especially in conjunction with successiveinterference cancellation (SIC) [12], [13] at the base station(BS). In order to account for time-varying QoS requirementsand channel conditions, various transmission parameters maybe adapted, including spreading factor [5], power [2] and datarate [9]. When no QoS is considered, it has been shown that ina downlink transmission the network throughput is maximizedwhen the BS transmits to at most one user at a time with themaximum power [10], [11].

In most of the existing literature, the optimization objectiveis the minimization of transmit power for a given signalto noise plus interference ratio (SNIR) of the received sig-nal [14]–[16]. In [17], the capacity is computed for a systemwith power control (PC) and multiple rates, i.e., multiple targetSNIRs. When all MTs transmit at the same rate, PC canbe optimized to maximize the number of active users, [18].Beyond PC, also the order of user detection in SIC (user order,UO), plays an important role in system performance [19],but studies have been focused on the minimization of powerconsumption rather than throughput enhancement [20], [21].In [3], the problem of RA for uplink CDMA with SIC wasanalyzed for a general weighted-sum of user rates. It wasshown that, when all received user signals have the samecross-correlation, users are optimally scheduled by alwaystransmitting at the maximum power and selecting the UOaccording to the weights. However, we will show that for abroadband asynchronous uplink, due to different broadbandchannels, attenuations and spreading codes, the correlationamong received user signals changes significantly and trans-mitting at the maximum power is not the optimal solution.

In this paper, we propose a new technique for optimizingPC and UO in SIC for an uplink CDMA system supportingmultimedia communications with differentiated QoS require-ments. In other words, we integrate PC and UO. The proposedoptimization operates across PHY and MAC layers, sinceMAC RA requires information on the interference level fromthe PHY layer and in turns power, rate and UO at the PHYlayer are determined by RA. Our objective is the maximizationof a weighted sum of the MT instantaneous rates, where theweights are selected to account for any QoS constraint. In turn,the optimization is performed by dynamically selecting UOand setting the transmit power/rate of each user. The resultingsolution includes a constraint on the maximum transmit powerper user, which is a typical physical limitation of MT. Since the

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1380 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 4, APRIL 2008

considered optimization problem is NP-complete, we resortto a suboptimal algorithm, based on the discrete stochasticapproximation (DSA) algorithm. The DSA algorithm was firststudied in [22] and [23] for the optimization of a functiondefined on a discrete set, when only a noisy estimate ofthe objective function is available. This approach has beensuccessfully applied in various communication problems, forspreading code optimization in CDMA systems [24], schedul-ing [25] and synchronization [26]. An immediate applicationof DSA to our optimization problem turns out to be memoryexpensive and slow in converge, due to two iterative loopsfor UO and PC. Hence, we resort to a suboptimal approachwhere UO and PC are jointly adapted. Moreover, memoryrequirement is optimized by a suitable statistical modeling ofthe throughput as a function of UO.

This paper is organized as follows. In Section II we describethe system model of a multimedia uplink CDMA system andderive the expression of the network throughput when the BSis equipped with SIC. In Section III we formalize the RA andPC problem. The DSA algorithm is presented in Section IVtogether with an efficient implementation. Numerical resultsare shown in Section V and conclusions are outlined in SectionVI.

II. SYSTEM MODEL

We consider an uplink CDMA transmission, where K MTsare transmitting from different locations to a common BS.Each MT may transmit a variety of multimedia traffic, withboth real time (RT) and non real-time (NRT) requirements.Transmission time is divided into slots, each of duration TS.The BS knows the channel conditions of all users at eachtime slot. According to channel conditions and transmissionrequests from the MTs, the BS determines the power and thetransmission rate for each MT, according to the RA algorithm.In order to simplify the data exchange and the RA algorithm,we assume that the transmit power and rate are unique for theentire slot. Once RA has been performed, the BS broadcaststhe transmission decisions to MTs [6].

A. CDMA transmission

MTs are identified by index k, with k = 1, 2, . . . ,K, associ-ated to the spreading code {ck,�}, � = 0, 1, . . . , NS−1, havingspreading factor NS and chip period Tc. In this paper weconsider short spreading codes, but the extension to systemsusing long spreading codes is straightforward. The signal ofMT k is transmitted with power Pk. Each slot contains Mdata symbols {dk(m)}, m = 0, 1, . . . ,M − 1, each spread bythe MT spreading code. We assume that each MT transmitswith a different coding/modulation technique and the powerof the data signal is unitary for normalization.

The signal propagates through a wideband wireless channelthat is assumed to be time-invariant for the duration of a slotand includes both path-loss and shadowing. Let us indicatewith hk(t) the impulse response of the composite channelgiven by the convolution of the transmit filter, the channelimpulse response and the receive filter.

By considering spreading as a filtering operation, wedefine the effective channel impulse response, which com-prises spreading and filtering with hk(t), as gk(t) =

∑Ns−1�=0 ck,�hk(t − �Tc). The received signal at the BS is the

sum of contributions from all the MTs plus noise, i.e.,

r(t) =K∑

k=1

zk(t) + w(t)

=K∑

k=1

M−1∑m=0

gk(t − mNsTc)√

Pkdk(m) + w(t) ,

(1)

where w(t) is a complex Gaussian noise with zero mean andpower spectral density N0/2 per dimension. An asynchronoustransmission fits into the model (1) by randomly delaying thechannel impulse responses.

