Effects of Subcarrier Power Allocation on an
Interference Avoidance Code Assignment Strategy
for Multirate MC-DS-CDMA Systems
Chih-Wen Chang, Member, IEEE, and Li-Chun Wang, Senior Member, IEEE
Abstract—In this paper, we propose a joint subcarrier power
allocation (SPA) and code assignment scheme for the synchronous multirate multicarrier direct-sequence code-division multiple-access (MC-DS-CDMA) system with time- and frequency-domain spreadings. Based on the newly defined metric multiple-access interference (MAI) coefficient, the proposed code assignment strategy can quantitatively predict the incurred MAI before as-signing a spreading code. The SPA mechanism aims to maximize the received signal power. In addition to lowering the MAI, the proposed code assignment strategy further considers the compact-ness of the assigned codes in the entire 2-D tree structure. The simulation results show that the proposed joint SPA and code assignment strategy not only can reach a better received signal quality but can also achieve a high call admission rate.
Index Terms—Code assignment, interference avoidance, multicarrier direct-sequence code-division multiple access (MC-DS-CDMA), multiple-access interference (MAI) coefficient, subcarrier power allocation (SPA).
I. INTRODUCTION
C
OMBINING the advantages of orthogonal frequency-division multiplexing (OFDM) and spreading spec-trum systems, multicarrier code-division multiple access (MC-CDMA) has the potential to be a strong candidate for future broadband wireless communication systems [1]–[3]. The advantages of the MC-CDMA system include the robustness against the frequency-selective fading channel, the flexibility in system design, and the low detection complexity [4]–[7]. Generally, MC-CDMA can be divided into the following three categories: 1) MC-CDMA with pure frequency spreading; 2) multicarrier direct-sequence CDMA (MC-DS-CDMA) with pure time spreading; and 3) MC-DS-CDMA with joint time and frequency spreading [(TF)-domain spreading]. By adjusting spreading gains in both the time and frequency domains, the MC-DS-CDMA with TF-domain spreading can outperform theManuscript received June 7, 2007; revised March 16, 2007 and July 25, 2007. This work was supported by the National Science Council, Taiwan, under Contract 94-2213-E-009-060, Contract 95-2218-E-006-041, and Contract 96-2221-E-006-020. The review of this paper was coordinated by Dr. K. Molnar.
C.-W. Chang is with the Institute of Computer and Communication Engi-neering, National Cheng Kung University, Tainan 701, Taiwan, R.O.C. (e-mail: cwchang@ee.ncku.edu.tw).
L.-C. Wang is with the Department of Communication Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, R.O.C. (e-mail: lichun@cc.nctu.edu.tw).
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2007.909300
other two MC-CDMA schemes in supporting versatile multirate services in diverse environments [8]–[12].
Furthermore, subcarrier power is another degree of freedom for the MC-DS-CDMA system. However, it is challenging to allocate subcarrier power in a multiuser environment. An optimal power allocation scheme with a maximized received signal power for a particular user may also produce excessive interference to other users, which may also lower the call admission rate. Thus, we are motivated to propose a joint subcarrier power allocation (SPA) and code assignment aimed at maximizing the signal power through SPA while eliminat-ing multiple-access interference (MAI) through a novel code assignment scheme. To achieve this goal, we first maximize the signal quality by allocating subcarrier power. On top of this allocated subcarrier power, we develop a code assignment strategy to maintain high call admission rates with less MAI. We define a new performance metric called the MAI coefficient. Through the bit-error-rate (BER) analysis associated with the SPA mechanism, we show that the MAI coefficient can quanti-tatively predict the incurred MAI before assigning a spreading code. Thus, with the help of the MAI coefficient, an interfer-ence avoidance code assignment can be designed to choose a code with the minimum incurred MAI. The simulation results show that the proposed joint SPA and interference avoidance code assignment strategy can significantly improve the received signal quality. Furthermore, the code assignment considers the 2-D code tree structure in assigning a code to a user. Thus, the code assignment can also maintain good call admission rates.
In the literature, the SPA mechanism, MAI elimination, and code assignment associated with the code tree structure are not jointly considered in the MC-DS-CDMA systems. From the aspect of SPA, some SPA mechanisms aimed at improving BER performance have been proposed [13], [14]. In [13], the SPA mechanism was considered in a nonspread spectrum multicarrier system. In [14], Long and Chew proposed an adaptive subcarrier allocation policy for the frequency-hopping MC-DS-CDMA systems to avoid collision between users when loading bits to subcarriers. From the aspect of MAI elimination, the interference rejection and interference-free spreading codes were proposed for the asynchronous MC-DS-CDMA in [15] and [16], respectively. In [17], an MAI-minimized signature waveform was proposed to minimize MAI for MC-DS-CDMA systems. From the code assignment aspect, Amadei et al. [18] and Manzoli and Merani [19] proposed a code assignment strategy based on dual quasi-orthogonal and Walsh codes to
Fig. 1. Two-dimensional OVSF code tree when the frequency-domain spreading factor is 4.
Fig. 2. Example of allocating a code with frequency-domain spreading factor M = 4 and time-domain spreading factor SF = 8 in the 2-D code tree.
reduce MAI in MC-DS-CDMA systems. However, in the above CDMA systems [14]–[19], all belong to the CDMA with 1-D time-domain spreading. For the MC-DS-CDMA system with TF-domain spreading, Yang et al. [10] proposed novel 2-D orthogonal variable-spreading factor (OVSF) codes but ignored the impact of frequency-selective diversity. Furthermore, the MAI rejection property of [10] may disappear because the zero autocorrelation sidelobes and the zero cross-correlation functions are no longer true when the subcarriers carrying the same data bit experience independent fading. In our previous paper [20], we proposed a novel inter-ference avoidance code assignment strategy without taking the SPA mechanism into consideration.
