Impact Of Varying Channel Model Mixtures On Radio Resource Management For The OFDMA Downlink

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1 86 International Journal of Communication etwors and Information Security (IJCIS Vol. 3, o. 2, August 20 Impact f Varying Channel Model Mixtures n Radio Resource Management For The FDMA Downlin Leonidas Sivridis, Xinheng Wang and Jinho Choi Swansea University, School of Engineering, Singleton Par, Swansea, SA2 8PP, U.K {392924, x.wang, j.choi}@swan.ac.u Abstract: Adaptive resource allocation can drastically increase the throughput of an rthogonal Frequency Division Multiple Access (FDMA system when the Channel State Information (CSI is accurately own. Unfortunately, in practice, perfect CSI is rarely possible. In this paper, we study the efficiency of the FDMA downlin for different vehicular user densities. In order to do so we assume that the transmitter ows the instantaneous CSI (ICSI of the pedestrian users but only the statistical CSI (SCSI of the users that exhibit high mobility (vehicular. We then address the problem of maximizing the sum-capacity of the system subject to user minimum Quality of Service (QoS requirements. It is shown that when only the user SCSI is own loading channels with a rate equal to the Lambert W function of the average SR leads to optimal channel utilization and important system throughput gains. Moreover, the impact of different channel models on the system throughput is investigated. The results show that the vehicular users can highly benefit from adaptive resource allocation under the assumption that their CSI is own by the transmitter. Keywords: FDMA, CSI, power delay profile, radio resource management.. Introduction rthogonal Frequency Division Multiple Access (FDMA is based on rthogonal Frequency Division Multiplex (FDM; and thus, inherits its ey benefits while allowing for multiuser diversity to be exploited []. This leads to more efficient radio resource management (RRM as spectrum can be allocated to users with the better channel conditions. For these reasons, RRM solutions for FDMA systems have attracted significant interest. The research in this area can be broadly divided into two categories, namely margin-adaptive and rate-adaptive. Margin adaptation is the minimization of the transmit power subject to minimum Quality of Service (QoS requirements for each user [2]. Examples of such wor are [3] and [4]. Rate adaptation is the maximization of the data-rates subject to QoS constraints [3]. These QoS constraints could be a combination of data rates, bit error rates or delays. An example of rate adaptation is presented in [5]. The solution to these problems depends on the availability of instantaneous Channel State Information (ICSI at the transmitter. When the ICSI is available the transmitter can optimally assign rates to users and outages will not occur. The wors in [3]-[5] assume that the ICSI is accurately own by the transmitter for all users. There are a number of reasons that lead to unavailable user ICSI at the transmitter. Firstly, feedbac of instantaneous CSI (ICSI will increase the overhead occupying more wireless resources, such as transmit power and bandwidth. Secondly, under significant user mobility, the small coherence time maes channel estimation procedures less accurate. ther reasons that contribute towards unavailable ICSI are prediction errors as well as feedbac/processing delays. Therefore, in some cases, it becomes more reasonable for the user to send bac statistical CSI (SCSI. This means that the users simply feedbac the mean of the sub-carrier SR distribution to the transmitter. However, this may result in some severe performance loss due to the lac of channel information. Multiuser FDMA downlin performance under imperfect CSI has been investigated in [6] [8]. In [6], the authors studied the impact of the channel estimation error, where the channel estimation error resulted from pilot-aided MMSE channel estimation. In [7], a cross-layer design was proposed to guarantee a fixed target-outage probability for slow-fading channels when pilots are used to obtain CSI and the users have heterogeneous delay requirements. In [8], the authors maximized the expected value of the sum-rate capacity (ergodic rates subject to user minimum rate and power constraints. In this paper, we show that for Rayleigh fading channels channels are optimally utilized by transmitting at a rate that is proportional to the Lambert W function of the average SR. A rate-adaptive resource allocation problem