optimal power allocation in ds-cdma with adaptive sic technique

Telecommun Syst (2014) 56:335–346DOI 10.1007/s11235-013-9847-2

Optimal power allocation in DS-CDMA with adaptive SICtechnique

Santi P. Maity · Sumanta Hati · Chinmay Maji

Published online: 30 August 2013© Springer Science+Business Media New York 2013

Abstract This paper proposes an optimal power alloca-tion in direct sequence-code division multiple access (DS-CDMA) system. The objective is to minimize total transmitpower, while simultaneously meeting the certain sum chan-nel capacity (data transmission rate) and outage probabil-ity constraints on Rayleigh fading channel. Then a weightedcorrelator with an adaptive successive interference cancela-tion (SIC) scheme is developed using neural network (NN)for an improvement in receiver performance. A closed math-ematical form of joint probability of error (JPOE) is derived.This determines the number of active users’ interfering ef-fect that needs to be canceled in order to achieve a desiredbit error rate (BER) value. Mathematical analysis shows thatbetter receiver performance can be achieved through largechange in weight up-gradation (w) for the strong users witha particular change in learning rate (η). Simulation results interms of sum capacity as well as weak user’s (users withpoor channel gain) capacity, outage probability and BERperformance duly support the effectiveness of the proposedscheme over the existing works.

Keywords DS-CDMA · Power allocation · SIC · Neuralnetwork · JPOE

S.P. Maity (B) · S. Hati · C. MajiDepartment of Information Technology,Bengal Engineering and Science University, Shibpur,Howrah 711 103, Indiae-mail: [email protected]

S. Hatie-mail: [email protected]

C. Majie-mail: [email protected]

1 Introduction

Spread spectrum (SS) modulation has proven to be efficientin data transmission over normal (common) as well as hos-tile channel (jamming scenario) due to its interference rejec-tion and anti-jamming capability [25]. Although SS modu-lation was originally developed for military communication,lot of other communication systems for civilian applicationsare also developed that are benefitted from its unique char-acteristics. As a matter of fact, its use is not only restrictednowadays in data transmission but also in various other di-verse areas; one such application is digital media protec-tion using data hiding. SS modulation based data hiding[17] or data hiding schemes integrated with SS modulation[18] leads to some typical applications like access controland error concealment of multimedia signals in fading chan-nel. As name implies, SS modulation demands excess band-width for message transmission than its minimum require-ment. However, at the same time, it allows multiple usersaccess of a common radio frequency channel in the samegeographical location that leads to code division multiple ac-cess (CDMA). CDMA may be implemented using direct se-quence (DS) or pseudo noise (PN), frequency hopping (FH)or time hopping (TH) mechanism, each one offers its relativemerits and demerits. Among different CDMA implementa-tions, DS method offers the best noise and anti-jamming per-formance along with the best discrimination against multi-path, a common issue in radio mobile channel [6].

Recently DS-CDMA and its multicarrier version likeMC-CDMA become promising to support multimedia ser-vices in mobile radio communications. In CDMA, multiplenumber of users share the same channel bandwidth at thesame time through the use of (near) orthogonal spreadingcodes. So it has potential to provide higher user capacity(more number of users) compared to its other close competi-

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336 S.P. Maity et al.

tors such as time division multiple access (TDMA) and fre-quency division multiple access (FDMA). CDMA systemshave an interesting property that their user capacity is typ-ically limited by multiple-access interference (MAI), ratherthan noise [19]. According to Shannon channel capacity the-orem, increase in signal power increases signal-to-noise ra-tio (SNR) for a given noise power. This in turn improvesthe system’s channel capacity (c) i.e. data transmission ratefor single user communication. However, in the presence ofmultiple users, if all users try to increase their data rates byincreasing their transmit power, the users interfere and boththe signal and interference power increase. Consequently,the signal-to-interference plus noise power- ratio (SINR)and therefore the users’ rates saturate at a constant value[11]. In other words, high SNR values of other users act asstrong interfering effect to the nearby users in multiuser sys-tem that transmits in the same radio frequency. This sug-gests that optimum power allocation is essential in order toincrease channel capacity and to reduce bit error rate (BER)values in fading channel. Power allocation also becomes animportant issue in multicarrier communication like orthog-onal frequency division multiplexing (OFDM) with multi-input multi-output (MIMO) system [2], to achieve boundedaverage queuing delay in wireless network [8] and as a formof game in multi-antenna terminals [3].

Fading is a typical problem in wireless mobile communi-cation system that causes variability in the amplitudes of thereceived signals. This is generated due to multipath prop-agation with variable path lengths and forms highly ran-dom nature of transmission channel. Fading is characterizedby various statistical models like Rayleigh, Rician, Nak-agami, Lognormal, Suzuki etc. where each model becomesappropriate depending on the various constituent compo-nents forming the mobile wireless channel [26]. Rayleighfading is popular to represent slow fading channel which af-fects the transmitting signals, causes link failure, interfereamong multipath and multiple users in degraded manner andcauses wrong detection of the received signal. Apart from anincrease in sum channel capacity, increased power allocationminimizes outage probability over fading channel. Outageprobability likes to mean that the probability with which thetarget data rate (as per Shannon’s channel capacity) cannotbe met due to variable gain in fading channel. Hence, users’power allocation in radio mobile CDMA system has twofoldconflicting effects. At one end, increase in transmit powerincreases data transmission capacity (meeting the requireddata rate) with low value of outage probability. On the otherhand, it causes an interfering effect on other users’ receivedsignals that leads to reduction in user capacity i.e. number ofusers. Hence, design problem for the first part of this work isas follows: minimizing the total transmit powers subject tosimultaneously meeting the target sum capacity and outageprobability constraints.