In this paper, we investigate the MAI impact caused by reusing time-domain spreading codes in the MC-DS-CDMA, which is not considered in [13]–[19]. Specifically, we consider the joint impact of MAI and the compactness of the code tree structure, as well as the SPA mechanism. Moreover, we consider a downlink MC-DS-CDMA system with a constant frequency diversity gain. The rest of this paper is organized as follows. The 2-D OVSF code tree structure and the signal model
in the MC-DS-CDMA system with TF-domain spreading are introduced in Section II. In Sections III and IV, we propose the SPA mechanism and define the performance metric MAI coefficient, respectively. Section V presents a joint SPA and in-terference avoidance code assignment strategy for the multirate MC-DS-CDMA system with TF-domain spreading. Simulation results are provided in Section VI. We give our concluding remarks in Section VII.
II. SYSTEMMODEL
A. Background
To spread in both the time and frequency domains, the OVSF code tree in a multirate MC-DS-CDMA system has a 2-D structure, as shown in Fig. 1. In the figure, the total spreading factor is SFf× SFt, where the frequency-domain
spreading factor SFf = 4 and the time-domain spreading
fac-tor SFt= 1∼ 8, respectively. As shown in the figure, each
branch of the code tree in the time-domain spreading is as-sociated with a frequency-domain spreading code. For ease
Fig. 3. Transmitter structure of the MC-DS-CDMA using TF-domain spreading codes.
of illustration, we spread the 2-D code tree in Fig. 1 onto a plane as in Fig. 2, where “ ” and “ ” stand for the “used code” and “candidate code” for a requested code of SFt= 8,
respectively. The orthogonality between any two codes can be maintained if they do not have an ancestor–descendant relationship. However, due to frequency-selective fading, the orthogonality of the OVSF codes positioned in the different branches of the 2-D code tree may not be satisfied. Two codes in the 2-D OVSF code tree are called related codes if they have an ancestor–descendant relationship in the time-domain spreading, such as C4,2(3)= [ 1 1 − 1 − 1 ] and
C8,3(2)= [ 1 1 − 1 − 1 1 1 − 1 − 1 ]. Note that in a frequency-selective fading channel, the orthogonality of the two related codes C4,2(3) and C8,3(2) are not guaranteed. For a clear illustration of the related codes, see the grid represen-tation of the 2-D code tree for the MC-DS-CDMA systems in [20].
B. Transmitted Signal
The transmitter structure in the MC-DS-CDMA system with TF-domain spreading is shown in Fig. 3. A serial-to-parallel converter is applied to reduce the subcarrier data rate by con-verting data streams with bit duration Tb,k(X)into U reduced-rate parallel substreams with new bit duration Tk(X)= U Tb,k(X) for user k in group X∈ {A, B, C}. Each substream experiences a frequency-flat (or nondispersive) fading. Then, for each sub-stream, a spreading code g(X)k (t) is used to spread data signals in the time domain. After being copied to M subcarriers, the data in each substream is multiplied by a frequency-domain spreading code{c(X)k [j]}. In this case, the frequency-domain spreading gain is M . The user group X is defined as follows. Let go(t) and co[j] be the time-domain spreading code and
the frequency-domain spreading code of the reference user, respectively. Then, similar to [9] and [12], the interfering users
in the MC-DS-CDMA system can be categorized into the following three groups:
(1) group A : 1 To To 0 g(A)k (t)go(t)dt= 0 1 M M j=1 c(A)k [j]co[j] = 0 (2) group B : 1 To To 0 g(B)k (t)go(t)dt = 0 1 M M j=1 c(B)k [j]co[j]= 0 (3) group C : 1 To To 0 g(C)k (t)go(t)dt = 0 1 M M j=1 c(C)k [j]co[j] = 0.
The transmitted signal of user k in group X∈ {A, B, C} can be expressed as s(X)k (t) = U i=1 M j=1 2Pk,i,j(X)b(X)k,i (t)g(X)k (t)c(X)k [j]
× cos2πfi,jt + ϕ(X)k,i,j
(1) where Pk,i,j(X), {fi,j}, and {ϕ(X)k,i,j} represent the transmitted
power, the jth subcarrier frequency, and the initial phase in the ith substream, respectively. The waveform of the ith
Fig. 4. Receiver structure of the MC-DS-CDMA using TF-domain spreading codes.
substream b(X)k,i (t) =∞h=−∞b(X)k,i [h]PT(X)
k
(t− hTk(X)) con-tains rectangular pulses of duration Tk(X), where b(X)k,i [h] =
±1 with equal probability. The time-domain spreading code gk(X)(t) =∞=−∞gk(X)[]PTc(t− Tc) represents the chip
se-quence of the rectangular pulses of duration Tc, where
g(X)k [] =±1 with equal probability. Note that the time-domain spreading factor of user k in group X is G(X)k =
Tk(X)/Tc.
C. Received Signal
The receiver structure of the MC-DS-CDMA using TF-domain spreading codes is shown in Fig. 4. Recall that each substream experiences flat Rayleigh fading. Then, the received signal of the reference user (denoted by ro) in the
synchronous transmission can be expressed as
ro(t) = U i=1 M j=1
2Po,i,jαo,i,jbo,i(t)go(t)co[j]
× cos(2πfi,jt + φi,j)
+ X∈{A,B,C} KX k=1 U i=1 M j=1
2Pk,i,j(X)αo,i,jb(X)k,i (t)
× g(X) k (t)c
(X)
k [j] cos(2πfi,jt + φi,j) + n(t) (2)
where Po,i,j and αo,i,j are the reference user’s transmission
power and the channel amplitude for the jth subcarrier of the ith substream, KX is the number of users in the group
X, and n(t) is the white Gaussian noise with a double-sided power spectrum density of N0/2. In (2), φi,j = ϕi,j+ ψi,j is
uniformly distributed in [0, 2π), where ϕi,j is the initial phase
of the reference user, and ψi,jis the channel’s phase of the jth
subcarrier in the ith substream.