is then solved. In a practical scenario users of different velocity are present in a cell. In this paper, we assume that the instantaneous CSI is own for pedestrian users whereas only the SCSI of mobile users (i.e users in a vehicle is own by the transmitter. perators commonly specify a certain percentage mix of different channel models to capture the propagation characteristic specifics of a given environment [9]. In 3PP Long Term Evolution (LTE systems the following channel models are used [8]: Extended Pedestrian A (EPA (This model covers pedestrian users with speeds up to 3 m/h, Extended Vehicular (EVA (this model covers mobile users with speeds up to 50 m/h and Extended Typical Urban (ETU (This model covers moving vehicles with speeds upto 90 m/h [0]. By varying the percentage of the active vehicular users the impact of the channel model mixtures on adaptive resource allocation for 3PP LTE can be studied. It is shown through simulation that under the assumption that the CSI is perfectly own for all active users, adaptive subcarrier allocation leads to higher gains for vehicular users than for pedestrian users. The rest of this paper is organized as follows: The system and channel models are described in Section 2. The methodology used to optimally load sub-carriers when only

2 87 International Journal of Communication etwors and Information Security (IJCIS Vol. 3, o. 2, August 20 SCSI is available is discussed in Section 3. In Section 4 we formulate our problem and describe the heuristic algorithm used to solve it. In Section 5 we present the importance of optimally loading sub-carriers and evaluate the efficiency of the FDMA downlin in different geographic locations. The paper is concluded in Section System and Channel Model 2. System model A downlin FDM system with K users and sub-carriers is considered. Each sub-carrier n has a total bandwidth equal to B. The user's minimum bit-rate is denoted by r. Resource allocation is performed for each sub-carrier, and sub-carriers cannot be shared between users. An assignment indicator c is defined for the th user and the n th subcarrier. Therefore, c when carrier n is allocated to user and 0 otherwise. Resource allocation is performed on a per sub-carrier basis and each user can be assigned one or more of the available sub-carriers. 2.2 Channel model The complex channel gain of sub-carrier n {,2,..., } of user {,2,..., K} is assumed quasi-static over the duration of one frame and is denoted by h. The channel gains h are assumed to follow a complex aussian distribution with zero mean and unit variance, h C(0,. The transmitter has an estimate of each user's channel gain denoted by which it uses to perform resource allocation. When the ICSI is perfectly own by the ^ transmitter P ( h h whereas in the case of completely unown CSI ( h h P( h h^ ^ P. 3. ptimal capacity of sub-carriers under SCSI and ICSI assumptions where p is the power allocated for transmission on this sub-carrier, B is the sub-carrier bandwidth and is the noise spectral density. 3.2 ptimal capacity of sub-carrier when only SCSI is available When the instantaneous channel conditions are unavailable by the transmitter but own at the receiver side, the capacity of each sub-carrier is viewed as a random variable and is given as: νp C( ν B log( +, (2 where ν is exponentially distributed as Rayleigh fading is considered. Here, p is the transmit power, and is the noise spectral density. Under these conditions, there is a nonzero probability that the actual channel conditions cannot support an assigned rate ρ. This value is given as [2]: ρ 2 γ P out P( C( ν < ρ e, (3 where γ is the average value of the user SR. In this case, it is observed that only the rate ρ 0 is compatible with P 0. out We define the goodput [3] as the average successfully transmitted rate. For user and sub-carrier n this value is expressed as: ρ P. (4 ( out In Figure curves of goodput vs data-rate are plotted for different values of the average SR γ 3. ptimal capacity of sub-carrier when ICSI is available When the ICSI is own by both the transmitter and the receiver, the base-station (BS can adapt its transmission strategy without errors. Therefore, in this case there is no notion of capacity versus outage where the transmitter sends bits that cannot be decoded. When the ICSI is own, the maximum capacity that can be reliably transmitted on a subcarrier n experiencing channel gain is the Shannon capacity []: p C B log( + h 2, ( Figure. oodput versus bit-rate curves for different values of the average user SR.