It is already mentioned that MAI in CDMA puts a limiton user capacity for an acceptable value of BER perfor-mance. Multiuser detection (MUD) [29] is proposed toachieve single user performance through the mitigation ofthe effect of MAI. Various forms of MUDs are suggested,among them few popular schemes are successive interfer-ence cancellation (SIC) [10], parallel interference cancella-tion (PIC) [7], partial PIC (PPIC) [13], block PIC (BPIC)[16] etc. Performance results along with the merits and thedemerits of each one in terms of BER, computation cost andcomplexity, time complexity and hardware requirement arereported in the literature. These various variants of inter-ference cancelation are broadly classified as SIC and PIC.SIC offers intrinsic advantages such as potential compatibil-ity with current commercial systems, allows use of strongerror-correcting codes (ECC), and is robust in an asyn-chronous environment [1]. Over and above, SIC schemesrequire the minimum amount of additional hardware com-pared to PIC schemes. Some disadvantages in SIC schemesare also seen. SIC suffers from couple of typical problems:firstly (i) one additional bit delay per stage cancellation isrequired. This leads to larger delay problem in order toachieve desired BER values through large number of inter-ference cancellation. Secondly, significant deterioration inBER performance occurs when initial estimation of the sig-nal strength of different users is not reliable. Thirdly, SICperformance largely depends on reordering of the signalstrengths whenever the power delay profile of radio mobilechannel changes.

To make SIC effective and useful, a trade-off must bemade between the (less) number of users’ interfering effectto be canceled sacrificing in BER value and the amount ofdelay that can be tolerated. At the same time the other pointto be considered is the precision of power ordering and theacceptable processing complexity. In other words, systemshould be capable to overcome the effect of non-reliability inthe initial data estimates. This can be achieved at an accept-able level of system complexity provided that the estimationof the parameters like amplitude and phase for the trans-mitted data is made accurately. Adaptive learning becomesessential and makes design of an adaptive SIC technique inDS-CDMA as other objective of this work.

The rest of the paper is organized as follows. Section 2discusses review of related works, limitations and scope ofthe present work. System model for DS-CDMA with op-timal power control is then proposed in Sect. 3. Section 4presents neural network assisted SIC scheme for improveddetection. Performance evaluation of the proposed schemeis presented in Sect. 5. Finally, the paper is concluded inSect. 6 along with scope of future works.

Optimal power allocation in DS-CDMA with adaptive SIC technique 337

2 Review of related works, limitations and scope of thepresent work

This section makes a brief review for optimal power alloca-tion and multiuser detection in CDMA system followed bytheir limitations and scope of the present work.

2.1 Review of related works

Channel capacity improvement by adaptive power allocationin CDMA and its multicarrier version i.e. MC-CDMA sys-tem is an important research topic. The optimized systemsinclude adaptive algorithm to minimize the total transmit-ted power [14], iterative transmitter and receiver optimiza-tion in CDMA networks [27] that is based on the alternatingminimization technique on the MSE (mean squared error)cost function, joint optimization of spreading codes and autility based power control [22]. Some of the methods alsoconsider joint rate and power control [24], joint transmitter-receiver optimization using multiuser detection and resourceallocation for energy efficiency in wireless CDMA networks(applying a game theoretic formulation, a non-cooperativegame for utility maximization is formulated) [5]. Techniquesused employ transmitter power control, receiver array pro-cessing and multiuser detection [23], etc. The objective ofthe optimized methods, in general, is to minimize total trans-mit power and maximize sum channel capacity.

On the other hand, literature on MUD is also quite rich.The optimum multiuser detector proposed in [28] achievessignificant performance improvement relative to single userreceiver. This improvement is achieved with the associatedcomputational complexity and cost that are increased expo-nentially with the number of users. Low complexity linear[15] and decision driven suboptimal MUD techniques arethen suggested. Several SIC schemes are reported in litera-ture based on analytic and intelligent (soft) computing ap-proaches. Error control code (ECC) is used in the work ofFang and Milstein [10] where an efficient SIC is proposedin convolution coded multicarrier DS-CDMA system. Duaet al. [9] propose two minimum probability of error basedspace-time multiuser detection algorithms. Yen and Hanzopropose [30] genetic algorithms (GA) assisted joint mul-tiuser symbol detection and fading channel estimation forsynchronous CDMA systems. The use of GA offers low costand tractable solution over analytical approaches.

An optimal power control algorithm for MC-CDMA withSIC is derived in [1] with an analytical bit-error rate expres-sion for an uncoded system. The first algorithm in [9] aimsto minimize the joint probability of error (MJPOE) for allusers. The work also proposes solution for the minimumconditional probability of error (MCPOE) that minimizesthe probability of error of each user conditioned on the trans-mitted bit vector. Bhattacharya and Biswas propose [4] two

stage interference cancellation scheme. Detectors switch dy-namically from SIC to RAKE depending on the channelcharacteristics. The authors reported that SIC behaves likea match filter at low SNR. On the other hand, at high SNRvalues, RAKE receivers are deployed to achieve better ca-pacity than conventional detectors.

