C
2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands.
Comparison of Downlink Power Allocation Mechanisms in Soft Handoff
for the WCDMA System with Heterogeneous Cell Structures
∗CHING-YU LIAO, LI-CHUN WANG†AND CHUNG-JU CHANG
Department of Communication Engineering, National Chiao Tung University, Taiwan
Abstract. Handoff in heterogeneous cellular networks is one of the hot topics for wireless networks beyond the third generation. We observe
that a power exhausting issue may occur in a code division multiple access (CDMA) system with mixed-sized cells. During soft handoff in the downlink transmission, a number of base stations transmit signals to a user simultaneously. Usually, a microcell has a more stringent limitation on the total available power than a macrocell. Thus, ignoring the impact of various cell sizes, the traditional downlink power allocation techniques for soft handoff may easily consume excessive power to serve soft handoff users, while leaving insufficient power for serving other regular users.
To resolve such an power exhausting issue in CDMA systems, we investigate different downlink power allocation techniques used in soft handoff subject to the impact of mixed-sized cells. For the single-site power allocation technique we consider the site selection diversity transmission (SSDT) technique, while for the multi-site power allocation we study the link proportional power allocation (LPPA), the quality balancing power allocation (QBPA), and the equal power allocation (EPA) techniques. We find that the multi-site LPPA technique can more efficiently allocate power to both handoff and non-handoff users than others. In an example with the ratio of the micrcocell radius/macrocell radius equal to 1/3, it is demonstrated that LPPA can improve the capacity over EPA, QBPA, and SSDT by 125, 30, and 5%, respectively. By taking account of measurement errors in the same case, the capacity improvements of LPPA over EPA, QBPA, and SSDT become 180, 41, and 23%, respectively.
Keywords: soft handoff, CDMA, power allocations, heterogeneous cellular structures
1. Introduction
Soft handoff is an important technique for the code divi-sion multiple access (CDMA) cellular system. Traditional soft handoff algorithms are mainly developed for the homogeneous cellular system. In practice, however, in order to extend the coverage area or increase system capacity, a cluster of mi-crocells may be employed at the boundaries of surrounding macrocells. Thus, a heterogeneous cellular network will oc-cur naturally as shown in figure 1. Although soft handoff has been extensively investigated in the literature, fewer works have concentrated on evaluating the soft handoff performance in heterogeneous cellular environments.
The major goal of this paper is to evaluate the impact of various cell sizes on CDMA systems from the downlink soft handoff performance perspective. We focus on the downlink soft handoff because for the future wireless Internet services the traffic volume in the downlink will be much higher than that in the uplink. We observe a “power exhausting” issue that may occur in the handoff process of a heterogeneous cellular network. The power exhausting issue results from the fact that
∗This work was supported jointly by the Lee and MTI Center for networking research, and the National Science Council, Taiwan under the contracts 90-2213-E-009-068 91-2219-E-009-016, and EX-91-E-FA06-4-4.
Part of results in this paper were presented at the IEEE Globecom, Nov. 2002, and the Sixth ACM International Workshop on Modelling, Analysis and Simulation of Wireless and Mobile Systems, (MSWiM’03), Sep. 2003.
†corresponding author.
E-mail: [email protected]
the total transmission power of a base station is constrained by a maximum value and a microcell usually has a more stringent limitation on the total available power than a macrocell. Thus, ignoring the impact of various cell sizes, the traditional down-link power allocation techniques for soft handoff may easily consume excessive power to serve soft handoff users, while leaving insufficient power for serving other regular users.
The previous works about downlink power allocation for soft handoff in CDMA systems can be summarized as follows. In [20], the authors examined the impact of soft handoff on downlink capacity of the CDMA system in a homogeneous cellular structure. It was mentioned that soft handoff can max-imize the diversity gain when the involved serving base sta-tions allocate the same amount of power to a user. In this paper, if the serving base stations allocate the same amount of power to the handoff user, we call it the equal power al-location (EPA) method. In [11], a simple quality balancing algorithm was proposed to adjust cell-site transmitter power for non-handoff and handoff users in the downlink. We call the power allocation method of [11] as the quality balancing power allocation (QBPA) method in this paper. In [4], it was shown that EPA-based downlink soft handoff may decrease system capacity due to unequal path gains from a handoff user to the two serving base stations. Furukawa [6] proposed a site selection diversity transmission (SSDT) technique for CDMA downlink transmissions to select a serving base station with the best link quality among the active set. In [19], the author proposed an enhanced SSDT technique to allow more than one base station to transmit signals to the handoff user. Blaise
Figure 1. The heterogeneous cellular model.
et al. [3] presented a a cost-function based differentiated power control technique to determine different power levels of each radio link from two base stations to the handoff user. Staehle et al. [18] proposed two proportional power allocation meth-ods, in terms of transmission power and target signal quality. In our previously proposed link proportional power
alloca-tion (LPPA) technique [21], the base staalloca-tion with better link
quality will be responsible for allocating more power to the handoff user. It was shown that LPPA can alleviate the power exhausting issue for the microcellular CDMA system. None of the aforementioned downlink power allocation for soft hand-off have been evaluated in a cellular system with mixed-sized cells.
With respect to the performance of heterogeneous CDMA cellular systems, some works have been reported in the litera-ture [10,12,16,22]. In [22], it was concluded that the capacity of a hierarchical cellular system can be improved by integrat-ing downlink power control of microcells and uplink power control of a macrocell. In [10] it was found that for a CDMA system with mixed-sized cells, the interference from adjacent macrocell may decrease the uplink capacity improvements re-sulting from cell splitting. In [16] the authors suggested tier selection algorithms to improve the uplink capacity of a mi-crocell/macrocell overlaying system. In [12], a macrodiversity scheme was proposed to enable a hierarchical CDMA system to share the same spectrum between the macrocell and the microcell by adopting the SSDT technique in the downlink and the maximal ratio combining technique in the uplink. To our knowledge, in an environment with a cluster of microcells surrounded by macrocells, the downlink capacity of such a CDMA system considering both handoff and power control has not been fully addressed in the literature.