3 88 International Journal of Communication etwors and Information Security (IJCIS Vol. 3, o. 2, August 20 Each sub-carrier can be optimally loaded by selecting the value of ρ which maximizes. These values of ρ for each,n pair can be given as: ( _ ρ W ln(2, (5 where W denotes the Lambert-W function, the solution to W ( x the transcendental equation W ( x e x. Therefore, the maximum goodput user can achieve on sub-carrier n is: W ( ln(2 2 W ( γ, n γ, n e. (6 ln(2 4. Problem Formulation We now formulate the resource allocation problem for the case where SCSI is only own at the transmitter side. The objective is to maximize the sum-goodput of the FDMA downlin under minimum user data-rate requirement constraints denoted by r. Equal power allocation across all sub-carriers is assumed as this reduces the complexity of the problems and minimally decreases the data throughput of a multiuser FDM system [4]. This is due to the nature of FDMA systems, where sub-carriers are commonly assigned to the users with the best channel gains [4]. For the SCSI based scheme, the problem can be mathematically formulated as follows: P : max Subject to C : K c n n c c B r B C 2: If c then c 0 ' n ' ote that the first constraint, C, ensures that the QoS requirement is met for all users, whereas the second constraint ensures that a single carrier is not shared between different users. By replacing the goodput with the Shannon capacity in P the formulation for the case of ICSI can be obtained. 4. Complexity of the Problem In P, both the goodput and the Shannon capacity can be pre-calculated for all users and channels before allocation. Therefore, these values can be treated as constants. Hence, P is actually an integer linear programming problem which is one of the earliest members of the P-hard class [5]. There exist K integer variables and K+ constraints, where the number of sub-carriers is high in practice (i.e 024/2048 used in our simulations. As the complexity of the problem grows exponentially with the values of K and K+ [6] it cannot be solved by using standard integer linear programming methods such as Branch and Bound. This is because the associated complexity will be too high for real time applications. Thus, a heuristic algorithm which will allocate resources to users needs to be developed. 4.2 Heuristic algorithm In this wor we use the heuristic algorithm presented in [5] to solve P. This algorithm first allocates sub-carriers to the users who can transmit the highest amount of data on them without taing any user QoS constraints into consideration. This will maximize the sum-capacity of the system [5]. Without considering the QoS constraints, the optimization problem becomes: max K c, n, n n Subject to C : If ' n c B c then c 0 ' The maximum can be easily achieved by setting: * arg max n and then letting * c and c 0 n, n, n ' n. * n This sub-carrier allocation solution clearly does not guarantee the fulfillment of every user s rate constraints in P. Initially, these sub-carriers were assigned to the user that can transmit the highest number of bits on them, namely. In order to meet all the user QoS requirements subcarriers need to be reallocated. This process will inevitably cause a decrease in the overall system throughput. According to [5], in order to achieve an optimum feasible solution in the end, the following conditions must be satisfied during the reallocation process: * n. A sub-carrier n that was originally assigned to user cannot be reallocated to other users if this reallocation will cause a violation of the user s data rate requirement. 2. Each sub-carrier reallocation should cause the least reduction in the overall throughput. 3. The number of reallocation operations should be ept as low as possible. The first condition ensures that the number of satisfied constraints increases monotonically in the sub-carrier reallocation process, so that the number of reallocation operations is finite. Conditions (2 and (3 can be realized by letting *, n, n δ, n n (7 *, n be the cost function of reallocating sub-carrier n from user * n to user. The cost function is proportional to the decrease in the overall throughput, and inversely proportional to the increase of the data rate of user, which affects the number of reallocation operations.

4 89 International Journal of Communication etwors and Information Security (IJCIS Vol. 3, o. 2, August 20 Sub-carrier reallocation is carried out on a user-by-user basis for all users whose rate constraints have not been satisfied in Step. In each stage, the sub-carrier with the lowest cost function denoted by n' is selected. However, if the data-rate constraint of the user to whom the sub-carrier was originally assigned to is violated a new n' is then identified. 4.3 Sub-optimal properties of the algorithm The sub-optimal properties of the heuristic algorithm used to perform resource allocation are demonstrated in Figure 2. The results of the algorithm are compared with the optimal results obtained through a brute-force search. The algorithm efficiency is defined as the ratio of the throughput achieved through the use of the algorithm to the throughput achieved through the brute-force search. The simulations are run 0,000 times. The values of the channel gains used for this simulation are according to the ITU Vehicular A power delay profile. Due to the long computational time, only eight subcarriers and three users are considered. The data-rate constraint is set to 00 bits whilst the noise power density equals 0-0 W/Hz. The power per sub-carrier is varied between 8 and 35 mwatts. Figure 2 shows that the algorithm exhibits excellent sub-optimal properties (within 99.99% of the brute force search method when SCSI is used to perform RRM. environment. The evaluation of LTE techniques demands channel models with increased bandwidth compared to UMTS models, to reflect the fact that the characteristics of the radio channel frequency response are connected to the delay resolution of the receiver [0]. In 3PP, the 20 MHz LTE channel models were based on a synthesis of existing models such as the ITU and 3PP models[0]. 