Feng-Seng Chu Kwang-Cheng Chen
Institute of Communication Engineering,National Taiwan University.
Taipei, Taiwan, R.O.C.
Abstract - Orthogonal Frequency Division Multiple Access (OFDMA) is a promising technique which can provide high capacity in future communication systems. The total capacity of OFDMA can be maximized by dynamically allocating sub-carriers among users according to channel condition.
However, it is quite challenging to properly allocate sub-carriers in mobile channels due to the time varying property.
Existing approach designed for static users assigned the sub-carriers with the best SNR to increase the total capacity but to lose fairness. Fairness can be restored by using max-min criterion or constraint limiting the ratios of user data rates to maintain some balance among users. But when users are mobile, the SNR considered should be replaced by the carrier to interference ratio (CINR) because of the presented inter-carrier interference (ICI) due to Doppler Spread. In this paper we successfully incorporate the ICI into our radio resource allocation algorithm to simultaneously optimize the total capacity and fairness for mobile users. The fairness and priority of user traffic are jointly considered in our adaptive algorithm. The algorithm is demonstrated outperforms the existing algorithm designed for static users, and very robust in realistic operation.
I. INTRODUCTION
Wireless broadband communications become an extremely attractive research to transport multimedia traffic. To provide such high bandwidth physical transmission, one of the key design issues is to decide an appropriate multiple access scheme. Orthogonal frequency division multiplexing (OFDM) is widely considered for high-spectral efficient wireless communications, and has been adopted in wireless LANs, UWB, WiMAX, etc. To further utilize cross-layer radio resource, orthogonal frequency division multiple access (OFDMA) is widely considered in wireless broadband communications.
OFDMA is a multiple access technique inherited the ability of OFDM to combat inter-symbol interference (ISI), which can provide higher spectral efficiency by appropriate distributing radio resource [1]. Existing research include allocation of radio resource among static users for OFDMA systems [2] [3] [4] [5], and some of them considering fairness [4] [5]. Mobility has rarely been considered in literatures. In this paper we first incorporate the Doppler Spread into system optimization, and propose an algorithm to distribute the sub-carriers among mobile users to maximize total capacity and maintain fairness. Although the oscillator deviation, channel/environment variations and user’s velocity all result in Doppler Spread we use generalized velocity to represent the combined effect of them.
The priority of each user was included as a part of fairness consideration which can be adaptively adjusted in our algorithm. We develop theoretical analysis and simulations to illustrate the advantages of the proposed algorithm over the static schemes without considering mobility. At last, we demonstrate our approach is quite robust to the frequency estimation which has been included for estimating Doppler Spread.
The organization of this paper is as follows. We first give the system model and formulate the radio resource allocation optimization for mobile OFDMA system in Section II. Some considerations were discussed in the same section. In section III, we give an experimental study to demonstrate the advantages of our algorithm over the existing static approach.
In Section IV, we consider a more realistic case including Doppler Spread Estimator and demonstrate the robustness of our algorithm against the frequency estimating error. Finally we give some discussions and conclusion in Section V.
II. SYSTEM MODEL A. Analysis of ICI
Inter-carrier interference (ICI) due to Doppler Spread results in the loss of orthogonality among sub-carriers. To include the mobility in our optimization, the ICI needed to be analytically analyzed [6].
Figure 1 depicts a discrete-time baseband equivalent model of OFDM system. bs represent the source bits, symbol generator outputs symbols an. The serial to parallel converter transfers blocks of symbols to the OFDM modulator, which use an N-point IFFT to modulate them onto the sub-channels.
A guard interval of length G is then be added to give a transmitted sequence corresponding to samples at t = iTs
1 sequence with guard interval.
Figure 1: Communication System Using OFDM.