Aiming to resolve the power exhausting issue for a CDMA system with mixed-sized cells, this paper investigates different downlink power allocation techniques used in soft handoff. To this end, we consider the single-site SSDT power allocation technique, while for the multi-site power allocation technique, we investigate LPPA, QBPA, and EPA. To obtain an over-all evaluation, in addition to power over-allocation and soft hand-off, through a process of distinguishing handoff users from regular power-controlled users, we further consider the dis-tributed constrained power control [1] and temporary removal algorithms [2]. Through simulations, it will be demonstrated that the LPPA technique can deliver higher system capacity in
Figure 2. A simplified heterogeneous cellular model.
a CDMA system with mixed-sided cells than other considered downlink power allocation techniques.
The rest of this paper is organized as follows. Section 2 describes the system model. Section 3 discusses the related downlink handoff power allocation algorithms. Section 4 illus-trates the power exhausting problem for downlink soft handoff in a heterogeneous cellular network. Section 5 analyzes system capacity. Section 6 details the operation of a CDMA system integrating soft handoff, power control, and removal proce-dures. Simulation model and numerical results are shown in Section 7. We give our concluding remarks in Section 8. We also prove the convergent characteristics of the LPPA algo-rithm in Appendix.
2. System model 2.1. Signal model
Consider a simplified heterogeneous cellular model with a single microcell adjacent to a macrocell as shown in figure 2. Denote RM and Rµas the radii of the macrocell M and the
microcell µ. In the figure, a user is located at H with the distance of rMand rµto the macrocell M and the microcellµ,
respectively.
Denote qi, j as the transmission power from base station i
to user j . Let(qi, j) be the downlink received bit
energy-to-noise density ratio (i.e., Eb/No). Then(qi, j) can be written
by (qi, j)= qi, j· Li, j· G (Pi− qi, j)· Li, j+ N k,k=i Pk· Lk, j+ ηo ≥ γreq, (1) where Li, j is the radio link attenuation from cell i to user j ;
G is the processing gain; Pi =
N
j=1qi, jis the total downlink
transmission power of base station i ; N is the number of active users in cell i ; ηo is the background noise; and γreq is the
required Eb/No. By including the effects of both path loss and
shadowing, Li, jcan be expressed by
Li, j =
A diα, j1+di, j
zi
β × 10ξi/10, (2)
whereα and β are the path loss exponents, di, jis the distance
from user j to the base station i , zi is the break point in cell
shadowing ξi is described by a distance dependent variable [13], i.e., σi(di, j)= σ1, di, j ≤ zi σ2, di, j > zi. (3)
The breakpoint zi is given by
zi =
4 hihms
λ , (4)
where hiis the antenna height of base station i , hmsthe antenna
height at the user side, andλ the wavelength. We define the cell boundary as the point at which user j receives the same power from both adjacent cells M andµ first [17]. Then at the cell boundary, we have
˜
PM× LM, j = ˜Pµ× Lµ, j, (5)
where ˜PMand ˜Pµrepresent the base station pilot power of a
macrocell and microcell, respectively. For simplicity, we only consider the effect of path loss in (5) first. Then, combining (2) and (5), we have ˜ PM ˜ Pµ = Lµ, j LM, j =R α M 1+RM zM β Rµα1+Rzµ µ β ∝ RM Rµ α+β × hµ hM β . (6) Note that (6) is valid only when the microcell radius is larger than the break point distance. When considering only the mi-crocell interference in (1), we have
qi, j ≥ γreq· (PM· LM, j + PµLµ, j) (G+ γreq)· LM, j , = γreq (G+ γreq)· PM+ Pµ Lµ, j LM, j , = γreq (G+ γreq)· PM+ PµDj10(ξµ−ξM)/10 , (7) where Dj = dµ−αµ1+dzµ µ −βµ d−αM M 1+dM zM −βM. (8)
To make macrocell users have the required Eb/No, the
max-imum allocating transmission power ˆqM can be obtained
by substituting the maximum total base station transmission power ˆPMand ˆPµin (7). Then, we have
ˆ
qM =
γreq
(G+ γreq)( ˆPM+ ˆPµ· Dj), (9) where Djis given in (8). For simplicity, we only consider the
effect of path loss in (5). Note that the total transmission power of the base station is dependent on the summation of the power allocated for each user. Note that ˆqMindicates the power level
allocated to a user at the macrocell boundary. From (6) and (9), the maximal downlink allocating power for a microcell user can be obtained as
ˆqµ= ˆqM·
LM, j
Lµ, j. (10)
In this paper, we adopt the maximum ratio combining in the downlink soft handoff. Thus, based on [7], the optimal received
Eb/Nofor user j during soft handoff is given by
(qM, j, qµ, j)= (qM, j)+ (qµ, j), (11)
where(qM, j, qµ, j) denotes the Eb/N0after the maximum
ratio combining for macrocell transmitting at the power level
qM, jand microcell transmitting at qµ, j, respectively;(qM, j)
and(qµ, j) are the received Eb/N0from the macrocell base
station and that from the microcell base station before com-bining, respectively.
3. Related work
A downlink handoff process consists of three different aspects: (1) decide when to execute the handoff; (2) manage resources among the base stations in the active set; (3) optimize handoff parameters. In this paper, we consider the second issue. To manage resources during downlink soft handoff is actually the issue of allocating power from multiple cells to a user. In the literature, different downlink power allocation techniques have been proposed, such as EPA [20], QBPA [11], SSDT) [6], and LPPA [21]. In the following, we denote qi,i, and Li as
transmission power, the received SIR and the link gain from base station i in an active setϒ , respectively. Represent |ϒ| as the size of the active sect and S I Rreq as the required link
quality for a handoff user.