B. SIC receiver

The SIC receiver performs the detection of signals insuccession and interference is removed before detection ofthe next signal. Signals from MTs are detected according tothe ordered vector K = [k1, k2, . . . , kK ], with

kp ∈ {1, 2, ...,K} and kp �= kq for p �= q. (2)

Step p in SIC corresponds to the detection of the signal comingfrom the MT with index kp and the removal of its contributionfrom the received signal.

In particular, let us indicate with rkp(t) the signal ob-

tained from r(t) after the removal of the signals of MTsk1, k2, . . . , kp−1. Initially, rk1(t) = r(t). The detection of MTsignal kp is performed by first applying a rake receiver torkp

(t) followed by a de-spreader that provides

dkp(m) =

1√Pkp

∫g∗kp

(−τ)rkp(mNSTc − τ)dτ . (3)

The signal {dkp(m)} is detected, decoded and re-encoded to

obtain an estimate of the transmitted data signal {dkp(m)}.

The received signal relative to MT kp is then estimated as

zkp(t) =

M−1∑m=0

gkp(t − mNsTc)

√Pkp

dkp(m) (4)

and subtracted from rkp(t) to provide the signal for detection

of the next MT, i.e.,

rkp+1(t) = rkp(t) − zkp

(t) , p = 1, 2, . . . ,K − 1. (5)

The forthcoming analysis assesses the achievable throughputof a system with SIC using coding and operating close tocapacity (see (13)). In these conditions, for sufficiently longslots, errors in detection and interference cancellation arenegligible, which is a realistic assumption for a SIC receiverusing decoding [29], contrary to the linear SIC receiver [16].Moreover, under the assumption of perfect interference can-cellation, rkp

(t) is affected by noise, inter-symbol interference(ISI) and interference of undetected MTs. Provided that thespreading factor NS is much larger than the normalized (toTc) root mean square delay spread of the channel (rmsds),ISI is negligible, as will be assumed in the following analysis.Hence, the dominant limiting factor is multiuser interference(MUI), which is strongly related to the particular propaga-tion channel and spreading sequence. Indeed, most works inliterature on SIC assume an equal correlation among all the

VERONESI et al.: CROSS-LAYER OPTIMIZATION FOR MULTIMEDIA TRAFFIC IN CDMA CELLULAR NETWORKS 1381

received user signals. Although useful for a first analysis, thisassumption is not realistic for channels characterized by asignificant multipath, as shown in [19] and [20], [21].

We define the average correlation among signals receivedfrom the MTs as

Ri,j(Δ) = E[di(m − Δ)d∗j (m)

], Δ = −1, 0, 1 , (6)

with i, j = 1, 2, . . . ,K, where we considered three values ofΔ to take into account asynchronous transmissions. Assumingperfect cancellation we obtain

Ri,j(Δ) =∫

g∗i (τ − ΔT )gj(τ)dτ . (7)

We define the power of the total correlation as |Ri,j |2 =|Ri,j(−1)|2+ |Ri,j(0)|2+ |Ri,j(1)|2, where we denote Ri,j asthe equivalent correlation among users. Moreover, we definethe interference plus noise power for MT kp as

Ikp=

K∑i=p+1

Pki|Rki,kp

|2 + N0Rkp,kp. (8)

Then, from (5), the SNIR of MT kp can be written as

SNIRkp=

Pkp|Rkp,kp

|2Ikp

, (9)

under the assumption that data signals of different MTs areuncorrelated and statistically independent of noise. From (9)we observe that CDMA is limited by MUI, and the SICreceiver only mitigates the problem by performing partialcancellation of interference.

Usually, correlation {Ri,j} and interference power Ikpare

not readily available at the BS and they must be estimated byeither using a training sequence or a decision-directed method.This yields uncertainties on the estimate of SNIRkp

.

III. RESOURCE ALLOCATION PROBLEM

As RA objective, we consider the maximization of the sumof the MT throughputs weighted by coefficients that accountfor the packet priority. This approach has been widely adoptedin RA algorithms [3], [30], [31] and it has been proven tobe stable. In particular, let T (SNIRkp

) be the instantaneousthroughput of MT kp, as a function of its SNIR, and letwkp

(s) be the associated weight at time slot s. By defining thepower vector P = [P1, P2, . . . , PK ] and the weighted sum-throughput as

T (P ,K, s) =K∑

p=1

wkp(s)T (SNIRkp

) , (10)

the RA aims at solving the problem

maxK,P

T (P ,K, s) , (11)

with respect to the PC vector P and the UO K, under theconstraint of a maximum transmit power per user, i.e., Pk ≤Pmax, k = 1, 2, . . . ,K, and UO satisfying (2).