5. Impact of optimal loading In this section, we compare the performance of optimally loading the sub-carriers with the case where carriers are loaded without considering outages. The performance is evaluated in terms of satisfied user probability and goodput. Twenty users each having a QoS constraint equal to 500 bps are considered. The users were uniformly distributed within a cell whose radius varies between 0.5 m and. m so that the value of the average SR of all users could be altered. The transmit power and noise power spectral density equal 46 dbm and -74 dbm/hz respectively. The performance is evaluated in multipath channel environments modeled as a tapped delay line with six taps as specified in the ITU Vehicular A channel model. In Figure.3 the importance of the average user SR on the sum-goodput of the system is presented. These gains are important and increase with the value of the average user SR. Therefore, maximizing over the expectation of the distribution as in [8] will lead to deteriorated performance. In Appendix A it is shown that as the user SR tends towards infinity the ratio of the goodput that can be achieved on a sub-carrier with optimal loading to the goodput that can be achieved on the same sub-carrier without optimal loading cannot exceed the value e. Figure 4 shows that significantly more user QoS requirements can be satisfied when the sub-carriers are optimally loaded. Figure 2. Performance efficiency of sub-optimal algorithm used to perform resource allocation. 5. Simulation Results In order to evaluate the importance of optimally loading sub-carriers with a rate given by Equation (5 we perform simulations for a system with 0 MHz of bandwidth divided into 024 sub-carriers. Results are presented in Section 5.. In Section 5.2 we study the spectral efficiency of the FDMA downlin for different vehicular user densities. Here, results are obtained for a bandwidth equal to 20 MHz..For this simulation, the Extended ITU models defined for the 3PP LTE system are used to model the multipath Figure 3. Impact of optimally loading sub-carriers on sum-goodput of the system

5 90 International Journal of Communication etwors and Information Security (IJCIS Vol. 3, o. 2, August 20 Probability of m eeting Q os constraint Average user SR (db Figure 4. Impact of optimally loading sub-carriers on satisfied user probability 5.2 Impact of different vehicular densities on system sum-goodput In this section we study the efficiency of the FDMA downlin for different vehicular user densities. We assume that the exact proportion of users adhering to each channel model is dependent on the location of the base-station. Furthermore, we consider that users that exhibit higher mobility ( those in vehicles are most liely to be found in a rural area. The exact values used in our simulation are given in Table I. ICSI SCSI Figure 5. oodput vs average user SR for different geographic locations of the transmitter In order to investigate the reasons why the highest overall system throughput can be found in rural areas the spectral response of the two power delay profiles (PDP's across 024 sub-carriers is plotted. Table I: Table showing the percentage of users whose multipath environment can be characterized by EVA and EPA profiles Location EVA(% EPA(% Rural Areas Urban Areas 0 90 Sub Urban Areas As under significant user mobility the CSI cannot be considered as perfect we plot two sets of results for Figure 5. For the first set of results simulations are performed under the realistic assumption that ICSI can only be used to allocate resources to the pedestrian users. For the second set of results we perform simulations under the assumption that ICSI can be used to allocate sub-carriers to both vehicular and pedestrian users. From Figure 5 it can be observed that when ICSI is only used to allocate resources to pedestrian users the highest overall system throughput can be achieved when the transmitter is in an urban area where a large number of pedestrian users can be found. However, if we assume that perfect CSI is available for all users then the highest overall system throughput can be found in rural areas. Figure 6. Spectral response of the ITU Extended Pedestrian and Extended Vehicular power delay profiles We notice from Figure 6 that more multipath is associated with the extended vehicular power delay profile. This is attributed to the much larger delay spread of the channels. Multiuser diversity can thus be better exploited when the user channels are characterized by the EVA PDP. Therefore, when the user CSI is own, adaptive sub-carrier allocation leads to higher gains in the vehicular environment compared to an area with little detected multipath propagation. In order to verify these results we locate all users at an equal distance from the transmitter. Results are shown in Figure 7. Again, we notice that when the ICSI of all users is perfectly own higher system throughputs are realized in rural areas where a large number of vehicular users can be found.