3.1. Equal power allocation
When a user requests handoff, it is implied that other base stations in the active set can provide better link quality than the original base station. Based on the EPA technique, base stations allocate power to a handoff user in the following two steps:
r
From the link quality of the original serving base stationi , obtain the required allocated power (denoted as qi) for a
particular user.
r
All the base stations in the active set will allocate qi|ϒ|to the handoff user.
3.2. Quality balancing power allocation
In [11], a simple quality balancing power allocation (QBPA) technique was introduced from a power control perspective. The basic idea of QBPA is to allocate more power to a user with poor link quality, while assigning less power to a user with better link quality. The QBPA technique allocates power to a handoff user according to the following principle:
q1L1= q2L2= · · · = q|ϒ|L|ϒ|. (12)
3.3. Site selection diversity transmission (SSDT)
Another interesting downlink transmission technique is the site selection diversity transmission (SSDT). The SSDT
technique always selects the best base station to serve the handoff users. Because of this, it can transmit the least power, thereby decreasing the downlink interference. Let qi
(i = 1, · · · , |ϒ|) be the required transmission power for base station i to achieve the required link quality S I Rreq.
Accord-ing to the SSDT technique, transmission power is allocated as follows: if = argimin q1, q2, · · · , q|ϒ| , (13) then qi = minq1, q2, . . . , q|ϒ| , if i = 0, if i = (14)
3.4. Link proportional power allocation (LPPA)
The link proportional power power allocation (LPPA) tech-nique was suggested in [21]. According to LPPA, the trans-mission power of a base station during handoff should be pro-portional to the link gain between the handoff user to its serv-ing base stations. In other words, LPPA aims to find a set of
qi (i= 1 to |ϒ|) such that
i ≥ SI Rreqand
q1: q2:· · · : q|ϒ|= L1: L2:· · · : L|ϒ|. (15)
4. The power exhausting issue
In this section, we will illustrate the power exhausting issue of a CDMA system with mixed-sized cells, as shown in figure 3. We assume that a macrocell M and a microcellµ simultane-ously serve user h at the cell boundary who is moving from the macrocell to the microcell. In the figure, the height of the blocks is defined as the maximal allocation power level of the cell and the width of the blocks is proportional to the link qual-ity, where LM,h and Lµ,h represent link quality from user h
to macrocell base station M and that to microcell base station
µ, respectively. We represent the equivalent received signal
quality of user h by the product of multiplying the allocation power and the link quality. For example, for the homogeneous cellular systems case as shown in figure 3(a), the required re-ceived signal quality equals 12 (6× 2) units before handoff. Here, we compare the following power allocation techniques: (1) EPA, (2) QBPA, (3) SSDT, and (4) LPPA.
For the homogeneous cellular systems as in figure 3(a), assume that user h has equal link quality between macrocell and microcell, and it receives the same signal strength from macrocell and microcell, respectively. In this case, all the three power allocation methods will be the same.
Consider a heterogeneous cellular systems as shown in figure 3(b). Let the link quality to the microcell be two times of that to the macrocell, i.e. Lµ,h= 2LM,h, and the maximum
transmission power in the macroell be two times of that in the microcell. Then the distributions of power allocation from the two serving base stations based on different techniques are discussed as follows.
Figure 3. Example for different soft handoff downlink power allocation tech-niques. (a) homogeneous cellular system and (b) heterogeneous cellular sys-tem.
r
Equal power allocation (EPA):qM,h= qµ,h = 3,
⇒ h= 18,
where qM,h and qµ,h are the allocated power from the
macrocell and that from the microcell, respectively; and
his the received signal quality.
r
Quality balancing power allocation (QBPA) [11]:qM,h= (12L/2)
M,h = 3, qµ,h = (12/2)
Lµ,h = 1.5,
⇒ h= 12.
r
Site Selection Diversity Transmission (SSDT):qM,h= 0, qµ,h = 3,
⇒ h = 12.
r
Link proportional power allocation (LPPA):qM,h qµ,h = LM,h Lµ,h = 1 2, qM,hLM,h+ qµ,hLµ,h= 12. qM,h= 1.2, qµ,h= 2.4, ⇒ h= 12.
Note that EPA will ask the serving base stations to allocate the same power in the two active links, thereby making a “micro-cell” waste too much power to obtain higher received signal quality. Thus, the handoff users from a macrocell will be very
likely to exhaust most of the power budget in the microcell. This is so called “power exhausting issue”. Based on the QBPA technique, the total allocated power to the user is 4.5, whereas the LPPA technique only require the total power of 3.6 to maintain the same signal quality before handoff. As for SSDT, we find that SSDT can allocate the least power to achieve the required signal quality for a handoff user. However, when con-sidering measurement errors during the base station selection procedure, SSDT many select a wrong base station, thereby consuming more power to serve handoff users. The impact of measurement errors on SSDT and other power allocation techniques will be compared in Section 7.
5. Capacity analysis 5.1. Modeling
In this section, we evaluate the capacity of a CDMA system with soft handoff in a simplified heterogeneous cellular envi-ronment with only one macrocell and one microcell, as shown in figure 2. Consider user h at location H . Let M → µ rep-resent the event of soft handoff when user h moves from the originally serving macrocell M to the adjacent microcellµ.
According to the EPA technique, base stations in the active set transmit the same power. Thus, the serving base station
M will allocate transmission power for user h according to
(7) with an upper limit defined in (9). Denote qµ,h and qM,h
as the transmitted power during handoff for macrocell M and microcellµ, respectively. Then, qµ,h and qM,hcan be written
as
qM,h= qµ,h =
1
2min(qM,h, ˆqM), for M → µ. (16) Note that qM,hindicates the allocated power during soft
hand-off, and qM,h is that before soft handoff. The factor of 12 in
(16) is related to the number of base stations involved in soft handoff, i.e. two base stations in our case.