Each user throughput is defined as the number of informa-tion bits that can be successfully received by the BS and anupper bound is provided by the Shannon capacity. In practice,the capacity is achieved up to a gap, provided that a large

number of modulation and coding formats are available fortransmission. Let Γgap be the signal to noise ratio (SNR) gapto achieve capacity. We define the normalized SNIR as

Γkp=

SNIRkp

Γgap. (12)

Then the throughput relative to user kp can be written as

T (SNIRkp) = log2

(1 + Γkp

), [bit/s/Hz] (13)

Hence, we can rewrite (10) as

T (P ,K, s) =K∑

p=1

wkp(s) log2

(1 +

Pkp|Rkp,kp

|2ΓgapIkp

). (14)

From (8), (9) and (14) we observe that the SNIR and, conse-quently the throughput are determined by the transmit powerof each user. Indeed, the power determines both the usefulsignal level and the interference on other users’ signals. Asa consequence, the optimization of the power that maximizesthe total weighted throughput is not a trivial problem.

Similarly to the problem in [20], [21], it can be shown thatproblem (11) can be modeled by a graph where the node setcomprises all active users and two additional nodes, sourceand termination. We assign to each user node i the powercoefficient Pi while each arc (i, j) is weighted by Ri,j. Now,the problem of finding UO and PC that maximize the weightedthroughput becomes the problem of finding an Hamiltonianpath [36] on the graph (i.e., a sequence of nodes from thesource to the termination node in which each node of the graphappears exactly once) that satisfies (11). Since the objectivefunction is a non-linear function of powers {Pi} while thepower constraints as well as the order constraints can beformulated as linear constraints [20], [21], we then concludethat the maximum weighted throughput problem is the searchof an Hamiltonian path on a graph by a non-linear objectivefunction, under linear constraints. Unfortunately, from [37] weconclude that the problem is NP-complete and its solutionrequires an exhaustive search of the optimum UO over theentire set of K! orderings. Hence, this approach is unfeasiblefor real systems with a possibly large number of active users.Therefore, to solve (11) we resort to a stochastic approach,based on the DSA algorithm [22], whose general frameworkis: i) to iteratively select the best UO and ii) to determinethe required PC for a given UO that maximizes the weightedthroughput.

For the choice of the weights in (10), various approachesmay be considered. For example, by setting wkp

(s) = 1 themax-rate RA is obtained. In general, rate and delay will bebalanced according to requirements and we refer to literaturefor various approaches. As an example of application of opti-mization methods to multimedia traffic, we follow the proposalof [32], which aims at satisfying the QoS requirements interms of minimum delay while exploiting channel conditions.Details on the choice of the weights are reported in AppendixI.

A. Power control for a given user order

We start performing PC that maximizes the weightedthroughput for a given UO K, with a constraint on the

1382 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 4, APRIL 2008

maximum available power per user. A closed-form solutionfor this problem is not available and we resort instead to aniterative algorithm similar to the technique proposed in [34]for PC with a single user receiver and here extended to a SICreceiver.

Let P = {P : 0 ≤ P ≤ Pmax} be the set of feasible powerallocations, with Pmax a K-size vector with all entries Pmax.For a given UO K, the following properties hold in P:

• T (P ,K, s) ≥ 0. In fact, SNIR is always greater than oneand consequently the logarithm is not negative.

• T (P ,K, s) is continuous and differentiable on P ∈ P .• For all β > 1, T (βP ,K, s) > T (P ,K, s).

From the maximum-minimum theorem [35, p. 89] we con-clude that T (P ,K, s) has a maximum on set P . Unfortunately,finding it is a hard task and proposed algorithms in theliterature usually achieve only local maxima. This is the casefor example of the iterative algorithms of [34], based on thegradient of the weighted throughput. Anyway, we also proposethis strategy for the SIC receiver.

From (14) and (8), the gradient of the weighted throughputturns out to be

∂T (P ,K, s)∂Pkp

=1

ln(2)

[wkp

(s)Γkp

(1 + Γkp)· 1Pkp

−p−1∑i=1

wki(s)

Γki

(1 + Γki)· |Rki,kp

|2Iki

].

(15)

In order to optimize PC, we set (15) to zero for p =1, 2, . . . ,K and obtain a non-linear system of equations thatcan be solved iteratively.

Let us define: i) P(ν)kp

, the power allocated to user kp at

iteration ν; ii) I(ν)kp

, the interference on user kp when using

the allocated power vector P (ν); iii) Γ(ν)kp

, the normalized

SNIR of user kp computed from (12) and (9) using {I(ν)k };

iv) NPC, the maximum number of PC iterations. By setting(15) to zero, the tentative allocated power that maximizes theweighted throughput is

P(ν+1)kp

=

⎡⎣ (1 + Γ(ν)

kp)

wkp(s)Γ(ν)

kp

p−1∑i=1

wki(s)Γ(ν)

ki

(1 + Γ(ν)ki

)· |Rki,kp

|2I(ν)ki

⎤⎦−1

,

(16)for p = 1, 2, . . . ,K. Considering the user power constraint, theallocated power for a given UO that maximizes the weightedthroughput is as follows

P(ν+1)kp

=

{Pmax if P

(ν+1)kp

> Pmax ,

P(ν+1)kp

otherwise.(17)

The functional (14) may have many local maxima. By sim-ulations, we verified that the initialization P

(1)kp

= Pmax/2provides a good performance in conjunction with our UOtechnique.