2.2 Limitations and scope of the work

Optimized systems reported in the literature focus primarilyon power control, minimization of transmit power, joint rateand power control for single carrier CDMA. To the best ofour knowledge, the issue is not well investigated that simul-taneously minimizes total transmit power subject to meetingthe target sum capacity (data transmission rate) constraintwith reliable delivery i.e. maintaining outage probabilityconstraint. On the other hand, the previously proposed al-gorithms of multiuser detection mostly focus on throughputimprovement along with reduction in computation complex-ity. The algorithms do not study the performance in an un-known and time varying channel parameters. Important sys-tem design aspects such as multipath, latency, and estima-tion error have often been neglected. The issues are mostlytaken care by adaptive multiuser detector system. Althoughblind adaptive multiuser detectors have the advantage thatthey eliminate the need for a training sequence in adaptationmode that leads to savings in bandwidth, but the overall sys-tem design is complicated and not many wireless standardstoday use blind algorithms.

To address the above mentioned problems, this work pro-poses power allocation algorithm in DS-CDMA system. Theobjective is to minimize total transmit power subject to si-multaneously meeting the sum (total) capacity rate con-straint and outage probability. A closed from solution foreach user’s transmit power is developed using convex opti-mization framework. Then an adaptive SIC technique is alsoproposed for the system using neural network (NN) [20].A learning algorithm is developed using single layer or multilayer feed forward NN for some known data sets (using su-pervised learning method). Then this network is used to es-timate the user signal’s amplitudes under Rayleigh fadingchannel that in turn designs weighted correlator. Mathemat-ical analysis shows that weight updating for the strong usersmust be higher compared to weak users. Performance of thesystem has been studied using variable learning rate.

Receiver performance improvement is another goal ofthis work. To address this problem, a closed form analyticalexpression of joint probability of error (JPOE) is also de-veloped. This analytical expression determines the requirednumber of users for which the interfering effect to be can-celled, out of a given number of active users. The aim is toachieve a certain acceptable JPOE value. Simulation resultsclosely follow the mathematical results. Lastly, the effects


of initial wrong ordering of the interfering signals based onthe correlation values of the different users are also stud-ied. Simulation results show that the proposed adaptive al-gorithm is capable to solve initial wrong ordering of a coupleof pair of users. This leads to achieve an acceptable level ofBER values.

3 System model for synchronous DS-CDMA withoptimal power allocation

In the present case, a DS-CDMA system with K number ofactive users is considered. It is also assumed that K userslike to transmit their information asynchronously over aRayleigh fading channel. In DS-CDMA system, each user’stransmitted data is spread in time domain using a uniquespreading code. Communication channel is assumed to beaffected by additive white Gaussian noise (AWGN) apartfrom time varying gain. It is assumed that channel state in-formation (CSI) is available at the transmitter for optimalpower control. Mathematically, the received signal imping-ing on a single antenna element at the base station can beexpressed as,

r(t) =K∑

j=1

α∑

i=−α

Ajhjbj (i)Sj (t − iT − τj ) + n(t) (1)

where Aj and bj (i) are the amplitude of the j th usertransmitted signal and ith symbol (±1), respectively int ∈ [iT , (i + 1)T ], T is the bit interval. The symbol τj indi-cates the time delay for the j th user’s received signal, hj isthe j th user’s Rayleigh fading channel gain, Sj (t) is the sig-nature waveform (spreading code) of the j th user and n(t)

is the AWGN with zero mean and a two sided power spec-tral density (PSD) of σ 2 W/Hz. The transmit power Pj forthe j th user can be obtained by squaring the signal ampli-tude of Aj . In the subsequent analysis, we will focus on cal-culation of power instead of amplitude for the j th user. Ingeneral, spreading codes should satisfy the following prop-erties.

(i) The signature waveforms are time limited in [0, T ] i.e.Sj (t) = 0 for t ∈ [0, T ],

(ii) Each signature/spreading waveform has unit energy i.e.∫ T

0 S2j (t)dt = 1 for all j .

The received signal in DS-CDMA system is correlatedwith the j th user’s signature waveform Sj (t) to decode j thuser data. Mathematically, correlation value is written as

yjj = ⟨r(t), Sj (t)

⟩ = Ajhjbj +K∑

i=1,i=j

ρ1,jA1h1b1 +nj (2)

where ρ1,j is the cross-correlation between the lth and j thuser’s signature waveforms, and is expressed as

ρ1,j =∫ T

0Sj (t)S1dt

nj = complex Gaussian with zero mean, E[nin∗j ] = 2σ 2 for

j = 1 and E[nin∗j ] = 2σ 2∗ρ1,j when j �= 1.