If the unequal power allocation principle is used, the two serving base stations will transmit signal power at different levels according to (7) and (9). That is,
qM,h=
1
2min(qM,h, ˆqM) for M→ µ
qµ,h = 1
2min(qµ,h, ˆqµ) for M→ µ (17) For a microcell user moving into a macrocell, i.e.µ → M, we can simply swap M andµ in (16) and (17) to obtain the allocated power for the macrocell and the microcell during handoff.
In this paper, we define handoff gain (or diversity gain) as the enhancement of the received Eb/No with handoff as
compared to the case without handoff. For hard handoff, a user is connected to the cell with better link gain. The hard handoff gain Ghardcan be written as
Ghard(M→µ) = max{(qM,h)(d B), (qµ,h)(d B)} −(qM,h)(d B).
Ghard(µ→M) = max{(qM,h)(d B), (qµ,h)(d B)}
−(qµ,h)(d B). (18)
For the soft handoff case, according to (11), the soft handoff gain Gsoftcan be obtained by
Gsoft(M→µ) = (qM ,h)(d B)+ (qµ,h )(d B)− (qM,h)(d B).
Gsoft(µ→M) = (qM ,h)(d B)+ (qµ,h )(d B)− (qµ,h)(d B). (19)
5.2. Capacity analysis
Soft handoff can improve the outage performance thanks to diversity gain, thereby increasing system capacity. In [20], the downlink outage probability is defined the probability of the total requested transmission power from all serving users of a base station exceeding the maximum total transmission power at a base station. That is,
Potg(M)= Prob{PM> ˆPM}. (20)
Recall that soft handoff is initiated when the following condi-tion is satisfied:
˜
PM· LM, j− ˜Pµ· Lµ, j ≤ η, (21)
where LM, j and Lµ, j are the link gains from user j to base
stations M and µ, respectively; η is the handoff threshold. Denote NM and Nµ as the number of users in the macrocell
and microcell, respectively. Let NshM and Nsh
µ be the number
of soft handoff users in the macrocell M and microcell µ, respectively. Thus, the total transmission power of mactocell
M in (20) can be calculated as PM= NM −NshM j=1 qM, j + Nsh M j=1 ˆqM/2 + Nsh µ j=1 ˆqµ/2, (22) where the sum of the second and the third terms (denoted as
Psh(M)) is equal to the total transmission power for soft handoff
users . From (9) and (10) we can obtain Psh(M). We further
substitute (7) for qM, j in (22), and obtain
YM = NM −NMsh
j=1
Dj· 10(ξµ−ξM)/10, (23)
where Dj is defined in (8). Let
χ = PˆM− K · PM· NM− NMsh − P(M) sh K · Pµ , (24)
where K = γreq/(G + γreq). Then Potg(M)in (20) becomes
Potg(M)= Prob YM > ˆ PM− KPM NM− NMsh − P(M) sh KPµ , = Q χ − m y σy , (25) where Q(x)=1 2 ∞ x e−t 2/2
dt. Note that since YMis a sum of
independent log-normal random variables, it can be approxi-mated by another log-normal random variable YM with mean
Figure 4. Capacity of (a) equal power allocation (EPA) and (b) unequal power allocation (UPA) with soft handoff against the ratio of radius of the microcell to that of the macrocellρ.
myand standard deviationσyby using the techniques in [15].
The outage probability for the microcell users in the forward link can be also obtained by using the same method. The sys-tem capacity is defined as the maximal number of users subject to the constraint of outage probability less than a certain value, say Potg(M)< 0.05. Thus we can obtain the capacity of macrocell
and microcell.
5.3. Analytical results
Figure 4(a) shows the capacity by using EPA for downlink soft handoff against the cell radius ratioρ. In the figure, the capacity is defined as the maximal number of users subject to the constraint of outage probability less than 0.05. To get some insights through analysis, we consider a simplified two cell model in figure 2 and apply (25) to calculate the system capacity. We observe that the power exhausting issue occurs in the microcell whenρ < 0.7 without any power constraint and whenρ < 0.5 with a power constraint. One can see that the smaller the value ofρ, the higher the macrocell capac-ity will be. The increase of macrocell capaccapac-ity as the value of ρ decreases is mainly because interference from the mi-crocell is reduced. Constraining the maximum transmission power can relieve the power exhausting issue in the microcell slightly although the improvement is not significant. Figure 4(b) demonstrates the capacity of a system using the unequal power allocation in soft handoff against the cell radius ratio. Unlike the EPA method, the UPA can maintain a good capac-ity for both microcell and macrocell fromρ = 0.5 ∼ 1.0. The power exhausting issue does not occur even withρ = 0.1. It is also noted that the power constraint can improve the capac-ity, especially when theρ is small. For ρ = 0.1 the capacity for the constrained UPA method increases microcell capacity about 30%.
6. Joint resource allocation mechanism
In this section, we discuss a joint resource allocation mech-anism, which incorporates downlink power allocation
tech-nique and other resource allocation algorithms, such as, soft handoff, power control, and removal procedures. In particu-lar, we use LPPA as an example in this joint resource alloca-tion mechanism. One can use other downlink power allocaalloca-tion techniques in this joint resource allocation mechanism.
Figure 5 shows the flowchart of the procedures of the joint resource allocation mechanism. As mentioned, this joint re-source allocation mechanism includes four key algorithms. First, based on soft handoff algorithm, an active set of candi-date handoff base stations is determined for each user. Second, the necessary allocated downlink power to each user is pre-estimated according to different techniques, i.e. EPA, QBPA, SSDT, and LPPA. Third, based on quality balancing strategy, a distributed constrained power allocation is adopted for non-handoff users. Four, if the balanced signal quality is lower than the required signal quality for all users in the system, removal algorithm is activated to release the system resources from users with poor link conditions. The iteration of power allo-cation stops when the signal quality meets the requirement. In the following, we detail the design for each algorithm.