IV. THE DISCRETE STOCHASTIC APPROXIMATION

ALGORITHM

The DSA algorithm is a technique to optimize (maximize)a function f(K) on a discrete set S, based upon its noisyestimate f(K), [22]. The basic idea of DSA is to build a

Markov chain having as states the elements of set S andconverging toward the maximum value of f(K) by successiveevaluations of f(K). Indeed, due to the noisy estimate, eachstate K has a non-null probability of yielding the maximumvalue of f(K) for a given set of estimates, [23].

The DSA algorithm proceeds iteratively by updating theestimate of all the state probabilities. At the end of the iterativeprocess, the state having the highest estimated probability isselected as the solution. We indicate with n the generic DSAiteration, in order to distinguish it from the PC iteration ν ofSection III-A.

In particular, let π(n)(K) be the estimate, up to iteration n,of the probability that state K is a maximizer of f , i.e.,

π(n)(K) = P[K is a maximizer of f ]. (18)

At iteration n, the DSA chooses the following three states:

• Krand, a state selected randomly in set S;• K(n)

prob, the state having the highest probability up to thecurrent iteration, i.e.,

K(n)prob = arg max

K∈Sπ(n−1)(K) ; (19)

• K(n−1)curr , the state selected at the previous iteration.

Among the three states, the new selected state, K(n)curr, maxi-

mizes the noisy objective function f(K), i.e.,

K(n)curr = arg max

K∈{Krand,K(n−1)curr ,K(n)

prob}f(K) . (20)

Next, the state probabilities are updated by increasing theprobability of state K(n)

curr and decreasing the probabilities ofall the other states,

π(n)(K) =

{(1 − μ(n))π(n−1)(K) + μ(n), K = K(n)

curr

(1 − μ(n))π(n−1)(K), K �= K(n)curr ,

(21)where μ(n) is a suitable decreasing function of n. It isseen that, as the number of iterations increases, the stateprobabilities converge to the average value, and the coefficientμ(n), together with the randomness of f(K), determines thespeed of convergence, [22].

A. Resource allocation by DSA

Our cross-layer RA requires that we optimize both PC andUO. By a direct application of DSA to the RA problem, thestates are all the UOs

S = {K = [k1, k2, . . . , kK ] : ki �= kj for i �= j, 1 ≤ ki ≤ K} ,(22)

and the function to be maximized is the weighted throughput

f(K) = maxP ,Pi<Pmax

T (P ,K, s) , K ∈ S . (23)

We observe that once the UO has been set, the maximumof T (P ,K, s) with respect to P can be computed using thealgorithm described in Section III-A. In this case the estimatedfunction f(K) is the weighted throughput (14) correspondingto the evaluated powers P (NPC)(K), for UO K.

The resulting algorithm is shown in Table I, where NDSA

is the number of iterations for the DSA loop.

VERONESI et al.: CROSS-LAYER OPTIMIZATION FOR MULTIMEDIA TRAFFIC IN CDMA CELLULAR NETWORKS 1383

TABLE I

GENERAL (I)DSA ALGORITHM FOR UO AND PC.

Initialization1) Choose at random an order K ∈ S. Set K(0)

curr = K.2) Set the probability vector π(0)(K′) = 0, ∀K′ �= K. Set π(0)(K) = 1.3) Set n = 1.

DSA loop4) Select at random an order Krand ∈ S.5) Select the UO with highest probability K(n)

prob =

arg maxK π(n−1)(K).PC loop

6) Iterate NPC times the PC algorithm of Section III-A to compute theweighted throughput T (P (NPC)(K),K, s) for UO’s Krand, K(n−1)

curr

and K(n)prob.

Comparison step7) Set K(n)

curr = arg maxK∈{Krand,K(n−1)curr ,K(n)

prob}T (P (NPC)(K),K, s).

8) Update the probability vector π(n) according to (21).9) End of DSA iteration

10) Increase n.11) If n < NDSA go to step 6), else end.

B. DSA with integrated power control and user order

It is seen that the above algorithm may have a very slowconvergence, due to the two iterative loops, the outer forUO and the inner for PC. Hence, we propose to integratethe two adaptive processes in a loop where at each iterationn we store both the current UO K(n)

curr and the correspond-ing allocated power vector P (n). The estimated function isf(K) = T (P (n−1),K, s).

In particular, once the current state K(n)curr has been selected,

P (n) is computed by just a one-step application of the PCiterative algorithm of Section III-A. We denote the DSA withintegrated PC and UO as IDSA.

We observe that at each iteration, IDSA compares theweighted throughput for UOs Krand, K(n−1)

curr and K(n)prob, using

the same allocated power P (n). As a result, the selectionprocedure may turn out to be biased toward a suboptimal UO,and not leading to the optimal solution. Indeed, by simulationsit is seen that in the cases of interest IDSA converges to theDSA solution. As a matter of fact, for an equal number oftotal iterations, NPC · NDSA, IDSA explores more UOs thanDSA, while slowly adapting the allocated power. Hence, ingeneral, IDSA shows a faster convergence than DSA.

C. IDSA with matrix implementation (IDSA-MI)

Concerning the implementation complexity, we observe thatset S on which DSA is applied has K! states and for each stateit is necessary to store and update its probability. This resultsin a factorial memory requirement. Hence, the conventionalDSA approach translates the NP problem (11) into a problemrequiring an exponential memory with respect to the numberof active users.