Without loss of generality, let the bit of interest be bo,s[0],
denoting the first bit in the sth substream from the reference user. After time-domain despreading, the output signal for the reference user in the vth subcarrier of the sth substream can be expressed as Yo,s,v= To 0 ro(t)βo,s,vgo(t)co[v] cos(2πfs,vt + φs,v)dt =√To 2 bo,s[0]
Po,s,vαo,s,vβo,s,v
+ X∈{A,B,C} KX k=1 Ik,s,v(X) + ns,v (3)
where Tois the bit duration of the reference user, βo,s,vare the
weights for a certain combining scheme, Ik,s,v(X) denotes the MAI induced from user k of group X to the vth subcarrier of the sth substream of the reference user, and ns,vis the white Gaussian
noise with zero mean and variance of (|βo,s,v|2/2)(No/T0).
The MAI terms Ik,s,v(X) in (3) can be expressed as
Ik,s,v(X) = Pk,s,v(X) αo,s,vβo,s,vc (X) k [v]co[v] To × To 0 b(X)k,s(t)g(X)k (t)go(t)dt. (4)
Then, combining M subcarriers, the decision variable of bo,s[0]
for the reference user becomes
Yo,s= M v=1 Yo,s,v =√To 2 bo,s[0] M v=1
Po,s,vαo,s,vβo,s,v
desired signal + X∈{A,B,C} KX k=1 M v=1 Ik,s,v(X) MAI + M v=1 ns,v (5)
where Yo,s,vis given in (3).
In (5), we face the problem of simultaneously maximizing the desired signal’s power and eliminating the MAI. Note that as a user maximizes its received signal power according to a particular SPA, it may result in excessive MAI to other users. The MAI occurs when user k adjusts Pk,s,v(X). It is difficult to please each user just by a particular SPA mechanism. One of the goals in this paper is to find a method to improve the desired signal quality and to control MAI.
III. SPA MECHANISM
The goal of this section is to propose an SPA mechanism that will optimize the signal of the desired user in (5). The transmission power is constrained to avoid the so-called party effect in the CDMA system. The party effect is a situation where all users continuously increase transmission power, but indeed, the signal quality is not improved due to increasing interference. The transmission power constraint imposed on the reference user can be expressed as
M
v=1
Po,s,v= Po (6)
where Pois assumed to be proportional to the reference user’s
transmission rate, as in [12], [21], and [22]. From (5), the SPA mechanism that will maximize the desired signal can be formulated as follows: maximize M v=1
Po,s,vαo,s,vβo,s,v
subject to
M
v=1
Po,s,v= Po. (7)
According to the maximal ratio combining criteria, the sub-carrier’s signal is maximized when βo,s,v= α∗o,s,v, with the
condition of a Gaussian-approximated MAI as in [6], [12],
and [20]. By applying the Lagrange multiplier method, we can obtain the Lagrange function as
J (Po,s,1, . . . , Po,s,M) = M v=1 Po,s,v|αo,s,v|2+ λ M v=1 Po,s,v− Po (8) where λ is the Lagrange multiplier. Differentiating (8) with respect to Po,s,vand setting it to zero, it follows that
1 2 Po,s,v
|αo,s,v|2+ λ = 0, v∈ {1, 2, . . . , M}. (9)
By solving (6) and (9), we can obtain
Po,s,v= |αo,s,v| 4
M
v=1|αo,s,v|4
Po (10)
which can maximize the desired signal in (5). Similarly, we can also have Pk,s,v(X) = α(X) k,s,v 4 M v=1α (X) k,s,v 4P (X) k (11)
where α(X)k,s,v is the channel amplitude for the sth subcarrier of the vth substream of the interfering user. Note that Pk(X)/Po=
R(X)k /Ro, where Roand R(X)k are the transmission rates of the
reference user and user k in group X, respectively. IV. MAI COEFFICIENT
In this section, we define a performance metric MAI coef-ficient to quantize the effect of MAI imposed on each code channel. After some derivations, we can define the received
Eb/N0 (denoted by γ), shown in (12) at the bottom of the
next page, where G0 is the time-domain spreading factor
of the reference user, and Ro and R(A)k are the
transmis-sion rates of the reference user and user, k in group A, respectively. The detailed derivations of (12) are discussed in Appendix A. Assume that the fading parameters in the MAI term of (12) are independent because the downlink MAI resulted from the subcarriers that reused time-domain spreading codes in different frequency-domain code trees. By observing the MAI term of γ in (12), we find that the term 2PoGo M v=1|αo,s,v|4E[|α(A)k,s,v|4/ M i=1|α (A) k,s,i|4] is common
to all the KA interfering users. As a result, we can just use KA
k=1
L(A)k −1 =0 R
(A)
k /[Ro(L(A)k )2] to characterize the
down-link MAI in the MC-DS-CDMA system. There are two possible scenarios, as described below.
1) MAI from high data rate users: In this case,
R(A)k /Ro= To/Tk(A)= L (A) k > 1. Subsequently, we can obtain KA k=1 L(A)k−1 =0 Rk(A) Ro L(A)k 2 = KA k=1 L(A)k−1 =0 1 L(A)k = KA k=1 1. (13)
2) MAI from low data rate users: Let L(A)k = 1 in the MAI term of (12). Then, it follows that
KA k=1 L(A)k−1 =0 R(A)k Ro L(A)k 2 = KA k=1 R(A)k Ro . (14)
Note that Rk(A)/Ro< 1 in this case.
By observing (13) and (14), we can define the downlink
MAI coefficient in the MC-DS-CDMA system with TF-domain
spreading as κ = KA k=1 min 1,R (A) k Ro . (15)
V. JOINTSPAANDINTERFERENCEAVOIDANCE
CODEASSIGNMENTSTRATEGY
A. Principles
In this section, we propose to integrate the SPA mechanism and the interference avoidance code assignment strategy to simultaneously optimize the received signal power and elim-inate the MAI. In principle, the joint scheme consists of the following two steps: 1) the SPA mechanism and 2) the code assignment, as shown in Fig. 5(a). In the first step, each user applies the SPA mechanism to greedily maximize his own received signal power. In the second step, the interference avoidance code assignment is used to pick a spreading code that produces less MAI, as shown in Fig. 5(b). Let{CSF,j(i) } be the set of candidate codes with TF-domain spreading factors M and
SF , respectively, where 1≤ i ≤ M, and 1 ≤ j ≤ SF . Denote Rc(CSF,j(i) ) as the set of codes related to C
(i)
SF,j. The joint SPA
and code assignment strategy is summarized in the following two steps.