6.1. Soft handoff algorithm
The soft handoff algorithm is used to determine the active setϒ for each user j . If the difference of the received signal strength of the pilot signal between the serving cell i and adjacent cell
k is less than the soft handoff thresholdη, i.e.
˜
Pi· Li, j− ˜Pk· Lk, j < η, for i = k, (26)
then base station k should be added into the active setϒ of user j .
6.2. Downlink power allocation for soft handoff users
We suggest to distinguish the handoff users from the non-handoff users. By doing so, the system can allocate resources more efficiently. All the existing downlink power allocation techniques for handoff, such as EPA, QBPA, SSDT, and LPPA, can be implemented in this joint resource allocation mecha-nism. In this paper, we focus on LPPA since LPPA with an
Figure 5. Flowchart of a generic joint resource allocation mechanism inte-grating four key techniques: (1) soft handoff, (2) downlink power allocation for handoff users, (3) downlink power control for non-handoff users, and (4) removal procedures.
iterative form and the convergence of the iterative LPPA algo-rithm have not been reported in the literature. In this section, we detail how LPPA can be implemented in an iterative man-ner and the convergence of the iterative LPPA algorithm will be proved in Appendix I.
As mentioned in [21], the principle of LPPA is to allocate more power to a link with better quality among the active set. Assume that all serving base stations in the active set
ϒ allocate power qi,h for user h. Denote ˆqi as the maximal
allocation power for an individual user in cell i , and(qi,h) as
the received Eb/Nofrom cell i . Considering the maximal ratio
combining for the downlink soft handoff, then we express the received Eb/Nofor us h during soft handoff as
h =
i∈ϒ
(qi,h). (27)
LPPA can be implemented in an iterative manner as follows:
r
Step 0: [Initialize]Let Yh(0) equal the maximum total allocation power ˜Yh,
where ˜Yh=
i,i∈ϒ ˆqi.
r
Step 1: [Set weighting factorswi,h]For each serving base station i , based on link gain,
deter-mine wi,h= Li,h i,i∈ϒLi,h , ∀ i ∈ ϒ. (28)
r
Step 2: [Distribute allocating power qi,h(n)]For each serving base station i ∈ ϒ, calculate the allocation power
qi,h(n)= Min{Yh(n)× wi,h, ˆqi}, ∀ i ∈ ϒ. (29)
r
Step 3: [Calculate Eb/No, and set tuning factorρh]Calculate the received Eb/No. Then set the tuning factor
ρh(n)= γreqh(n).
r
Step 4: [Check Stop Criterion] IF (ρh(n)= 1.0 and Yh(n)= ˜Yh)Yh(n+ 1) = ρh(n)× Yh(n),
GOTO Step 2. ELSE DONE.
Note that in (28), the allocated power is proportional to the link quality.
6.3. Downlink power control for non-handoff users
After allocating power to the handoff users, it is important to adopt an efficient resource allocation scheme to serve the non-handoff users. We suggest adopting QBPA of [11] to serve non-handoff users, but with a slight modification. We incor-porate the concept of the constrained power control mecha-nism of [8] into QBPA by constraining the power allocated to each user to a maximum allowable power. By doing so, each non-handoff user can achieve the same signal quality in the downlink. Meanwhile, if a user who requests the power exceeding the the maximum allowable power, it is better to initiate soft handoff to serve such a user. In other words, the downlink power allocation for soft handoff, such as LPPA, can be applied in this situation.
Table 1 System parameters.
System parameters value
macrocell’s radius(km), RM 3
microcell’s radius(km), Rµ 1.5
cell radius ratio(Rµ/RM),ρ 1/2
mobile’s antenna height(m), hms 1.5
macrocell antenna height(m), hM 20
microcell antenna height(m), hµ 10 macrocell’s max. transmission power(watt), ˆPM 20
macrocell’s max. allocating power(watt), ˆqM 1
2 slope path loss exponent,α, β 2, 2 Standard deviation of 2-slope shadowing,σ1, σ2 4.0, 8.0
Soft handoff threshold(dB),η 2
6.4. Removal algorithm
After allocating power to handoff and non-handoff users, if the signal quality of the serving users is still below the required threshold, then the system may executes the removal algo-rithm. This means power resource is insufficient to support all the serving users. Thus, removal algorithm is activated to remove the user with the weakest link quality. The system can thus utilize the extra power from this user to serve other users who can improve their link quality to a satisfactory level. The pilot power in heterogeneous cellular systems is dependent on cell sizes. The criterion for selecting a user to be removed can simply choose the user with the largest ratio of allocat-ing power to user j over the maximum allowable power for each user in cell i , i.e. max{qi, j
ˆqi }, where the denominator ˆqiis
dependent on the cell sizes.
In this paper, we develop two removal algorithms. For Re-moval Algorithm 1 (RV1), the system will remove the selected user based on the above criterion no matter if the selected one is handoff user or not. Removal Algorithm 2 (RV2), the system will only remove non-handoff users and leave handoff users a higher priority to remain in the system. Numerical results will be given in the next section to compare the performance of these two removal algorithms.