As [6], the received sequence from the multi-path channel has the form
The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06)
where Hm,jis the channel impulse response at path m and instant i. After removing the guard interval and demodulating by FFT, we can use the result of [7] [8] to separate the desired part and the ICI part of the received sequence in frequency domain as
is the ICI effect of sub-carrier n from the sub-carrier l in the same OFDM symbol.
fd f
= ∆
ε is the normalized frequency offset. fd =vc*fc is the Doppler Frequency Shift due to user generalized velocity v and center frequency fc, ∆f is the sub-carrier space.
B. Optimization Formulation
We can formulate our optimization of radio resource allocation based on above mathematical form of ICI effect in mobile OFDM system. Figure 2 is the proposed OFDMA system. The Doppler Spread due to each user’s generalized velocity was estimated by the frequency estimator, which will be further discussed in section IV. We assume all other channel information is known at the transmitter in this paper and introduce the proposed sub-carriers allocation algorithm.
There are K users in the system and the kth user has data rate equal to Rk bits per second. The serial data from the K users are fed into one sub-carrier allocation block which allocates sub-carriers to different users. We sssume the OFDMA system occupies total signal bandwidth B with N data sub-carriers and each data sub-carriers bandwidth is B/N.
Maximum allowable total power for all users is Ptotal. Each of the K users has instantaneous generalized velocity vk
corresponding to Doppler Frequency Shift fdk and thus normalized frequency offset εk.
Our objective is to optimize the sub-carriers allocation in order to maximize total capacity and maintain fairness among users under the total power constraint. We introduce the adaptation rule to be the fairness consideration. The benefit of introducing this rule is we can explicitly control the user data rates subject to system requirement.
Mathematically, the optimization considered in this paper is formulated as Equation (5). Where Pk,n is the power assigned to user k’s sub-carrier n, hk,n is channel gain on user k’s sub-carrier n. The second constraint using the indicator ωk.n to show that each sub-carrier can only be assigned to one user.
N0 is the power of additive white Gaussian noise (AWGN).
( ) the user priority weighting pk and the generalized user velocity vk of the kth user. Which can be arbitrary selected for different relationship from user data rates to user priorities and user generalized velocities. The system designer may consider the fairness is both providing higher data rates for high priority users and giving lower data rates to high generalized velocity users when all users have the same priorities, or just granting the sub-carriers according to user priorities without considering generalized velocities. The definition of fairness can be controlled by the system designer.
The constraint (iii) is the adaptation rule we proposed for considering fairness which denotes the user data rates can be adaptively adjusted. We uniformly distribute Pk,n among all sub-carriers in this paper because the total data throughout is close to total capacity even with flat transmit power spectral density [1] [12].
Equation (5) is the optimization of the adaptive fair radio resource allocation under mobile channels. This equation can be readily solved by standard numerical package such as AMPL [9]. Some differences between mobile and static environments will be discussed later.
C. Alternative Criterion and Constraint
In Equation (5), the criterion is to optimize the total capacity, but there is another criterion being used in static algorithm. Max-min criterion has been used to maximize the minimum capacity of all users and maintain some fairness among users. However, max-min approach is inappropriate for mobile channels, because the power of ICI is much greater than the additive noise [8]. If we maximize the minimum capacity, all users will be given almost equal data rates. It is inappropriate when different users have different priorities. It should be noted, the adaptation rule is essential, or the user with the least velocity gains all sub-carriers. Please note that, all users needed to be included in this constraint to avoid a user getting no sub-carrier allocation.
The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06)
Figure 2: The Proposed OFDMA System
III. EXPERIMENTAL STUDY
In this section we consider an OFDMA system with 64 sub-carriers and 4 users (A,B,C,D). We select f(pk vk,) = pk/vkz and and z = 1 in this and next section as an example. The generalized velocity of each user is assumed to be known at the transmitter as Table 1 in this ideal case. We consider a more realistic case in the next section.
Table 1: Generalized User Velocity in the Experimental Study
User A B C D
Generalized Velocity (Km/Hr)
30 60 70 90
We list the six cases we considered in this section. The simulation results were demonstrated in Table 2 and Table 3.
’L’ and ‘H’ after the generalized user velocity denote user’s priority. ‘Ctotal’ denotes the total capacity.