Step 1) Each user implements the SPA mechanism accord-ing to (10) and (11).
Step 2) With the aid of the MAI coefficient, the interference avoidance code assignment strategy has the follow-ing three stages, as shown in Fig. 5(b).
Stage 1) Estimate the incurred MAI when assigning code
CSF,j(i) by calculating the sum of the MAI coef-ficient increments of the codes in Rc(CSF,j(i) ).
If the incremental MAI coefficients of any two
Fig. 5. Flow chart of the joint SPA and interference avoidance code assign-ment strategy. (a) Two steps of the joint SPA and code assignassign-ment strategy. (b) Three stages of the interference code assignment strategy.
candidate codes tie, go to the next stage. Other-wise, the smallest sum of the incremental MAI coefficients in the set of Rc(CSF,j(i) ) is selected.
The decision rules are detailed as follows. a) For the nth code in Rc(CSF,j(i) ) denoted by
Cn∈ Rc(CSF,j(i) ), we calculate its
incre-ment of the MAI coefficient [∆κ(Cn)] if
CSF,j(i) is chosen.
b) Denote ∆κ[Rc(CSF,j(i) )] as the sum of
∆κ(Cn) for Cn∈ Rc(CSF,j(i) ). Then, we can have ∆κ Rc CSF,j(i) = Cn∈Rc C(i)SF,j ∆κ(Cn). (16)
c) Select the codes with min{∆κ[Rc(CSF,j(i) )]}.
γ = PoGo M v=1 |αo,s,v|4 2 M v=1 KA k=1 L(A)k−1 =0 R(A)k Ro |αo,s,v|4 L(A)k 2E α(A) k,s,v 4 M i=1 α(A) k,s,i 4 PoGo MAI + PN M v=1 |αs,v|2 noise −1 (12)
d) If there is only one code with min{∆κ[Rc(CSF,j(i) )]}, the code
assign-ment process ends, otherwise, go to the next stage.
Stage 2) Compare the sum of the MAI coefficients of the codes in Rc(CSF,β(α) ), where{C
(α)
SF,β} is the code
set with the same sum of increment of the MAI coefficients in the first stage. Then, assign the code with the smallest sum of MAI coefficients. If two candidates tie, go to the next stage. The rules in the second stage are detailed as follows. a) Similar to the first stage, we calculate
the MAI coefficient of the nth codes in Rc(CSF,β(α) ), which is denoted by κ(Cn).
b) Denote κ[Rc(CSF,β(α) )] as the sum of κ(Cn),
where Cn ∈ Rc(CSF,β(α) ). Then, we can have
κ Rc CSF,β(α) = Cn∈Rc CSF,β(α) κ(Cn). (17)
c) Pick the codes with min{κ[Rc(CSF,β(α) )]}.
d) If there is only one code with
min{κ[Rc(CSF,β(α) )]}, the code assignment
process ends, otherwise, go to the last stage. Stage 3) Select a code in {CSF,δ(γ) } according to the crowded-first-code principle, as suggested in [23], where {CSF,δ(γ) } is the code set with the same sum of MAI coefficients in the second stage.
B. Example
Consider a situation in which a user requests a code with a time-domain spreading factor SF = 8. Referring to Fig. 2, the candidate codes for this request are
{C(1) 8,6, C (1) 8,7, C (1) 8,8, C (4) 8,7, C (4) 8,8, C (2) 8,1, C (2) 8,2, C (4) 8,1, C (4) 8,2}. Based
on the definition of the related codes, we can divide the candidate codes into three groups, as shown in Fig. 2. To be more specific, Groups 1 to 3 are affected by the interference from the users with the allocated codes {C4,3(2), C2,2(3), C4,3(4)}, {C(2) 4,4, C (3) 2,2}, and {C (1) 2,1, C (3)
4,1}, respectively. Now, we give an
example to illustrate the joint SPA and interference avoidance code assignment strategy. Consider codes {C8,6(1), C8,7(1), C8,1(2)}
to be the representatives of their respective groups in the 2-D code tree in Fig. 2. In other words, the MAI coefficients of codes within a group are the same.
SPA Procedure: As mentioned in Section V-A, the first step
of the proposed scheme is to allocate the power to subcarriers according to (10).
Interference Avoidance Code Assignment: Now, the
interfer-ence avoidance code assignment strategy is applied to select a code that produces less MAI.
a) Compare the increment of the MAI coefficient
[δκ(·)]: First, we compare the increment of the MAI
coeffi-cient∆κ(·). According to the definition of the related codes,
one can find that the related codes for code C8,6(1)are C4,3(2), C2,2(3), and C4,3(4). Thus, we have
Rc C8,6(1) = C8,6(1), C4,3(2), C2,2(3), C4,3(4) . (18)
Based on (15), the incurred MAI coefficient ∆κ[Rc(C8,6(1))]
after allocating code C8,6(1)is equal to ∆κ Rc C8,6(1) ! = Cn∈Rc C8,6(1) ∆κ(Cn) = ∆κ C8,6(1) + ∆κ C4,3(2) + ∆κ C2,2(3) + ∆κ C4,3(4) = 4.25 (19) where ∆κ C8,6(1) = min 1,R (2) 4,3 R(1)8,6 + min 1,R (3) 2,2 R(1)8,6 + min 1,R (4) 4,3 R(1)8,6 = min " 1,2 1 # + min " 1,4 1 # +min " 1,2 1 # = 3 (20) ∆κ C4,3(2) = min 1,R (1) 8,6 R(2)4,3 = 1 2 (21) ∆κ C2,2(3) = min 1,R (1) 8,6 R(3)2,2 = 1 4 (22) ∆κ C4,3(4) = min 1,R (1) 8,6 R(4)4,3 = 1 2. (23)
Similarly, we can obtain ∆κ[ Rc( C8,7(1)) ] = 2.75
and ∆κ[ Rc( C8,1(2)) ] = 2.75. Because ∆κ[ Rc( C8,7(1)) ] =
∆κ[Rc(C8,1(2))] = 2.75, the code assignment enters the second
stage to compare codes C8,7(1)and C8,1(2).
b) Compare the sum of the MAI coefficient[κ(·)]: In
this stage, the sum of the MAI coefficients of related codes
κ(·) for codes C8,7(1)and C8,1(2)are compared.