In order to obtain a feasible approach we consider an imple-mentation based on a factorization of the state probabilities.We consider the probability that user i precedes user j in theUO, i.e.,

Ψi,j = P[p < q : kp = i, kq = j , with K = [k1, k2, . . . , kK ]] ,(24)

with i, j = 1, 2, . . . , K, i �= j. At each IDSA iteration westore an estimate of {Ψi,j} into the K ×K matrix Φ(n). Thediagonal of Φ(n) is set to zero and its values are never used.

When UO K(n)curr is selected, Φ(n) is updated as follows. Let

us consider the first user k1 in the ordered vector K(n)curr. This

user precedes all the other users in K(n)curr and correspondingly

entries Φ(n)k1,j , for all j �= k1, are increased in the probability

matrix. For the second user k2, all entries Φ(n)k2,j , for all j �=

k1, k2, are increased, and so on. In general, let us define theset of [K(K − 1)]/2 couples

I(K(n)curr) = {(ki, kj) : i < j, ki, kj ∈ K(n)

curr} . (25)

The updated probability matrix is

Φ(n)i,j =

{(1 − μ(n))Φ(n−1)

i,j + μ(n), (i, j) ∈ I(K(n)curr)

(1 − μ(n))Φ(n−1)i,j , (i, j) /∈ I(K(n)

curr) .(26)

Now, we approximate the probability of UO K as theproduct of probabilities Φ(n)

i,j relative to order K, i.e., theprobabilities that user kp precedes users kp+1, kp+2, . . . , kK ,for p = 1, 2, . . . ,K and we write

π(n)(K) ≈K∏

p=1

K∏j=p+1

Φ(n)kp,kj

. (27)

In order to find the UO with the highest probability [step5) of Table I] using matrix Φ(n−1), we resort to a greedyalgorithm that, instead of maximizing over the probabilities(27), maximizes the probability of each pair user-position. Asa first step, we determine the first user in K(n)

prob as the onehaving the highest probability, i.e., for p = 1 we determine

k1 = arg maxk

∏j �=k

Φ(n−1)k,j . (28)

Then, the row k1 of Φ(n−1) is set to zero and the columnk1 of Φ(n−1) is set to one. Next, the second user in K(n)

prob

is selected by using (28) on the reduced matrix. In general,at iteration p, after the selection of user kp by (28), the rowkp of Φ(n−1)

k,j is set to zero and the column kp of Φ(n−1)k,j is

set to one. The new matrix is used for the choice of the nextuser and the procedure is iterated K times to determine allthe users of K(n)

prob.

V. NUMERICAL RESULTS

We assess the performance of the proposed cross-layer RAtechnique in terms of both network and physical layer parame-ters. For the network parameters we consider the packet delay,the packet loss probability and the total network throughput.As physical layer parameters we consider the consumed powerper user.

We compare the proposed optimization algorithm againsttwo approaches: the maximum-power weight-ordering(MPWO) technique and the power ordering (PO) technique.In MPWO [3] all users with wkp

(s) > 0 are at the maximumpower, i.e., Pkp

= Pmax for p = 1, 2, . . . ,K, and users areordered with increasing weights, i.e., wkp

(s) < wkp+1(s). Inthis case the SNIR becomes

SNIRkp=

Pmax|Rkp,kp|2

Pmax

∑Kq=p+1 |Rkq,kq

|2 + Rkp,kpN0

. (29)

1384 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 4, APRIL 2008

TABLE II

PARAMETERS OF THE SIMULATION SCENARIO.

PARAMETER VALUEchannel rmsds 0.5 μs

cell radius 580 mTS 1 msTc 50 ns

pathloss exponent 3.5std. deviation shadowing 6 dB

NS 32Pmax 10 mWΓgap 1Sv 10σ 4 kbpsa 3.9 s−1

Lmin 815 bytesLmax 320000 bytesTmes 296 slotsTrs 1000 slotsTpc 300 slots

Dmax,RT 2%Dmax,NRT 20%

WRT = WNRT 100ms

It has been shown [3] that MPWO is optimum when themutual interference among users is a constant, i.e., Ri,j = Rj,j

for all i �= j.In the power ordering (PO) approach users are ordered with

decreasing channel gains, i.e., Rkj ,kj≥ Rki,ki

, j < i, i, j =1, 2, . . . ,K, and Pki

= Pmax for all users with wki(s) > 0.

For a fair comparison, weights wkp(s) are updated as

described in Appendix I for both MPWO and PO.Simulation scenario. The parameters of the simulation

scenario are reported in Table II. We consider a UMTS-likeenvironment where the channel includes pathloss, log-normalshadowing and an exponentially decaying power delay profile.The channel is block fading as each slot is characterized byindependently generated channel. MTs are uniformly distrib-uted within the cell and each terminal is assigned a differentHadamard code. Transmission from terminals is asynchronouswith uniform random delays. We assume that the noise is suchthat a terminal transmitting with maximum power from theborder of the cell achieves an average SNR of 10 dB.

As examples of RT and NRT traffics, we consider video andweb sources, respectively, while the extension of the proposedmodels to other sources is straightforward. A description ofthe traffic generation is reported in Appendix II while itsparameters are reported in Table II. The average rate of NRTtraffic is 123 kbps.