Case I : The proposed algorithm but without the adaptation rule (without considering fairness).
Case II : The proposed algorithm but the adaptation rule only include two users
Case III : Max-Min Criterion
Case IV : The proposed algorithm with all users have the same priorities (pA=pB= pC=pD=1) Case V : The proposed algorithm with user C has high Priority. (pc = 3 and pA=pB=pD=1)
Case VI: The proposed algorithm with user C has higher priority (pc = 5 and pA=pB=pD=1)
Case I represents just maximizing the total capacity of all users, not taking account of user priorities and fairness among users. From the results we can see the user with the least velocity takes away all the sub-carriers. Giving the user with the least generalized velocity more sub-carriers in effect increasing total capacity, and the total capacity and fairness become trade-ff in mobile channels. Case II denotes we just include the maximum generalized velocity user and minimum generalized velocity user in the adaptation rule, and maximizing the total capacity. We can see only the user had been included in the adaptation rule get sub-carriers.
Table 2:
Demonstrating the Necessity of Adaptation Rule and the Deficiency of Max-Min Criterion for Mobile Channels
User A User B User C User D Ctotal
Case I 341.8 0 0 0 341.8
Case II 218.8(L) 0(L) 0(L) 72.9(L) 291.7 Case III 64.1(L) 63.3(L) 62(L) 60.3(L) 249.7 Case III changes the criterion to maximize the minimum capacity of all users. It seems some fairness among users was achieved, but user priorities have not been considered. It means even if the user C has high priority and the other users are low priority users, max-min criterion still gives the same result as case III which grants all users almost equal data rates and can not be adaptively adjusted.
Case IV is our proposed algorithm, maximizing total capacity with priority and fairness consideration. To demonstrate our algorithm is adaptive, case V and VI consider the cases when user C is high priority user and the other users are low priority users. By choosing pA=pB=pD=1 and pC>1, we can see the ratios of data rates among users can be adaptively adjusted in our algorithm.
Table 3: Simulation Results to Demonstrate the Adaptation for User Priorities of the Proposed Algorithm
User A User B User C User D Ctotal
Case IV 122.7(L) 56.3(L) 51.7(L) 41.2(L) 271.9 Case V 83.6(L) 41.8(L) 108(H) 28(L) 261.4 Case VI 64.2(L) 32(L) 137(H) 21(L) 254.2 We then compare the proposed radio resource allocation algorithm to the static approach [4], which does not consider the mobility.
Table 4: Comparing the Adaptation of the Proposed Algorithm and the Static Algorithm
User A B C D
Channel condition from K users Add guard
The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06) The results of comparison have been demonstrated in Table
4. Considering the first case, User B,C,D have high priorities, the system should give them higher data rates even they have higher generalized velocities. The proposed algorithm satisfies this requirement, but the static algorithm can not achieve that. In the second case we can see the same deficiency of the static algorithm. Although user B has high priority, the static algorithm still gives him lower data rate.
We have numerical demonstrated the differences between static and mobile algorithms. In the next section, we consider a more realistic case and discuss the frequency estimator in Figure 2.
IV. ROBUST TO PHYSICAL TRANSMISSION
A. Frequency Estimator
We assumed the generalized velocity of each user is known at the transmitter in above ideal case. But in fact we need an estimator to estimate the Doppler Spread due to generalized user velocities. The frequency estimator in Figure 2 was used to estimate Doppler Frequency Shift.
B. Block Diagram
Earlier research already demonstrated effective estimation of Doppler Frequency Shift, which is shown in Figure 3 [10]
[11]. Consequently, it is enough to consider random behaviors of frequency estimation in studying the proposed algorithm.
Figure 3: Block Diagram of Frequency Estimator
C. Evaluating the Effect of Estimating Error
The estimating error from frequency estimation introduces several effects. First, the fairness among users considered in the adaptation rule was assumed to closely relate to the user generalized velocities and thus the estimated Doppler Frequency Shift. The estimating error destroys fairness.