(a) Calculate κ[Rc(C8,7(1))]: According to the definition
of the related codes, we can find that Rc(C8,7(1)) =
Rc(C4,4(2)) ={C (1) 8,7, C (2) 4,4, C (3) 2,2}. Similarly, we have Rc(C2,2(3)) ={C (1) 8,5, C (1) 8,7, C (2) 4,3, C (2) 4,4, C (4) 4,3, C (3) 2,2}. Then, it follows that κ Rc C8,7(1) ! = Cn∈Rc C8,7(1) κ(Cn) = κ C8,7(1) + κ C4,4(2) + κ C2,2(3) = 5.5 (24)
where κ C8,7(1) = min 1,R (2) 4,4 R(1)8,7 + min 1,R (3) 2,2 R(1)8,7 = min " 1,2 1 # + min " 1,4 1 # = 2 (25) κ C4,4(2) = min 1,R (1) 8,7 R(2)4,4 + min 1,R (3) 2,2 R(2)4,4 = min " 1,1 2 # + min " 1,4 2 # = 1.5 (26) κ C2,2(3) = min 1,R (1) 8,5 R(3)2,2 + min 1,R (1) 8,7 R(3)2,2 + min 1,R (2) 4,3 R(3)2,2 + min 1,R (2) 4,4 R2,2(3) + min 1,R (4) 4,3 R(3)2,2 = min " 1,1 4 # + min " 1,1 4 # + min " 1,1 2 # + min " 1,1 2 # + min " 1,1 2 # = 2. (27)
(b) Calculate κ[Rc(C8,1(2))]: Referring to Fig. 2, it is clear that
Rc C8,1(2) = Rc C4,1(3) = C8,1(2), C4,1(3), C2,1(1) (28) Rc C2,1(1) = C8,1(2), C8,3(2), C8,4(2), C4,1(3), C4,2(3), C8,3(4), C8,4(4), C2,1(1) . (29) Similar to (24), we can have
κ Rc C8,1(2) ! = Cn∈Rc C8,1(2) κ(Cn) = κ C8,1(2) + κ C4,1(3) + κ C2,1(1) = 5.75 (30) where κ[C8,1(2))] = 2, κ[C4,1(3))] = 1.5, and κ[C2,1(1))] = 2.25 can be calculated by the same approach as (27). Because code C8,7(1) will have less total MAI in the set of its related codes than code C8,1(2), it is chosen to serve the requested call.
VI. SIMULATIONRESULTS
In this section, we demonstrate the effectiveness of the proposed joint SPA and code assignment strategy. We first show the advantages of using the proposed SPA mechanism. Then, with the SPA mechanism, we illustrate the impact of an MAI-coefficient-based interference code assignment strategy by comparing the various code assignment strategies [random
assignment (RM), pure crowded-first-code assignment (CF) without considering MAI, and the interference avoidance as-signment (IA + CF) methods] in terms of the received Eb/N0
and call admission rate.
A. Simulation Setup
1) Simulation Environment: In the simulation, we consider
a downlink MC-DS-CDMA in a single-cell environment. Fol-lowing the assumptions in [7] and [12], the subcarriers carrying the same data bits are assumed to experience independent flat Rayleigh fading. The background noise is modeled by white Gaussian noise with a double-sided power spectrum density of N0/2 and a transmitting Eb/N0= 12 dB. A new call is
modeled by a Poisson arrival process with the arrival rate (λ) of 1/2 per time unit and the departure rate (µ) selecting from the set {1/32, 1/48, 1/64, 1/80, 1/96, 1/112, 1/144, 1/176}. Thus, there are, on average, λ/µ = 16∼ 88 active calls in the system. With U = 128 parallel substreams, the frequency-domain spreading factor (M ) is 8, and the time-frequency-domain spread-ing factors (SF s) are 4, 8, 16, or 32. Each call requests a code of 8R (SF = 4), 4R (SF = 8), 2R (SF = 16), or R (SF = 32) with a probability according to the code traffic pattern [1 1 2 8], where R is the basic data rate. A code traffic pattern of [a b c d] means that the times of requesting
data rates 8R, 4R, 2R, and R are proportional to a : b : c : d, respectively. The data rate of each user is fixed during its call holding time. To clearly indicate the traffic load brought by the active calls with different data rates, we define an effective traffic load in the following. With the time-domain spreading factor selecting from SF = [4 8 16 32] and the code traffic pattern of [a b c d], the effective traffic load
(ρ) is defined as ρ = λ µ× 8R× a + 4R × b + 2R × c + R × d a + b + c + d × 1 32R. (31) For λ = 1/2 and µ = 1/80 and the code traffic pattern [1 1 2 8], the effective traffic load ρ is 250% of the uti-lization of the time-domain resources.
2) Call Admission Control: In the call admission control,
we consider the average received Eb/N0. For an MAI
co-efficient (κ), the average received Eb/N0 can be calculated
by taking the average of (42) over the M subcarriers’ fading channels. A incoming call is blocked if accepting this new call decreases the signal quality of any active calls in the system be-low the required received Eb/No= 5 dB. We simulate 10 000
incoming calls for each combination of λ and µ.