For DSA and IDSA algorithms the coefficient for the updateof the probability vector is μ(n) = 1 [22].

Comparison between DSA and IDSA. We first comparethe DSA and IDSA algorithms for RT traffic with an averagerate m = 250 kbps. For each slot, for DSA we consideredNDSA = 50 and NPC = 10 while for IDSA we consideredNDSA = 500 and obviously NPC = 1. Fig. 1 shows theweighted throughput as a function of the iteration number forK = 32 active users. From the figure we see that IDSA has amuch faster convergence than DSA, because it explores moreUOs than DSA. Hence, forthcoming results are presented onlyfor IDSA with NDSA = 250 iterations per slot. Indeed inpractice, results shown in Fig. 1 represent an upper bound onthe convergence time, associated with the worst case scenario

0 100 200 300 400 5004.8

4.9

5

5.1

5.2

5.3

5.4

5.5

5.6

5.7

iteration number

wei

ghte

d th

roug

hput

IDSADSA

Fig. 1. Weighted throughput as a function of the iteration number per slotfor DSA and IDSA algorithms. RT traffic with an average rate m = 250kbps and K = 32 active users.

of a block fading channel with independent realizations at eachslot. In fact, when channels of adjacent slots are correlated,the iterative RA algorithm can be initialized with the solutionobtained at the previous slot. In this case the number ofiterations needed to achieve convergence is smaller. Note alsothat when the channel is varying during a slot, the capacity(13) should be replaced by the ergodic capacity.

Packet delivery probability and excess delay. A first QoSparameter is the percentage of packets delivered to the des-tination. We remember that RT packets have a deadline timeafter which they are discarded from the queue. Fig. 2 showsthe probability of discarded packets for a RT transmission, asa function of the RT traffic average rate m, while the rate ofNRT traffic is as from Table II. We see that the proposed DSA-based RA has a significantly higher probability of deliveringRT packets than both MPWO and PO. Concerning the NRTtraffic, Fig. 3 shows the probability the NRT packets havean excessive delay, as a function of the offered RT traffic.We observe that IDSA is able to significantly reduce theprobability of packets with excessive delay with respect toexisting techniques.

Average delay. Another interesting QoS parameter is theaverage delay for both RT and NRT traffic. Figures 4 and 5show the mean delay of RT and NRT traffic, respectively, as afunction of the average rate of RT traffic m. We observe thatin general IDSA yields a much lower mean delay than bothPO and MPWO.

Mean allocated power. In the considered multiuser sce-nario, increasing the transmit power yields potentially a higherthroughput but also a higher interference level for other users.Fig. 6 compares the different RA schemes in terms of meanallocated power. The result is that IDSA has a reduced powerconsumption with respect to both PO and MPWO. Hencewe conclude that the proposed technique is not only able toguarantee a better fairness among users but it also provides alower power consumption for MTs, which are usually stronglylimited by battery duration.

Network goodput. Fig. 7 shows the goodput of the net-

VERONESI et al.: CROSS-LAYER OPTIMIZATION FOR MULTIMEDIA TRAFFIC IN CDMA CELLULAR NETWORKS 1385

1 1.5 2 2.5 3 3.5 4 4.5

x 105

10−4

10−3

10−2

10−1

100

average rate of RT traffic [bps]

prob

. of d

isca

rded

pac

kets

16 users32 users

Fig. 2. Probability of discarded packet as a function of the RT traffic averagerate m. Solid lines: IDSA. Dashed lines: PO (empty markers), MPWO (filledmarkers).

1 1.5 2 2.5 3 3.5 4 4.5

x 105

10−2

10−1

100

average rate of RT traffic [bps]

prob

. of e

xces

s de

lay

pack

ets

16 users

32 users

Fig. 3. Probability of excessive delay for NRT packets as a function ofthe RT traffic average rate m. Solid lines: IDSA. Dashed lines: PO (emptymarkers), MPWO (filled markers).

work, i.e., the number of bits per second that effectivelyreach the application. Goodput does not include the partialtransmission of RT packets that are discarded because notcompletely transmitted before the deadline. Note that the targetof the RA is not to increase goodput but to balance goodput,priority and fairness among users. Still, from Fig. 7 we observethat the IDSA, which provides the better fairness, also yieldsa similar or even better goodput than the other two techniques.Lastly, note that goodput shows a floor for a high traffic rate,due to the mutual interference among users, as to be expectedin a CDMA uplink.

Computational complexity and memory requirements.Computational complexity and memory requirements of theproposed schemes are now provided. In order to assess thecomputational complexity, we compare both the number ofcomplex multiplications and the number of comparisons, sinceUO requires a large number of comparisons. For the memoryoccupation, we provide the order of required memory cellswith respect to the number of users. Table III summarizes

1 1.5 2 2.5 3 3.5 4 4.5

x 105

0

0.02

0.04

0.06

0.08

0.1

0.12

average rate of RT traffic [bps]

mea

n de

lay

of R

T tr

affic

[ms]

8 users16 users32 users

Fig. 4. Mean delay of RT traffic as a function of the RT traffic averagerate m. Solid lines: IDSA. Dashed lines: PO (empty markers), MPWO (filledmarkers).