7. Simulation results 7.1. Simulation model
In this, we compare the performance of the link proportional power allocation (LPPA), the equal power allocation (EPA), the quality balancing power allocation (QBPA), and the site se-lective diversity transmission (SSDT) techniques in a CDMA system with various cell sizes subject to measurement errors. Figures 6(a) and (b) illustrate our simulation platform, in which a central macrocell is split to four or nine microcells. That is, we study the cases ofρ = 1, 1/2 and 1/3, where ρ represents the cell radius ratio between the microcell and the macrocell. The simulation methodology and assumptions are summa-rized as follows:
r
We consider squared-shaped cells to simplify the cell split-ting issue. Since this work emphasizes the comparison of downlink power allocation techniques in soft handoff for CDMA systems with various cell sizes, the main conclu-sions drawn from the simulation using the squared-shaped cells will not be significantly different from those using the hexagonal-shaped cells.r
The snapshot simulation method is adopted in this work as [3,7,11,18]. Although the snapshot evaluation method can not capture the time correlation of a fading channel, it is still a viable approach to compare the relative per-formance differences between power allocation techniques considered in this paper.r
Users are assumed to be uniformly distributed in each cell.Figure 6. Examples of heterogeneous cellular network (a)ρ = 1/2, (b) ρ = 1/3.
r
Other important system parameters are listed in Table 1, in which the soft handoff thresholdη = 2 dB, the maximum active set size|ϒ| = 3, and the values of the pilot power design and the maximum allocation power for each user are obtained according to (6), and (10), respectively.r
The system capacity is defined as the number of serving users with outage probability less than 0.05. Because in this paper a performance outage event occurs when serving base stations have insufficient power to provide the required signal quality, we can also define the outage probability as the ratio of the number of disconnected (removed) users to the total number of users. Thus the total capacity Ctot isdefined as the sum of macrocells and microcells capacity.
Ctot=
Nc× Cc, ρ = 1.0
NM× CM+ Nµ× Cµ, ρ < 1.0
where Cc is the system capacity per cell. Note that Nc
is the number of cells in the homogeneous cellular sys-tems, where Nc= 9 in our homogeneous cellular model.
For the heterogeneous cellular systems, CMand Cµ
repre-sent macrocell and microcell capacity, respectively. Here, we consider two cases as shown in figure 6, where (a) is forρ = 1/2, NM = 8 and Nµ= 4, and (b) is for ρ = 1/3,
NM = 8 and Nµ= 9.
7.2. Homogeneous cellular case
Figure 7 compares system capacity versus average outage probability for five different soft handoff power allocation techniques, including EPA, SSDT, QBPA, LPPA-RV1, and LPPA-RV2. In a homogeneous CDMA cellular system, one can observe that QBPA, SSDT and LPPA are better than EPA. The LPPA-RV2 technique enhances 23.1 and 8.5% capacity over the EPA and QBPA techniques, respectively. Further-more, SSDT outperforms LPPA-RV1 and LPPA-RV2 up to 9.1 and 10%, respectively. Note that SSDT has been viewed as the optimal downlink transmission scheme in a homoge-neous CDMA network.
In order to observe the impact of the measurement error on the downlink power allocation techniques, we consider a measurement error of 3 dB during cell-selection process.
Figure 7. Averaged outage performance in the homogeneous cellular systems (ρ = 1.0 ) for the EPA, QBPA, SSDT, LPPA-RV1 and LPPA-RV2 techniques.
Figure 8. Averaged outage performance in the homogeneous cellular systems (ρ = 1.0 ) with measurement error for the EPA, QBPA, SSDT, LPPA-RV1 and LPPA-RV2 techniques.
Comparing figure 7 to figure 8, we observe that measurement errors degrade system capacity by 18.1, 13.7, 7.7, 2.2, and 1.3% for SSDT, EPA, QBPA, LPPA-RV1, and LPPA-RV2, re-spectively. As shown in the figure, SSDT is the most sensitive to the measurement error since only one link is adopted for transmissions. If the selected link is not the best link due to measurement errors, more transmission power may be wasted. On the other hand, subject to measurement errors and for the outage probability equal to 0.05, LPPA-RV1 and LPPA-RV2 improve system capacity by 1.8 and 3.8% as compared to SSDT, respectively. Note that in a more stringent requirement on outage probability, the capacity gain of applying the LPPA technique becomes more significant.
7.3. Heterogeneous cellular case
Figure 9 compares the system capacity of all the aforemen-tioned downlink power allocation techniques in soft handoff under the heterogeneous cellular systems withρ = 1/2. Fig-ures 9(a) and (b) are the average macrocell and microcell ca-pacity, respectively. As shown in the figure, because EPA may
Figure 9. Averaged outage performance in the heterogeneous cellular systems (ρ = 1/2 ) for the EPA, QBPA, SSDT, LPPA-RV1 and LPPA-RV2 techniques.
waste too much power in serving soft handoff users, the sys-tem with EPA encounters the “power exhausting issue”. This problem would get worse in the heterogeneous cellular sys-tems where adjacent cells have different cell sizes. Thus, based on (30), all the power allocation techniques deliver higher total capacity than EPA. The capacity improvements of LPPA-RV2 relative to EPA and QBPA are 76.9 and 19.3% respectively. Compared to SSDT, the capacity of LPPA-RV2 is 2.9% less in the heterogeneous cellular systems withρ = 1/2.
Next we evaluate the impact of measurement errors on the performance of the heterogeneous cellular system with
ρ = 1/2. As shown in figure 10, measurement errors degrade
system capacity by 23.4, 17.6, 8.4, 2.2, and 1.0% for EPA, SSDT, QBPA, LPPA-RV1, and LPPA-RV2, respectively. For
Figure 10. Averaged outage performance in the heterogeneous cellular sys-tems (ρ = 1/2 ) subject to measurement errors for EPA, QBPA, SSDT, LPPA-RV1 and LPPA-RV2 techniques.
Figure 11. Averaged outage performance in the heterogeneous cellular sys-tems (ρ = 1/3 ) for the EPA, QBPA, SSDT, LPPA-RV1 and LPPA-RV2 techniques.