3.1 Power allocation

The transmit power of each user is adjusted so that totaltransmit power is minimized, while goal is to meet a certainoutage probability and sum capacity. Hence, the objectivefunction can be written as follows:

minK∑

j=1

Pj (3)

Outage probability for the link between j th user pair i.e. j thtransmitter and receiver link is given by [12]

Pout = 1 − e− γth

Gj Pj (4)

where, γth is the threshold signal-to-noise ratio (SNR) in thefading channel. The symbol Gj contains parameters such asthe antenna gains, path loss, shadowing, noise power, andsimilar parameters [21] and Pj is the transmitted power ofthe j th user. The constraint for the outage probability nowcan be written as

1 − e− γth

Gj Pj ≤ X (4a)

Similarly, sum of K users’ data transmission rate i.e. ca-pacity meeting a certain data rate R (given by Shannon’scapacity theorem ) can be written as follows:

K∑

j=1

�f log2

(1 + h2

jPj

σ 2l + N0

)≥ R (4b)

One of the constraints of this power allocation strategy is tomeet a certain sum (total) data transmission (channel) capac-ity. Since data is transmitted over radio mobile channel, thesum capacity rate constraint is not guaranteed always withcertainty due to the fading nature of the channel. In otherwords, time varying channel gain fails to meet this sum datarate constraint with some probability, of course, low prob-ability is desired. Adaptive power allocation, based on thechannel gain, would lower this outage probability. Henceoptimal power allocation for different scattered users withvarious paths (hence variable channel gain) to be adjustedso that not only the target sum capacity rate is attained butalso to meet this rate with high probability i.e. probability


(outage probability) not to meet the target rate will be low.The symbol �f in (4b) is the transmission bandwidth, theMAI power is σ 2

I = f (ρ,Pj ,h2j ). For the simplicity of anal-

ysis, we substitute σ 2I = ρPjh

2j in our subsequent analysis.

Since our power allocation problem minimizes total transmitpower, while meeting simultaneously a certain sum capacityrate and outage probability, the Lagrangian for (3), (4a) and(4b) can be written as

L = minK∑

j=1

Pj + λ1(1 − e

− γthGj Pj − X

)

− λZ

(K∑

j=1

�f log2

(1 + h2

jPj

σ 2j + N0

)− R

)(5)

Optimal power Pj for the j th user can be obtained by differ-entiating L in (5) with respect to Pj (∂L/∂Pj = Lpj) andthen setting it to zero.

Now, taking derivative of (5) w.r.t. Pj , we have,

LPj= 1 − λ1

γth

GjP2J

e− γth

Gj Pj − λ2�f

(1

h2j Pj

ρPj h2j +N0

)

×(

(ρPjh2j + N0)h

2j − ρh4

jPj

(ρPjh2j + N0)2

)(6)

After simplifying, (6) becomes as follows:

LPj= 1 − λ1

γth

GjP2j

e− γth

Gj Pj

− λ2�fh2

jN0

(ρPjh2j + N0)(ρPjh

2j + N0 + h2

jPj )(7)

Similarly, differentiating (5) w.r.t. λ1 (∂L/∂λ1 = Lλ1) andλ2 (∂L/∂λ2 = Lλ2), we have

Lλ1 = 1 − e

γthGj Pj ≤ X (8)

and

Lλ2 = �f log2

(1 + h2

jPj

ρPjh2j + N0

)≥ R (9)

To calculate j th user’s power Pj , let us assume that λ1 = 0,λ2 �= 0. Then equating (7) to zero, we have

1 = λ2�fh2

jN0

(ρPjh2j + N0)(ρPjh

2j + N0 + h2

jPj )(10)

or

λ2 = (ρPjh2j + N0)(ρPjh

2j + N0 + h2

jPj )

h2jN0�f

(11)

Now from (9)

�f log2

(1 + h2

jPj

ρPjh2j + N0

)= R (12)

or

1 + h2jPj

ρPjh2j + N0

= 2R

�f

or

h2jPj

ρPjh2j + N0

= [2

R�f − 1

]

or

h2jPj = (

ρPjh2j + N0

)(2

R�f − 1

)

or

h2jPj = (

2K�f − 1

)ρPjh

2j + N0

(2

K�f − 1

)

or

[h2

j − (2

R�f − 1

)ρh2

j

]Pj = N0

(2

R�f − 1

)

or

Pj = N0(2R

�f − 1)

[h2j − (2

R�f − 1)ρh2

j ](13)

We have to check that calculated Pj value must satisfythe outage probability constraint in (8). Again putting thevalue of Pj in (11), we get λ2, and λ2 > 0, which meetsthe Karusk-Kuhn-Tucker (KKT) condition. Hence optimalpower for different users can be obtained from (13).