1 1.5 2 2.5 3 3.5 4 4.5

x 105

0

0.005

0.01

0.015

0.02

average rate of RT traffic [bps]

mea

n de

lay

of N

RT tr

affic

[ms]

8 users16 users32 users

Fig. 5. Mean delay of NRT traffic as a function of the RT traffic averagerate m. Solid lines: IDSA. Dashed lines: PO (empty markers), MPWO (filledmarkers).

the complexity for various UO and PC schemes. We observethat the complexity of (I)DSA is dominated by the squareof the number of explored UOs (N2

DSA) and the square ofthe number of users (K2). As the memory occupation, for(I)DSA it grows proportionally to KNDSA, while for IDSA-MI it grows as K2, i.e., the size of the probability matrix.A comparison of (I)DSA(-MI) techniques with MPWO andPO shows that the proposed techniques have a much highercomplexity and memory occupation than existing techniques.However, since K is in general not very large, complexitymay not be a problem. On the other hand, the performanceadvantage of the proposed technique is significant.

VI. CONCLUSIONS

We proposed an iterative technique for optimizing PCand UO in SIC for differentiated traffic, suited to enablemultimedia applications in multiuser scenarios. By meansof a cross-layer optimization, based on a discrete stochasticapproximation method, we were able to optimize each user

1386 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 4, APRIL 2008

TABLE III

COMPUTATIONAL COMPLEXITY AND MEMORY OCCUPATION OF UO AND PC SCHEMES.

Technique Complex Multiplications Comparisons O(Memory)

DSA, IDSA NDSANPC

�3K + 5

K(K−1)2

�+ NDSANPCK+ KNDSA

N2DSA + NDSAK 3NDSA + N2

DSA

IDSA-MI NDSANPC

�3K + 5

K(K−1)2

�+ NDSAK2+ NDSANPCK+ K2

NDSA

�K2 +

K(K−1)2

�+ NDSAK

�K(K−1)

2+ 3

�NDSA

MPWO, PO K +K(K−1)

2K log2(K) K

1 1.5 2 2.5 3 3.5 4 4.5

x 105

4

5

6

7

8

9

10x 10

−3

average rate of RT traffic [bps]

mea

n us

er p

ower

[W]

8 users16 users32 users

Fig. 6. Mean allocated power per user as a function of the RT traffic averagerate m. Solid lines: IDSA. Dashed lines: PO (empty markers), MPWO (filledmarkers).

power/rate and at the same time guarantee fairness and reducethe delay of packet transmissions. For multimedia transmis-sions over a UMTS-like scenario, the proposed techniqueallows to increase the goodput of RT traffic by about 50% anddecrease the mean delay of NRT traffic by about 25%, withrespect to existing techniques. This significant performanceadvantage comes at the price of a much higher computationalcomplexity due to the large number of iterations per slotneeded to achieve convergence, at least in a block fadingchannel with independent realizations.

APPENDIX ICHOICE OF THE WEIGHTS

We choose the weights according to [32], which aims atsatisfying the QoS requirements in terms of minimum delaywhile exploiting the channel conditions. We consider threeindices, two for fairness and one for the channel quality.Concerning the channel condition at slot s, we consider thechannel gain at the detection point normalized to the sum ofall other user channel gains [33], i.e.,

Ich(k, s) =Rk,k∑Kj=1 Rj,j

. (30)

1 1.5 2 2.5 3 3.5 4 4.5

x 105

0

5

10

15x 10

6

average rate of RT traffic [bps]

netw

ork

good

put [

bps]

8 users16 users32 users

Fig. 7. Network goodput as a function of the RT traffic average rate m. Solidlines: IDSA. Dashed lines: PO (empty markers), MPWO (filled markers).

The normalized channel index Ich(k, s) provides a first as-sessment of channel quality independently of the allocatedpowers, while using (9) as channel index would require toknow in advance the user powers.

We account for fairness, based on the delay that each user’spacket experiences at the MT, with two indices. The first indextakes care of the packets in the queue, while the second indexis referred to the average user performance. In particular, letus indicate with Dmax,RT(k) (Dmax,NRT(k)) the deadline, inslots, of the oldest packet of user k in the RT (NRT) queue andwith ςRT(k) (ςNRT(k)) the corresponding slot number whenthe packet entered into the queue. For RT and NRT queues ofuser k at slot s we define a first fairness index [32]

ξRT(k, s) =[s − ςRT(k)]Dmax,RT(k)

, (31)

ξNRT(k, s) = min(

[s − ςNRT(k)]Dmax,NRT(k)

, 1)

. (32)

Note that when ξRT(k, s) = 1, RT packets are droppedbecause the deadline is strictly enforced. For NRT packets in-stead, even when the deadline is reached packets are still keptin the queue for future transmission, but they are consideredto have an excessive delay.