EPA, the power exhausting issue occurs more easily , thereby having insufficient power to serve other regular non-handoff users, especially in the microcell. Clearly, the measurement error may worsen the impact of the power exhausting issue. On the other hand, since LPPA can distribute the required al-location power among serving base stations, the sensitivity on measurement errors is relatively smaller than SSDT. When comparing to the system capacity including the impact of mea-surement errors, both LPPA-RV1 and LPPA-RV2 improve the system capacity of the SSDT technique by 9.6 and 13.1%, respectively.
Figure 11 compares the performance of different power al-location techniques in the case ofρ = 1/3. In the case without measurement errors, LPPA-RV2 and LPPA-RV1 improve the system capacity by 4.8 and 1.7% over SSDT. Furthermore, the capacity of t LPPA-RV2 is 29.6 and 124.8% higher than the QBPA and EPA techniques.
Figure 12 shows the same cellular environment as figure 11 but includes measurement errors. As shown in the figure, the measurement error exacerbates the impact of the power ex-hausting issue for EPA, QBPA, and SSDT. We find that LPPA-RV2 improves system capacity by 22.8%, 40.7%, 181.4% compared to SSDT, QBPA, and EPA. Therefore, it is con-cluded that LPPA-RV1 and LPPA-RV2 can successfully over-come the power exhausting issue in the heterogeneous cellular systems, even with measurement errors.
Based on the previous discussions, we have three important observations.
r
For the heterogeneous cellular systems with smaller cell radius ratio, the system capacity is increased because of cell splitting. However, serving soft handoff users may also easily cause the serious power exhausting issue.r
We find that measurement errors will degrade system ca-pacity. Both EPA and SSDT are more sensitive to the mea-surement error than LPPA and QBPA. This is becauseFigure 12. Averaged outage performance in the heterogeneous cellular sys-tems (ρ = 1/3 ) subject to measurement errors for the EPA, QBPA, SSDT, LPPA-RV1 and LPPA-RV2 techniques.
Figure 13. Total capacity performance with and without measurement error for EPA, QBPA, SSDT, LPPA-RV1 and LPPA-RV2 techniques in the (a) homogeneous cellular system, (b) heterogeneous cellular system withρ = 1/2, (c) heterogeneous cellular system with ρ = 1/3.
the LPPA can effectively distribute the required allocation power among the serving base stations.
r
Measurement errors exacerbate the power exhausting is-sue in the heterogeneous cellular systems. Therefore, the system capacity of EPA, QBPA, SSDT techniques are de-graded even more seriously.Figure 13 shows the total system capacity for the considered power allocation techniques with soft handoff. For the case without measurement errors, SSDT outperforms other tech-niques except in the heterogeneous cellular case, e.g.ρ = 1/3. For SSDT in the heterogeneous cellular system, because the maximum allocation power constraint is more stringent, the required allocation power may easily exceed the power
constraint when serving soft handoff users. When incorpo-rating measurement errors, the SSDT performance is signifi-cantly degraded because only one single link is used to serve the soft handoff user. If the selected link is not the best link, SSDT may waste too much transmission power in serving a soft handoff user, thereby more likely causing the power exhausting issue especially in the heterogeneous cellular sys-tems. From the figure, we have the following observations:
r
Compared to the SSDT, QBPA and LPPA techniques, EPA is the least efficient technique, and very sensitive to mea-surement errors. Thus, the system capacity using EPA is the lowest among all the considered power allocation tech-niques.r
For QBPA, the basic idea is to allocate less power in a better link, or vice versa. If using QBPA for both non-handoff and non-handoff users, it may waste too much power in serving soft handoff users. QBPA can slightly ease the power exhausting issue and result in higher system capacity than EPA.r
As for LPPA, the required allocation power for the soft handoff users will be distributed jointly by all base stations in the active set. If the allocated power of one active link is larger than the maximal allowable power, the rest of the required allocation power will be in charge by other active base stations. This is the reason why the LPPA technique is less sensitive for the measurement error.r
For the homogeneous cellular systems, LPPA-RV2 im-proves capacity over EPA, QBPA, and SSDT by 38.1, 15.4, and 3.8%. Meanwhile, for the heterogeneous cellular sys-tems withρ = 1/3, LPPA-RV2 further improves the capac-ity by 181.4, 40.7, and 22.8% as compared to EPA, QBPA, SSDT, respectively.r
LPPA outperforms other power allocation techniques in both the homogeneous and the heterogeneous cellular sys-tems even with measurement errors. Note that LPPA-RV2 is always slightly better than LPPA-RV1 because it pro-vides protection for soft handoff in the removal algorithm. This kind of protection strategy for soft handoff is a use-ful technique to enhance the efficiency of utilizing radio resource.8. Concluding remarks
In this paper, we have evaluated different downlink power al-location techniques, including EPA, SSDT, QBPA, and LPPA, for soft handoff of a CDMA system with mixed-sized cells. Our simulation results demonstrate that LPPA can more effec-tively alleviate the power exhausting issue than others. Specif-ically, by taking account of the effects of different cell sizes, LPPA can prevent a microcell base station from wasting too much transmission power in serving handoff users. Conse-quently, the LPPA technique can deliver higher system capac-ity than other downlink power allocation techniques in both the homogeneous and heterogeneous cellular systems even with
measurement errors. In summary, we find that it is important to design a handoff mechanism from both power efficiency and link reliability perspectives. This concept and the methodology can be useful in developing other radio resource algorithms for mobile wireless networks.
Appendix: Proof of convergence of the LPPA technique
Here, we prove the convergence of the link proportional power allocation (LPPA) technique in Section 3. Assume that qi,his
allocation power for one soft handoff user h among all serving base stations i in the active setϒ.