3) Code Assignment Strategy: Consider a call request for a
code with rate 2kR, where k is an integer ranging from 0 to
3. Then, a code assignment strategy should be implemented to pick a candidate code to accommodate this new coming call. A candidate code is defined as a free code with rate 2kR, and
its ancestor and descent codes are not used. In this paper, we consider three code assignment methods, namely RM, CF, and IA + CF. Now, we introduce the RM and CF methods.
Fig. 6. Example of the variations of the fading channels at different subcar-riers and the corresponding SPAs, where the number of subcarsubcar-riers is M = 2, and the transmission power constraint is Po= 1. (a) Amplitude of the first
subcarrier. (b) Amplitude of the second subcarrier. (c) Allocated power to the first subcarrier. (d) Allocated power to the second subcarrier.
RM: If there is one or more candidate codes in the 2-D
code tree, the RM method randomly selects a code without considering the code tree structure and the impact of MAI.
CF: If there is one or more candidate codes in the 2-D
code tree, the CF method picks a code whose ancestor code has the fewest free codes and thereby leaves more space for future high-rate users to increase the call admission rate [23]. Note that the CF method considers the code tree structure but not the impact of MAI.
B. Effect of SPA
Fig. 6 shows an illustrative example of the variations of the channels at different subcarriers and the corresponding SPAs, where the number of subcarriers is M = 2, and the trans-mission power constraint is Po= 1. As shown in the figure,
according to the rule of (10) and (11), the power allocated to a subcarrier is proportional to the amplitude of that subcarrier. Moreover, the sum of the power allocated to the first and second subcarriers is equal to Po= 1.
Fig. 7(a)–(c) compare the proposed joint SPA and code as-signment strategy (IA + CF + SPA) with the pure interference avoidance code assignment strategy (IA + CF) in terms of the (a) average received Eb/N0, (b) average call admission rate,
and (c) standard deviation (STD) of the received Eb/N0 with
various effective traffic loads. One can see that with the help of SPA, the proposed IA + CF + SPA method performs much better than the pure IA + CF method both in terms of the average received Eb/N0 and the average call admission rate.
Furthermore, the advantage of using the proposed SPA mecha-nism grows as the traffic load increases. Referring to Fig. 7(a), from the average received Eb/N0 aspect, the improvement
by using the proposed SPA mechanism increases from 0.3 to 1.9 dB for ρ = 1.5 and 3.5, respectively. As shown in Fig. 7(b) as well, the improvement of the call admission rises from 4% to 10% for ρ = 1.5 and 3.5, respectively. Moreover, thanks
Fig. 7. Comparison between the proposed joint SPA and code assignment strategy and the pure interference avoidance code assignment strategy in terms of the (a) average received Eb/N0, (b) call admission rate, and (c) STD of the
received Eb/N0with various effective traffic loads.
to SPA, the STD of the received Eb/N0 can be significantly
reduced, as shown in Fig. 7(c). At ρ = 1.5, the STD of the received Eb/N0reduces from 2.6 to 1.4 in the decibel domain.
This is because SPA can make the received signal quality more robust against the fading channel. One should note that the STD of the received Eb/N0 for both IA + CF and IA + CF + SPA
Fig. 8. Comparison of (a) the average received Eb/N0 and (b) the call
admission rate against the effective traffic load for the proposed joint SPA and code assignment (IA + CF + SPA), SPA-aided crowded-first-code assignment (CF + SPA), and SPA-aided random assignment (RM + SPA) strategies.
increases in the range of 1≤ ρ ≤ 1.5 and begins to decrease as
ρ increases. When the traffic load is light at ρ = 1, the
interfer-ence avoidance code assignment strategy can effectively select codes for all users without producing extra MAI. However, as the traffic load increases to ρ = 1.5, some users may use codes experiencing few interferers, whereas some other users may not. As the traffic load continues to grow, all the active codes may have a similar amount of interference.
C. Effect of Interference Avoidance Code Assignment Strategy
Fig. 8(a) and (b) compare the average received Eb/N0 and
call admission rate against the effective traffic load for the pro-posed joint SPA and code assignment (IA + CF + SPA), SPA-aided crowded-first assignment (CF + SPA), and SPA-SPA-aided random assignment (RM + SPA) strategies. First, in terms of received Eb/N0, IA + CF + SPA performs better than RM +
SPA for 1≤ ρ < 4, whereas in the higher traffic load region of ρ≥ 4, the received Eb/N0of IA + CF + SPA is lower than
that of RM + SPA. With higher traffic load, IA + CF + SPA
can accommodate more users than RM + SPA because IA + CF + SPA skillfully assigns code channels to avoid producing excessive MAI, whereas RM + SPA blocks call requests owing to the careless code assignment. Thus, with more users in the system, a user tends to be affected by more interferers, which results in the lower Eb/N0for the IA + CF + SPA method.
Second, for the same reason, the received Eb/N0 of the
CF + SPA method becomes lower than RM + SPA in the re-gion of ρ > 1.5. Third, the RM + SPA method performs the worst in terms of the call admission rate because it randomly assigns codes without considering the code tree structure or MAI. Fourth, comparing IA + CF + SPA and CF + SPA, the IA + CF + SPA method can have a higher received Eb/N0than
the CF + SPA method, whereas the call admission rate of the IA + CF + SPA is slightly lower than the CF + SPA method. For example, the average received Eb/N0 at ρ = 2.5 is 8.6
and 9.6 dB for CF + SPA and IA + CF + SPA, respectively. However, the call admission rate of the IA + CF + SPA is 2% lower than CF + SPA. Note that the CF + SPA method can make the tree structure of the allocated codes more compact, thereby gathering more larger code resources for higher rate users and having a higher admission rate. However, the IA + CF + SPA method aims to first avoid MAI before applying the CF method. Moreover, for the region of 1.5≤ ρ ≤ 4, the CF + SPA method has the poorest Eb/N0 performance, even
compared to the RM + SPA method. This also justifies the advantages of the IA + CF + SPA method.