4 Neural network assisted SIC for improved detection

This section briefly discusses NN assisted SIC scheme. NNis used to design adaptive system that improves detectionperformance. A weighted correlator is designed using NNto estimate each user’s signal amplitude. The weights areupdated based on the variable channel characteristics. Thisupdated weights in turn overcomes the improper ordering ofthe received signal strengths for the different users in SICwhen power profile of the channel changes. The workingprinciple of SIC depends on the ordering of the receivedsignals based on their strengths and performance largely de-pends on accuracy of the ordering. Correlation value ob-tained from the received signal of j th user with its signaturewaveform Sj (t) reflects it’s signal strength. Figure 1 showsNN based amplitude estimation for the j th user, where cor-relation vector for the j th user is obtained from (2)


Fig. 1 Neural network based amplitude estimation for j th user

Mathematically the summation unit’s output can be ex-pressed as,

Ij =n∑

s=1

WS ∗ yjj (s) =n∑

s=1

WS ∗[Ajhjbj (s)

+K∑

i=1,i �=j

ρ1,jA1h1b1(s) + nj (s)

](14)

=n∑

s=1

Ws ∗ Ajhjbj (s) +n∑

s=1

IOS +n∑

s=1

INS (15)

where IOS = Ws ∗ ∑KI=1,I �=j ρ1,jA1h1b1(s) is the inter-

ference due to all users other than j th user and INS =WS ∗ nj (s) is the weighted noise term. Here ws (also de-noted as wi in subsequent analysis) is denoted as weightfactor associated with ith bit. The symbol Ij indicates as theoutput of the summation unit and Dj is the output of neuronfor the j th user. Back propagation algorithm is now appliedto adjust the weight factors w1,w2, . . . ,wn, with target out-put for j th user is Tj = Ajhj . At the same time, the com-puted output for j th user by the neuron is OJ = Dj = Aj hj .The error signal can be written as

Ej = 1

2[Tj − Oj ]2 = 1

2[Ajhj − Dj ]2 (16)

According to gradient descend law, the weight factors areupdated with the amount

�W = −n ∗ ∂E

∂W(17)

η = learning rate parameter, ∂E∂W

is the gradient of theerror. The corresponding weight, for ith bit, is updated at as

�Wi = −n ∗ ∂Ej

∂Wi

(18)

Use of the chain rule allows us to write

∂Ej

∂Wi

= ∂Ej

∂Dj

.∂Dj

∂Ij

.∂Ij

∂Wi

(19)

A non-linear filter, known as activation function, is used toobtain Dj , the final output of the neuron. Here sigmoid func-

tion is used as activation function and is written mathemati-cally as follows:

Dj = 1/(1 + exp(−λIj )

)(20)

where λ = sloping parameter. From Fig. 1, it can be written

Ij = W1 ∗ Yjj (1) + W2 ∗ Yjj (2) + · · · + Wn ∗ Yjj (n)

=n∑

i=1

WiYjj (i) (21)

Now we differentiate Eqs. (16), (20) and (21) w.r.t. Dj , Ij

and Wj , respectively and putting them in Eq. (19), we have

�Wi = +η∗λ∗Dj ∗Yjj (i)∗(1−Dj)∗(Aj ∗hj −Dj) (22)

According to back propagation algorithm, after ‘t +1’ num-ber of iterations, ith weight factor will be updated to

[Wi]t+1 = [Wi]t + [�Wi]t+1 (23)

Using a variable learning rate (ηi ), the rate of change of �W

with respect to η can be written as follows:

∂�Wi

∂ηi

= [λ ∗ Yjj (i) ∗ exp(−λIj ) ∗ Aj ∗ αj

∗ (1 + exp(−λIj )

) − 1]/[L] (24)

where L = [1 + exp(−λIj )]3. From the above in (24), wefind that the rate of change of �Wi with respect to ηi islargely effected by the term (Aj ∗ hj )

2. This highlights thefact that the stronger users weight updating must be higher.

4.1 Mathematical expression for JPOE

This subsection determines that in an SIC receiver interfer-ence due to ‘m’ number [m ≤ K] of users must be canceledto get desired joint probability of error (JPOE). It is assumedthat ‘n’ numbers of correlation values of j th user (corre-sponding to ‘n’ no of bits) are available as the inputs to theneural network to obtain the output Ij as the estimation ofthe j th user’s amplitude. This determines the estimated am-plitude as

Aj ∗ hj = h ∗ ϕ(Ij ) = h ∗ 1/(1 + exp(−λIj )

)(25)

After canceling the ‘m’ users’ interferences, the receivedsignal for the ith bit would become,

rm(i) =K∑

l=m+1

Al ∗ αl ∗ bl(i) ∗ Sl(t − iT − τl)

+m∑

l=1

[Al ∗ αl ∗ bl(i) − Al .αl .bi (i)

]


× Sl(t − iT − τl) + n(i) (26)

Match filtering is now used to find the interfering signal dueto the rest of the users. The correlation vector for kth user,where [m < k ≤ K] and bit decision of ith bit for the kthuser are given by in (27) and in (28), respectively as follows:

ykk = ⟨rm(t), Sk(t)

⟩ = Ak ∗ hk ∗ bk

+k∑

l=m+1,l �=k

ρlk ∗ Al ∗ hl ∗ bl

+m∑

l=1

ρlk(Al ∗ hl ∗ bl − Al ∗ hl ∗ bl) + nk (27)

and

bk(i) = sgn[ykk(i)

](28)

Let b = [bm+1, bm+2, . . . , bk]T denotes the estimated bitvector, where bk denotes the estimated bit for the kth userwhen [m < k ≤ K]. It is assumed that all bit vectors areequally likely (with probability p = 1

2(K−m) ). Hence, JPOEdenoted by PE can be expressed as,

PE =∑

∀b

p(b �= b/b)p(b)

=∑

∀b

[1 − p(b = b/b)

](1/2(K−m)

)

= 1 − (1/2(K−m)

)∑

∀b

p(b = b/b) (29)

We consider large number of bits transmission for eachuser. Hence, it can be shown that each correlation vector ofys = [ym+1,m+1, ym+2,m+2, . . . , yk,k]T tends to have Gaus-sian distribution. Probability density function (pdf) can beexpressed as follows:

pys(xk) = 1/√

(2π)σk ∗ e−(xk−μk)2/2σ 2

k (30)

Where the mean and the variance values are given by μ =[μm+1,μm+2, . . . ,μk]T and by σ 2 = [σ 2,

m+1, σ2m+2, . . . ,

σ 2k ]T , respectively.