Proposition. If a power control algorithm has an “effective”
solution, then for any initial power vector, a “standard” power control algorithm will converge to a unique power vector that achievesγreqfor any power level qi,h[23]. The power control
algorithms that have iterative nature can be described by the following general function:
Yh(n+ 1) = I (Yh(n)). (30)
where I is the interference function. In the following, we brief
Yh(n) to Yhfor convenience. Thus, we define the interference
function as: I (Yh)= γreq i,∈D(min(qi, ˆqi)) × Yh. (31)
Definition: Assume all the link gain and background noise for users are positive. An interference function I is “standard” if it is satisfies the following conditions for all non-negative power vectors:
r
Positivity : I (Yh) > 0.r
Monotonicity : Yh ≥ Y h⇒ I (Yh)≥ I (Y h).
r
Scalability :∀ α > 1, I (Yh)≥ I (αYh).Since all the link gains and background noise between soft handoff user h and serving base stations i, i ∈ ϒ are positive, the positivity and monotonicity properties are trivial satisfied. For the scalability property, consider the effect of power con-straint, there are two kinds of cases in the resulting power vector: Case 1: ∀ qi,h = min(Yh· wi,h, ˆqi,h)< ˆqi ∀ qi,h = αYh· wi,h< ˆqi ⇒ αYh· wi,h> Yh· wi,h ⇒ (αYh· wi,h)> (Yh· wi,h) ⇒ i,i∈ϒ (αYh· wi,h)> i,i∈ϒ (Yh· wi,h).
Thus, I (αYh)= γreq i,i∈ϒ(αYh· wi,h) (αYh)< α I (Yh). (32) Case 2: ∃ k, k ∈ ϒ s.t. qk,h = min(Yh· wk,h, ˆqk,h) = ˆqk i,i∈ϒ (Yh· wi,h) = i=k, i∈ϒ (Yh· wi,h)+ k (ˆqk) ⇒ i,i∈ϒ (αYh· wi,h) = i=k, i∈ϒ (αYh· wi,h)+ k (ˆqk) > i, i∈ϒ (Yh· wi,h).
From case 1, we can also obtain the same results as (32) in case 2. Therefore, the scalability property is also proved. After the preceding discussion, we can prove that the proposed LPPA algorithm is a standard power control algorithm so that always exist an effective solution Yhfor one soft handoff user h.
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Ching-Yu Liao received the B.S. and M.S. degrees in electrical engineering from Huafan Institute of Technology and National Central University (NCU), Taiwan, in 1995 and 1997, respectively. She is cur-rently working toward the Ph.D degree in commu-nication engineering at National Chiao Tung Uni-versity (NCTU), Hsinchu, Taiwan. Also, she joins the program of Graduate Student Study Abroad (GSSA), which is sponsored by National Science Council, Taiwan, R.O.C., being a visiting graduate student in Dept. of Electrical Engineering at University of British Columbia, Vancouver, Canada, in 2004. Her research interests include handoff tech-niques, radio resource management, heterogeneous cellular networks, etc. E-mail: [email protected]
Li-Chun Wang received the B.S. degree from Na-tional Chiao Tung University, Taiwan, in 1986, the M.S. degree from National Taiwan University in 1988, and the Ms. Sci. and Ph. D. degrees in electri-cal engineering from the Georgia Institute of Tech-nology, Atlanta, in 1995, and 1996, respectively. From 1990 to 1992, he was with the Telecommuni-cations Laboratories of the Ministry of Transporta-tions and CommunicaTransporta-tions in Taiwan (currently the Telecom Labs of Chunghwa Telecom Co.). In 1995, he was affiliated with Bell Northern Research of Northern Telecom, Inc., Richardson, TX. From 1996 to 2000, he was with AT&T Laboratories, New Jersey, USA, where he was a Senior Technical Staff Member in the Wireless Communications Research Department. Since August 2000, he has been an Associate Professor in the Department of Communication Engineering of Na-tional Chiao Tung University in Taiwan. His current research interests are in the areas of cellular architectures, radio network resource management, and
cross-layer optimization for high speed wireless networks. Dr. Wang was a co-recipient of the Jack Neubauer Memorial Award in 1997 recognizing the best systems paper published in the IEEE Transactions on Vehicular Technol-ogy. He is holding three US patents and one more pending. Currently, he is the associate editor of the IEEE Transactions on Wireless Communications. E-mail: [email protected]
Chung-Ju Chang was born in Taiwan, R.O.C., in August 1950. He received the B.E. and M.E. degrees in electronics engineering from National Chiao Tung University (NCTU), Hsinchu, Taiwan, in 1972 and 1976, respectively, and the Ph.D degree in electri-cal engineering from National Taiwan University (NTU), Taiwan, in 1985. From 1976 to 1988, he was with Telecommunication Laboratories, Direc-torate General of Telecommunications, Ministry of Communications, Taiwan, as a Design Engineer, Su-pervisor, Project Manager, and then Division Director. There, he was involved
in designing digital switching system, RAX trunk tester, ISDN user-network interface, and ISDN service and technology trials in Science-Based Industrial Park. In the meantime, he also acted as a Science and Technical Advisor for the Minister of the Ministry of Communications from 1987 to 1989. In 1988, he joined the Faculty of the Department of Communication Engineering and Center for Telecommunications Research, College of Electrical Engineer-ing and Computer Science, National Chiao Tung University, as an Associate Professor. He has been a Professor since 1993. He was Director of the In-stitute of Communication Engineering from August 1993 to July 1995 and Chairman of Department of Communication Engineering from August 1999 to July 2001. Now, he is the Dean of the Research and Development Of-fice in NCTU. He was an Advisor for the Ministry of Education to promote the education of communication science and technologies for colleges and universities in Taiwan since 1995. He is also acting as a Committee Mem-ber of the Telecommunication DeliMem-berate Body. His research interests in-clude performance evaluation, wireless communication networks, and broad-band networks. Dr. Chang is a member of the Chinese Institute of Engineers (CIE).