VII. CONCLUSION
In this paper, we have proposed a joint SPA and code assign-ment strategy for the multirate synchronous MC-DS-CDMA with TF-domain spreading. In the proposed joint scheme, we first optimized the received signal power using an SPA mech-anism. Then, an MAI-coefficient-aided interference avoidance code assignment strategy was applied to eliminate MAI. The MAI coefficient was used to predict the quantity of the MAI imposed on each code channel. Through simulations and analy-sis, we have demonstrated that the proposed joint SPA and code assignment method can simultaneously effectively enhance the received Eb/N0 and maintain a high call admission rate.
In-teresting future research topics include the application of the concept of the MAI coefficients to the MC-DS-CDMA sys-tem when combined with the multiple-input–multiple-output antenna technology [13] or power control mechanisms [24].
APPENDIXA
In this Appendix, we derive (12). To facilitate the calculation of Ik,s,v(X) , we consider two scenarios according to the relation between To (the bit duration of the reference user) and Tk(X)
(the bit duration of the interfering user k in group X).
MAI From High Data Rate Users(To> Tk(X))
In this case, the ratio of bit duration of the desired users to the interfering user of group X∈ {A, B, C} can be
written as L(X)k = To/Tk(X), where L (X) k is a positive integer. Rewrite (4) as Ik,s,v(X) = Pk,s,v(X) αo,s,vβo,s,vc (X) k [v]co[v] To To 0 b(X)k,s(t) × g(X) k (t)go(t)dt = Pk,s,v(X) αo,s,vβo,s,vc (X) k [v]co[v] L(X)k Tk(X) × L(X)k−1 =0 b(X)k,s[] Tk(X) 0 g(X)k (t)go(t)dt. (32)
Based on the definition of the user group in Section II-B, we can have Ik,s,v(B) = Ik,s,v(C) = 0 because $T
(B) k 0 g (B) k (t)go(t)dt = 0, and $T (C) k 0 g (C)
k (t)go(t)dt = 0. That is, the time-domain
spreading codes of the users in groups B and C are orthogonal to the reference user. Recall that b(A)k,s[] =±1 with equal probability. Thus, it follows that
b(A)k,s[]
Tk(A)
Tk(A)
0
gk(A)(t)go(t)dt =±1 (33)
with equal probability. Consequently, (32) can be simplified as
Ik,s,v(A) =
Pk,s,v(A) αo,s,vβo,s,vc
(A) k [v]co[v] L(A)k L(A)k−1 =0 ∆[] (34)
where ∆[] =±1 with equal probability.
MAI From Low Data Rate Users(To≤ Tk(X))
In this case, we express Ik,s,v(X) as
Ik,s,v(X) = Pk,s,v(X) αo,s,vβo,s,vc (X) k [v]co[v] To To 0 b(X)k,s(t) × g(X) k (t)go(t)dt = Pk,s,v(X) αo,s,vβo,s,vc (X) k [v]co[v] To b(X)k,s[0] × To 0 gk(X)(t)go(t)dt. (35)
Similar to the case of the MAI from high data rate users, we have Ik,v(B)= Ik,v(C)= 0, and b(A)k,s[0] To To 0 gk(A)(t)go(t)dt =±1. (36)
Thus, it follows that
Ik,s,v(A) =
Pk,s,v(A) αo,s,vβo,s,vc(A)k [v]co[v]∆[0] (37)
where ∆[0] is defined in (34). Note that (37) is the special case of (34). Specifically, we can obtain (37) by letting L(A)k = 1 in (34).
Let βo,s,v= α∗o,s,v for the maximum ratio combining
scheme. With Ik,v(B)= Ik,v(C)= 0, we substitute (10), (11), (34), and (37) into (5) and obtain
Yo,s= % Po 2 To bo,s[0] M v=1|αo,s,v|4 M i=1|αo,s,i|4 + KA k=1 M v=1 L(A)k−1 =0 & Pk(A) Po × α(A) k,s,v 2|αo,s,v|2c(A)k [v]co[v] % M i=1α (A) k,s,i 4L(A)k ∆[] +√1 Po M v=1 ns,v . (38)
Following [20], we assume that the MAI can be approximated by a zero-mean Gaussian-distributed random variable. Thus, the normalized decision variable Yo,s can be modeled by a
Gaussian random variable with mean
E[Yo,s] = bo,s[0]
' ( ( )M v=1 |αo,s,v|4 (39) and variance Var[Yo,s] = M v=1 KA k=1 L(A)k−1 =0 Var & Pk(A) Po α(A) k,s,v 2 |αo,s,v|2 M i=1|α (A) k,s,i|4 ×c (A) k [v]co[v]∆[] L(A)k +1 2 " Eo N0 #−1 M v=1 |αo,s,v|2 = M v=1 KA k=1 L(A)k−1 =0 Pk(A) Po |αo,s,v|4 L(A)k 2E α(A) k,s,v 4 M i=1 α(A) k,s,i 4 +1 2 " Eo N0 #−1 M v=1 |αo,s,v|2. (40)
Define the received Eb/N0(denoted by γ) as expressed in (41),
transmission rates of the reference user and user k in group A, respectively. Note that Eo= PoToand N0= PnTc, where Po
and Pnare the transmission power of the reference user and the
noise power. As in [21] and [22], R(A)k /Ro= Pk(A)/Pomeans
that a high-rate user needs more power.