Now

p(b = b/b)

=∫ Um+1

Lm+1· · ·

∫ UK

LK

· · ·K∏

k=m+1

pys(xk)dxm+1 · · ·dxk (31)

where LK = 0, UK = ∞ if bk = 1 and LK = −∞, UK =0 if bk = −1. Now the expression of JPOE is given by

PE = 1 − (1/2(K−m)

) ∗∑

∀b

∫ Um+1

Lm+1·∫ UK

LK

1/√

(2π)

× σk ∗ e−(xk−μk)2/2σ 2

k

PE = 1 − (1/2(K−m)

) ∗∑

∀b

[K∏

k=m+1

Q(−bk ∗ μk/σk)

]

(32)

where, Q(x) = 1/√

(2π) ∗ ∫ ∞x

e(−t2/2)dt .The function Q(x) is the complementary error function.

5 Performance evaluation and discussion

The section presents the simulation results for performanceanalysis of both power control and SIC scheme. In the firstpart, we evaluate the performance of our proposed powerallocation scheme in DS-CDMA system by studying sumtransmission capacity as well as capacity of the weakest user(having the worst channel gain), total transmit power andoutage probability. In the next part, performance of receiveroperation is shown using proposed SIC scheme. To run sim-ulations, we have considered the following parameter val-ues, bandwidth �f = 0.3125 MHz, sum channel capacityrate constraint R = 1.5 × 106 bps, average cross correlationvalues of the code patterns ρ = 0.1, noise power N0 = 10−6

watts, number of users K = 20, outage probability 0.01 andaverage power gain for Rayleigh fading channel is 1 dB.

Figure 2 shows performance results of total transmitpower vs sum channel capacity. The result is compared with

Fig. 2 Sum channel capacity vs. total transmit power


Fig. 3 Worst user capacity vs. total transmit power

other methods reported in the literature [5, 22, 27]. Graph-ical results show that the proposed power allocation offersthe best performance compared to the exiting works. Nu-merical values in the graph also show that this sum capac-ity improvement for the proposed scheme is more than twotimes (double) at 3×10−6 watt power compared to the worstperformance shown by [22], while 1.3 times improvementcompared to [5]. We also study the channel capacity of theweakest user (users having the poor channel gain) and per-formance is shown is Fig. 3.

Figures 2 and 3 show that proposed power allocationscheme not only improves the sum channel capacity but alsomaintains the fairness i.e. data transmission capacity of theweakest user (user with the worst channel gain).

Performance here is also the best achieved one comparedto [5, 22, 27]. This ensures that a certain quality of services(QoS) even for the weakest user is also ensured. Improve-ment in sum as well as weak user channel capacity is dueto the consideration of low outage probability (0.01) forthe simulation results. Figure 4 shows a 3D (dimensional)plot among outage probability, total transmit power and sumchannel capacity. As expected, increase in transmit powercauses decrease in outage probability and increase in chan-nel capacity, that are reflected in Fig. 4 for the proposedscheme as well as for [5, 22, 27]. However, the conflict-ing trade-off problem is well balanced with the improvedrelative performance results for the proposed scheme com-pared to other three methods. This clearly highlights the factthat how efficient proposed power allocation is compared toother schemes.

Figure 5 shows the efficacy of the proposed SIC scheme.This is shown as average BER performance improvementdue to the effect of the number of users’ signal cancella-tion i.e. the effect of interference cancelation on BER perfor-mance. Simulation results are shown here at different SNR

Fig. 4 3D plot of outage probability, total transmit power and sumchannel capacity

Fig. 5 Average BER vs number of users at different SNR values when50 % users’ interfering effect is cancelled

values but without applying power control mechanism. Var-ious parameter values considered are the number of bits perusers is 1000, process gain (PG) is 23 dB and 50 % users’signal are cancelled. Results show that average BER in-creases with the increase of the number of users due to anincrease in MAI. At the same time, BER values decreasewith the increase in SNR values. It is mentioned here thatBER performance shown is obtained without the use of er-ror control code (ECC). It is obvious that the use of ECCwould further lower BER values.

Similar to that of Fig. 5, BER performance is also shownintegrating both optimal power control and multistage inter-ference cancelation for the proposed SIC. One such simu-lation result is shown in Fig. 6 for average BER vs numberof users at 14 dB SNR value. Simulation results show thatoptimal power control has an effect on sum channel capac-ity improvement with fairness for weak user. Not only that,it has also significant role in MAI value that leads to effi-cient reduction (lowering) in BER. The later performance


improvement is possible due to NN assisted SIC. Here alsoBER performance is shown after cancelation of 50 % user’sinterfering effect. It is observed that with the increase ofnumber of stages, BER performance is improved lot, how-ever, at the cost of computation and time delay. Graphicalrepresentation shows that at user number 30, the respectiveBER value for the proposed power control scheme but with-out SIC is 0.013.