Furthermore, the Doppler Frequency Shift has been used to allocate sub-carriers; the estimating error may influence the total capacity. For simulating those effects, we consider an OFDMA system with four users and 64 sub-carriers at fc = 3.2 GHz. All users are assumed to have the same priority but different generalized velocities. The error of estimation is normalized to the theoretical Doppler Frequency Shift fd.
Table 5 list the configuration we used in simulation to evaluate the effect of estimating error. The first line is user generalized velocity vk (Unknown to Transmitter); the second line is the theoretical Doppler Frequency Shift fdk under those generalized velocities. We first choose the estimating error equal to (0.1)fdk to give a detail analysis of the effect of estimation, and then we further discuss the conditions for larger estimating error.
Table 5: Configuration to Evaluate Estimating Error
User A B C D
Under the scale of estimating error, we list all types of frequency estimating error and the simulation result in Table 6. “+” after user k denotes the estimator overestimate the fdk
by (0.1)fdk and “-” after user k denotes the estimator underestimate the fdk by (0.1)fdk. ‘Ctotal’ denotes total capacity and ‘Ideal’ denote the ideal case considering the theoretical Doppler Frequency Shift.
Table 6: Simulation Results to Evaluate the Frequency Estimating Error under Sixteen Error Types Error type User A All simulation results of user data rates and total capacities under the sixteen kind of frequency estimating error were listed in Table 6. We can observe the ratios among user data rates are changed. It is reasonable because we assume the transmitter uses the generalized velocities and thus the
The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'06) estimated Doppler Frequency Shift as a part of fairness
consideration. If the Doppler Spread from one user was underestimated, this user was granted more sub-carriers than ideal case. If the Doppler Spread from the user with least generalized velocity was underestimated, the user will be given more sub-carriers, and in effect, increasing the total capacity. We observe again that fairness and total capacity are trade-off in mobile OFDMA.
In Table 6 we can also observe the total capacity is quite robust to the frequency estimating error. We further discuss this phenomenon by two other cases. In Table 7, we use five cases of user generalized velocities to demonstrate the robustness of our algorithm against the estimating error. In Table 8, the robustness was demonstrated by the six scales of the estimating error.
In Table 7, the maximum deviation percentages from the theoretical total capacity under all estimating error types listed in Table 6 were computed, when the estimating error has been limited to (0.1)fd. Noticing the first and second cases, when all users have the same generalized velocities, the total capacity does not change due to frequency estimating error. We can also observe that the total capacity become more robust to the frequency estimating error when the generalized velocities of all users are closer.
Table 7: Robustness of Our Algorithm against Estimating Error under Different Generalized User Velocities Generalized User
Velocity (km/hr) A B C D
Maximum Deviation Percentage from Theoretical Total Capacity due to Frequency Estimating
Error type Listed in Table 6
50 50 50 50 0%
60 60 60 60 0%
50 60 70 80 0.6%
30 60 70 90 1.61%
20 20 90 90 1.68%
From Table 8 we can see the proposed algorithm still can give a good result even the estimating error as large as (0.5)fd. It can also be observed that the lower of the estimating error, the lower of the deviation from theoretical total capacity.
Table 8: Robustness of Our Algorithm against Different scales of Estimating Error Estimating
Error Maximum Deviation Percentage from Theoretical Total Capacity due to Frequency Estimating Error
type Listed in Table 6
(0.01) fd 0.48%
In this paper we proposed a fair adaptive radio resource allocation algorithm for mobile OFDMA systems and demonstrated its robustness, which outperforms the algorithm without considering mobility. The priorities of users and fairness among users are incorporated into our algorithm by using the adaptation rule, and the fairness consideration has been demonstrated to be essential in mobile channels because of the trade-off between total capacity and fairness. We have demonstrated the criterion we used is more appropriate when considering mobility. We also demonstrated the proposed algorithm is very robust to the estimating error of the Doppler Spread Estimation.
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