APPENDIXB
In this Appendix, we use the Laguerre integration to eval-uate the error rate performance of the synchronous multirate MC-DS-CDMA system with TF-domain spreading when the SPA mechanism is applied. Substituting the MAI coefficient κ of (15) into the received Eb/N0of (12), we obtain
γ = M v=1 |αo,s,v|4 2κE α(A) k,s,v 4 M i=1α (A) k,s,i 4 M v=1 |αo,s,v|4 + " Eo N0 #−1 M v=1 |αo,s,v|2 −1 . (42)
Because |αo,s,v| and |α(A)k,s,i| are the amplitudes of the
Rayleigh-fading channel,|αo,s,v|2 and|α(A)k,s,i|2 are the
expo-nentially distributed random variable with mean E[|αo,s,v|2] =
E[|α(A)
k,s,i|2] = 1. To ease the notation, we denote zov=
|αo,s,v|2and zki=|α(A)k,s,i|2. Then, the probability density
func-tion of zovand zkvare expressed as
fzov(zov) = e −zovU (z ov) (43) fzki(zki) = e −zkiU (z ki) (44) where U (t) = * 1, t≥ 0 0, t < 0. (45) Then, E[|α(A)k,s,v|4/M i=1|α (A)
k,s,i|4] of (12) can be expressed as
E α(A) k,s,v 4 M i=1α (A) k,s,i 4 = E + |zkv|2 M i=1|zki|2 , = ∞ 0 · · · ∞ 0 |zkv|2 M i=1|zki|2 fzk1(zk1)· · · fzkM(zkM)dzk1· · · dzkM = ∞ 0 · · · ∞ 0 |zkv|2 M i=1|zki|2 e−zk1· · · e−zkMd zk1· · · dzkM. (46) Due to the tediousness and complexity of the calculations, we suggest the application of the Laguerre polynomial ap-proach of [25] to calculate (46). Based on the Laguerre poly-nomial approach, the integration for a function q(x)e−xcan be computed by ∞ 0 q(x)e−xdx = H i=1 ωiq(xi) (47)
where xi and ωi are the abscissas and the weight factor of
the Laguerre polynomials with order H, respectively. By ap-plying the Laguerre integration into (46), we can calculate E[|α(A)k,s,v|4/M i=1|α (A) k,s,i|4] as E α(A) k,s,v 4 M i=1α (A) k,s,i 4 = H i1=1 · · · H iM=1 wk1,i1· · · wkM,iM |zkv,iv| 2 M j=1|zkj,ij|2 . (48) γ = E 2[Y o,s] 2Var[Yo,s] = M v=1 |αo,s,v|4 2 M v=1 KA k=1 L(A)k−1 =0 Pk(A) Po |αo,s,v|4 L(A)k 2E α(A) k,s,v 4 M i=1 α(A) k,s,i 4 + " Eo N0 #−1 M v=1 |αo,s,v|2 −1 = PoGo M v=1 |αo,s,v|4 2 M v=1 KA k=1 L(A)k−1 =0 R(A)k Ro |αo,s,v|4 L(A)k 2E α(A) k,s,v 4 M i=1α (A) k,s,i 4 PoGo MAI + Pn M v=1 |αs,v|2 noise −1 (41)
For a binary phase-shift keying modulation with coherent detection, the conditional error probability for the given αo,s,v
is equal to
P (e|αo,s,1, . . . , αo,s,M) = Q(
2γ) (49)
where Q(x) = (1/√2π)$x∞e−t2/2dt. Recall that z ov=
|αo,s,v|2. Hence, the total error probability can be expressed as
P (e) = ∞ 0 · · · ∞ 0 Q 2γ|zo1, . . . , zoM × fzo1(zo1)· · · fzoM(zoM)dzo1· · · dzoM = ∞ 0 · · · ∞ 0 Q 2γ|zo1, . . . , zoM × e−zo1· · · e−zoMdz o1· · · dzoM. (50)
By applying the Laguerre integration into (50), we can further simplify the total error probability P (e) as
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Chih-Wen Chang (S’02–M’06) received the B.S.
and M.S. degrees in electrical engineering from National Sun Yat-Sen University, Kaohsiung, Taiwan, R.O.C., in 1998 and 2000, respectively, and the Minor M.S. degree in applied mathematics and the Ph.D. degree in communication engineering from National Chiao Tung University, Hsinchu, Taiwan, in 2005 and 2006, respectively.
Since August 2006, he has been an Assist-ant Professor with the Institute of Computer and Communication Engineering, National Cheng Kung University, Tainan, Taiwan. His current research interests include cognitive radio, optimization, and cross-layer design in wireless communication systems. Dr. Chang was awarded the IEEE Student Travel Grant for the 2006 Inter-national Conference on Communications and membership into the Phi Tau Phi Scholastic Honor Society in 2006.
Li-Chun Wang (S’92–M’96–SM’06) received the
B.S. degree from National Chiao Tung University (NCTU), Hsinchu, Taiwan, R.O.C., in 1986, the M.S. degree from National Taiwan University, Taipei, Taiwan, in 1988, and the M.Sci. and Ph.D. degrees from the Georgia Institute of Technology, Atlanta, in 1995 and 1996, respectively, all in electrical engineering.
From 1990 to 1992, he was with the Telecommu-nications Laboratories, Ministry of Transportations and Communications, Taiwan (currently the Telecom Labs, Chunghwa Telecom Company). In 1995, he was affiliated with Bell Northern Research, Northern Telecom, Inc., Richardson, TX. From 1996 to 2000, he was a Senior Technical Staff Member with the Wireless Commu-nications Research Department, AT&T Laboratories. Since August 2000, he has been an Associate Professor with the Department of Communication Engineering, NCTU, where he became a Full Professor in August 2005. His current research interests are in the areas of adaptive/cognitive wireless networks, radio network resource management, cross-layer optimization, and cooperative wireless communication networks. He is the holder of three U.S. patents. He has published over 30 journals and 70 international conference papers.
Dr. Wang has served as an Associate Editor for the IEEE TRANSACTIONS ON
WIRELESSCOMMUNICATIONSfrom 2001 to 2005 and the Guest Editor of the special issue on “Mobile computing and networking” for the IEEE JOURNAL ONSELECTEDAREAS INCOMMUNICATIONSin 2005 and the special issue on “Radio resource management and protocol engineering in future IEEE
broadband networks” for the IEEE Wireless Communications Magazine in
2006. He is a corecipient (with G. L. Stuber and C.-T. Lea) of the 1997 Jack Neubauer Best Paper Award from the IEEE Vehicular Technology Society.