Similar performance measures (BER values) after 1st,2nd and 3rd stage interference cancelation become 0.0029,

Fig. 6 Average BER vs number of users at SNR 14 dB when 50 %users’ interfering effect is cancelled at multistage and with optimalpower control

0.0023 and 0.0017, respectively. The corresponding BERvalues at user number 40 are 0.07, 0.0045, 0.0035 and0.0023, respectively.

Table 1 shows relative performance results (average BERvalues) for interference cancellation (IC) over match filters(MF) with and without power control. Interference cance-lation determines other way the number of users for whichinterference cancelation and the number of users for whichmatch filtering (MF) are done. Simulation is done at SNR =10 dB. Results show that with the decrease in number ofusers for which interference cancellation done, average BERvalue increases. Results also show that an acceptable BERvalue is possible to achieve when 20 % of the total activeuser’s interfering signal is cancelled. After that no signifi-cant improvement in BER value is seen even if more num-ber of users’ interfering signals are cancelled. This high-lights the effectiveness of the proposed learning algorithmthat solves the inherent delay problem (as less number of in-terference cancellation required) in SIC in order to achievean acceptable BER value. It is also observed here that powercontrol scheme shows improved performance compared tonon-power (without power) control scheme.

Effectiveness of the proposed adaptive algorithm totackle initial wrong ordering of the signal strength of theusers in SIC is shown in Table 2. Ordering of different pairsof users is shown as (a, b) where the users ‘a’ and ‘b’ havechanged their positions. It is shown that BER values do notchange significantly, after a certain (large) number of pair ofusers changes positions. Simulation results also show thatlearning algorithm keeps BER value to an acceptable level

Table 1 Average BER corresponding to number of users with interference cancellation (IC) and match filtering (MF)

IC done no. of users MF done no. of users BER w/out PC BER with PC

20 0 0.0055 0.0016

16 4 0.0315 0.0112

12 8 0.0410 0.0226

8 12 0.0540 0.0315

4 16 0.0645 0.0456

0 20 0.1320 0. 1124

Table 2 BER performance after change in initial ordering of the users based on the signal strength at the receiver

No. of interchange Pair of users BER w/out PC BER with PC

0 none 0.0200 0.0124

1 (1,4) 0.0301 0.0243

2 (1,3), (2,5) 0.0420 0.0345

3 (1,2), (3,4)

(5,6)

0.0560 0.0467

4 (1,8), (2,7)

(3,6), (4,5)

0.0680 0.0612


Fig. 7 JPOE vs. number of users

even when eight users are ordered wrongly out of twentyusers.

Finally Fig. 7 shows the graphical result for JPOE vsnumber of users. Simulation is done at SNR 10 dB with pro-cess gain 23 dB and number of bits per user is 1000. Inter-ference for 50 % users are cancelled first from the receivedsignal to calculate BER values. Then the minimum value ofBER (expected for the strongest user) is assumed as JPOEfor all users. Now number of users for which interferencecancellation (IC) must be done, out of total number of users,is calculated so that BER for each user must lie below theJPOE value. It is observed that simulation results closelyfollow the mathematical/analytical result. Performance re-sult is then compared with the existing work. Results alsoshow significant performance improvement of the proposedSIC compared to MUD in [9]. As expected, BER perfor-mance improvement is again improved with the increase innumber of interference cancellation stages but at the cost oflittle computation cost.

To validate the simulation results shown for the pro-posed SIC scheme, a general purpose hardware platformAgilent EXA signal analyzer N9010A is used. The EXAseamlessly integrates a broad range of standards basedmeasurements with Agilent’s industry leading 89600 vec-tor signal analysis software-all in a single instrument.Operational measurement application software providespreconfigured test routines for 802.16e Mobile WiMAX,W-CDMA,HSDPA/HSUPA,GSM/EDGE/EDGE evolution.The transmitted signal is generated through Agilent madeN5182A MXG RF vector signal generator (VSG). We haveused omni-directional dipole antenna for transmission andreception of signal over a range of ∼100 ft at different powerlevel stetting of VSG and without using external amplifier.The length of the antenna is made variable ranging from20 cm to 175 cm, roughly operating in the range of 85MHz

Fig. 8 Receiver performance verification in signal analyzer for powercontrol system with match filtering

to 300 MHz. Figure 8 shows performance of match filterreceiver operation with power adaptive BPSK modulation.

A 2 × 2 grid is selected where leftmost upper one indi-cates constellation, right one indicates trellis key, a form ofthe quality of the received signal. The leftmost bottom oneindicates spectrum for the demodulated signal, and the rightone EVM statistics with continuous transmission of bit pat-tern. The error vector magnitude (EVM) values lie in therange of ∼6 to 7 percentage RMS that corresponds to theBER in the range ∼0.04–0.05 as found in theoretical simu-lation.

Figure 9 shows similar constellation representation forthe received signal after SIC stage 3. Relative improvementin constellation and EVM value with respect to Fig. 8 in-dicates relatively better demodulated signal quality whichis indicated by relatively low BER value ∼0.006–0.005 inthe software simulation. This relative quality of the demod-ulated signal i.e. BER value is supported by the correspond-ing EVM value ∼1–2 percentage RMS.