The second fairness index accounts for the history of userk, i.e., for its average performance up to slot s. Let us indicate

VERONESI et al.: CROSS-LAYER OPTIMIZATION FOR MULTIMEDIA TRAFFIC IN CDMA CELLULAR NETWORKS 1387

with LRT(k, s) (LNRT(k, s)) the percentage of discarded (de-layed) RT (NRT) packets of user k up to slot s, averaged overa window WRT (WNRT). Let Lmax,RT(k) (Lmax,NRT(k)) bea parameter indicating the maximum tolerated discard (excessdelay) rate for user k. The second fairness index is defined as

ηRT(k, s) = min(

LRT(k, s)Lmax,RT(k)

, 1)

, (33)

ηNRT(k, s) = min(

LNRT(k, s)Lmax,NRT(k)

, 1)

(34)

for RT and NRT traffic queues, respectively.From indices ξRT(k, s), ξNRT(k, s), ηRT(k, s) and

ηNRT(k, s) we obtain a fairness priority index for each of thetwo queues, relative to RT and NRT traffic, respectively, as

φRT(k, s) ={

ξRT(k,s)+ηRT(k,s)4 if ηRT(k, s) < 1

1 if ηRT(k, s) = 1 ,(35)

φNRT(k, s) ={

ξNRT(k,s)+ηNRT(k,s)4 if ηNRT(k, s) < 1

1 if ηNRT(k, s) = 1 .(36)

The fairness user index is then derived as

η(k, s) =φNRT(k, s) + φRT(k, s)∑K�=1 φRT(�, s) + φNRT(�, s)

. (37)

Lastly, indices Ich and η are combined to obtain the weightfor user k as

wk(s) ={

η(k, s) + [1 − η(k, s)]Ich(k, s) if η(k, s) > 00 if η(k, s) = 0 ,

(38)and if η(k, s) ≤ 0 the power of user k is set to zero.

Once PC and UO have been performed, for each userpackets are transmitted by choosing the RT traffic firstif φRT(k, s) ≥ φNRT(k, s), or the NRT traffic first ifφRT(k, s) < φNRT(k, s).

APPENDIX IITRAFFIC MODEL

Each video source is obtained by aggregating the traffic ofSv independent minisources, each characterized by an ON-OFF Markov chain [27], [28]. When in the ON state, theminisource generates bits at a constant rate Rv, while no trafficis generated in the OFF state. The number of slots spent in theON (OFF) state is geometrically distributed with mean TON

(TOFF). We indicate with m and σ the mean and standarddeviation of the bit-rate of a video source. Then the parametersof the video source are obtained as

TON =1

aTS

(1 +

m2

Svσ2

)(39a)

TOFF =1

aTS

(1 +

Svσ2

m2

)(39b)

Rv =m

Sv+

σ2

m, (39c)

where a characterizes the slope of the auto covariance of thebit-rate.

For each web source we consider a Markov chain with twostates: packet call and reading [27]. When in the packet call

state, the source generates a number of messages geometricallydistributed with mean Tpc. Each message has a duration inbytes ranging from Lmin to Lmax and the duration is generatedas L = �x�, where x is random variable having as probabilitydensity function a truncated Pareto function

p(x) =ζLζ

min

xζ+1[1(x − Lmin) − 1(x − Lmax)]

+(

Lmin

Lmax

)ζ

δ(x − Lmax) ,

(40)

with 1(x) the step function, δ(x) the Dirac delta functionand ζ = 1.1. The inter-arrival time between messages isgeometrically distributed with mean Tmes. The number of slotsspent in the reading state is also geometrically distributed withmean Trs and in this state no traffic is generated.

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Daniele Veronesi was born in Rovereto, Italy, onAugust 4, 1979. He received the Laurea degreein Telecomunication Engineering (2003) from theUniversity of Padova, Italy. From January 2004 toDecember 2006, he has been a Ph.D. student atthe University of Padova. During the academic year2005, he has been six months at the University ofMassachusetts, Amherst (USA) as exchanging Ph.D.student. After receiving the Ph.D. degree (2006) hejoined STMicroelectronics as a consulting digitaldesign engineer.

Stefano Tomasin (S’99-M’04) received the Laureadegree and the Ph.D. degree in TelecommunicationsEngineering from the University of Padova, Italy, in1999 and 2002, respectively. In the Academic year1999–2000 he was on leave at the IBM ResearchLaboratory, Zurich, Switzerland, doing research onsignal processing for magnetic recording systems.In the Academic year 2001–2002 he was on leaveat Philips Research, Eindhoven, the Netherlands,studying multicarrier transmission for mobile appli-cations. He joined the University of Padova first

as contractor researcher for a national research project (2002) and then asAssistant Professor (2005). In the second half of 2004 he was visiting facultyat Qualcomm, San Diego (CA) doing research on receiver design for mobilecellular systems. His current research interests include signal processingfor wireless communications, access technologies for multiuser/multiantennasystems and cross–layer protocol design and evaluation.

Nevio Benvenuto (S’81-M’82-SM’88) received theLaurea degree from the University of Padova,Padova, Italy, and the Ph.D. degree from the Univer-sity of Massachusetts, Amherst, in 1976 and 1983,respectively, both in electrical engineering. From1983 to 1985 he was with AT&T Bell Laboratories,Holmdel, NJ, working on signal analysis problems.He spent the next three years alternating betweenthe University of Padova, where he worked on com-munication systems research, and Bell Laboratories,as a Visiting Professor. From 1987 to 1990, he was

a member of the faculty at the University of Ancona. He was a member ofthe faculty at the University of L’Aquila from 1994 to 1995. Currently, he isa Professor in the Electrical Engineering Department, University of Padova.His research interests include voice and data communications, digital radio,and signal processing.