6 Conclusions and scope of future works

An optimized power allocation algorithm in DS-CDMA isproposed that minimizes total transmit power, while simul-taneously meet the sum capacity and outage probability rateconstraints. Consideration of outage probability not onlymeets sum channel capacity rate constraint but also main-tains a high data rate capacity for weak user that leads to


Fig. 9 Receiver performance verification in signal analyzer for powercontrol system after 3rd stage SIC

QoS assurance. Then an adaptive SIC scheme is proposedto achieve improved receiver performance. Performance ofthe proposed adaptive algorithm is studied under various ob-servations. It has been observed that the learning from thecorrelation values of the received signal with the spread-ing codes causes significant improvement over conventionalSIC at the cost of a slight increase in complexity. Perfor-mance is improved with the increase of hidden layers in-side the NN, in other words, by increasing the complexity.This concept is very effective when the numbers of users arevery large. BER performance is also improved using vari-able learning rate. It is also observed that the system is ableto tackle the problem of wrong ordering of the user signalsaccording to their signal strengths by learning itself from theenvironment. A closed loop analytical form of JPOE for thisparticular system is developed and given a particular num-ber of active users (K), how many users’ signals need to becanceled in order to obtain a desired JPOE is also derived.Simulation results closely support the mathematical results.Simulation results are also validated in general purpose re-ceiver hardware platform Agilent N9010A.

The following issues may be considered as future work.

(i) Proposed power allocation in DS-CDMA scheme canbe extended for multicarrier version i.e. MC-CDMAsystem as this one is effective to tackle inter symbol in-terference (ISI) problem at high data rate transmissionover fading channel.

(ii) Proposed algorithm can also be extended and stud-ied for various spreading codes like Walsh-Hadamardcodes, carrier interferometry codes used for CDMAsystem to increase user (number of users) capacity.System design can also be integrated with proper errorcontrol code (ECC) to improve BER performance.

(iii) Proposed power allocation scheme can also be ex-tended under interference constraint scenario so thatalgorithm may be designed for CDMA/MC-CDMAbased cognitive radio network (CRN).

Acknowledgements This work is the outcome of the project on “De-velopment of high power and spectral efficiency multiuser system forbroadband wireless communication” funded by Ministry of Communi-cation and Information Technology, Govt. of India vide administrativeapproval no. 13(2)/2008-CC & BT dated 31.03.2008 and the first au-thor acknowledges this financial support.

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Santi P. Maity received his B.E.in Electronics and CommunicationEngineering and M.Tech degree inMicrowaves, both from the Uni-versity of Burdwan, India in 1993and 1997, respectively. He receivedhis Ph.D. degree in Engineering(Computer Science and Technol-ogy) from Bengal Engineering andScience University, Shibpur, Indiain 2008. During January, 2009 toJuly, 2009 and February, 2011 toJuly, 2011 he did postdoctoral workconcerning watermarking in luredapplications in the “Laboratoire des

Signaux et Systems (CNRS-Supelec-Universite Paris-Sud 11)” inFrance. He is at present working as Associate Professor and Head at

the Department of Information Technology, Bengal Engineering andScience University, Shibpur, India. Prior that he worked as AssistantProfessor in the same department from September 2006–September2009. He also worked as Lecturer in Electronics and Telecommunica-tion Engineering department of the same university from 2000 to 2006,K.G. Engineering Institute, Bishnupur, Bankura, India and Haldia In-stitute of Technology, Haldia, India, from 1997 to 2000.His research areas include digital image watermarking, multiuser de-tection in CDMA, power allocation in OFDM based cognitive radio,compressive sampling, VLSI watermarking and optical informationprocessing. He successfully completed as principal investigator of aproject “High Power and Spectral Efficiency Multiuser System forBroadband Wireless Communication” sponsored by Department of In-formation Technology, Government of India. He has contributed about100 research papers in well-known and prestigious archival journals,international refereed conferences and as chapters in edited volumes.He also guided two Ph. D students in these research areas and coupleof other students are working.

Sumanta Hati received the B.E de-gree in Electronics and Communi-cation engineering from BurdwanUniversity, India in 2005 and M.Edegree in Electronics and Telecom-munication engineering from Ben-gal Engineering and Science Uni-versity, India in 2007. Currently heis working toward the PhD degreein the department of InformationTechnology at the Bengal Engineer-ing and Science University, India.His research interests are in the areaof signal processing for digital andwireless communication.

Chinmay Maji received his B.E. inElectronics and TelecommunicationEngineering from Jadavpur Univer-sity, Kolkata, India in the year 2008.He worked as Software Engineer inWipro Technology, India from 2009to 2010. He did his M.E. in Informa-tion and Communication Engineer-ing in Department of InformationTechnology of Bengal Engineeringand Science University, Shibpurm2012. He is currently working asAssistant Professor in Electronicsand Communication Engineering ofBankura Unnayani Institute of En-

gineering, West Bengal, India. His research interest includes power al-location and interference minimization in cognitive radio network.

optimal power allocation in ds-cdma with adaptive sic technique

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