6 9 International Journal of Communication etwors and Information Security (IJCIS Vol. 3, o. 2, August 20 Simple algebraic manipulations and application of Del Hospital s rule to the second and third factor yield: W( ( γ + lim exp[ ]( ( ( log2 (+ W( γ + W( γ exp( ( (2 lim ( lim( log 2 (+ exp( ( (2 exp( ( ( e. Figure 7. oodput vs average user SR when users are located at an equal distance from the transmitter and the ICSI of all users is perfectly own 6. Conclusion In this paper, adaptive resource allocation has been performed for users whose instantaneous channel realizations are unavailable at the transmitter but own by the receiver. Sub-carriers were optimally loaded by transmitting at a rate that is proportional to the average user SR of the Lambert W function. Using the proposed approach, numerical results showed that significantly higher throughput can be obtained and that these throughput gains increase with the average user SR. In our simulation we use this method to optimally load sub-carriers which are allocated to vehicular users. It is shown that in geographical areas with a high proportion of vehicular users a significant throughput loss is observed due to the lac of CSI. However, under the assumption that the CSI of the vehicular users is own, adaptive resource allocation leads to higher throughput gains in areas where a large number of vehicular users can be found. Appendix The ratio of the goodput that can be achieved on a subcarrier through optimal loading to what can be achieved without optimal loading can be written as: W ( ln(2 2 W( lim exp[ ]( ( log (+ γ ln( log ( + exp( ( (2 2 2 Using the Lambert function identity, this can be written as W ( exp W ( (ln( lim exp[ ]( ( ( log 2 (+ γ ln( ln( + exp( ( (2 References [] S. Pietrzy, FDMA for Broadband Wireless Access, Artech House, London, UK, [2] B. Evans and I.B Wong, Resource Allocation in Multiuser Multicarrier Systems, Springer Science and Media, [3] D. Kivanc and. Liu, Computationally efficient bandwidth allocation and power control for FDMA, IEEE. Trans. Wireless Communications., vol.2, no.6, pp 50-58, ovember [4] J. Jang and K.B. Lee, Transmit Power Adaptation for Multiuser FDM Systems, IEEE Journal on Selected Areas in Communications, vol.2, no.0, pp 7-78, February [5] Y. Zhang and K.B. Letaief, Multi-user Adaptive Subcarrier and bit allocation with adaptive cell selection for FDM systems, IEEE. Trans. Wireless Communications, vol. 3, no. 5, September 2004, pp , September [6]I.C. Wong and B. L. Evans, ptimal resource allocation in the FDMA downlin with imperfect channel owledge, IEEE Trans. Commun., vol. 57, pp , Jan [7] D. Hui and V. Lau, Delay-sensitive cross-layer designs for FDMA systems with outdated CSIT, in Proc. IEEE Wireless Commun. and etworing Conf., pp , Mar [8] F. Brah, J. Louveaux, and L. Vandendorpe, CDIT- Based Constrained Resource Allocation for Mobile WiMAX Systems, EURASIP Journal on Wireless Communications and etworing, vol. 2009, [9] M. Rahnema, UMTS etwor Planning, ptimization, and Inter-peration with SM, John Wiley and Sons, [0] S. Sesia, I. Toufi, and M. Baer, LTE: The UMTS Long Term Evolution: From Theory to Practice, John Wiley and Sons, [] D.Tse and P.Viswanath, Fundamentals of Wireless Communications, Cambridge University Press, [2] E.Biglieri, J.Proais, and S.Shamai, Fading Channels Information Theoretic and Communication Aspects, IEEE Transactions on Information Theory, vol. 44, no 6, pp , ctober 998. [3] S. Stefanatos and. Demetriou, Downlin FDMA Resource Allocation under partial Channel State Information, in Proc. IEEE ICC 09, pp. -5, June [4] W. Rhee and J.M. Cioffi, Increase in capacity of multiuser FDM system using dynamic sub-channel allocation, in Proc. IEEE Veh. Technol. Conf., Spring 2000, pp

7 92 International Journal of Communication etwors and Information Security (IJCIS Vol. 3, o. 2, August 20 [5]. Siersma, Linear and Integer Programming, ew Yor: Marcel Deer, 996. [6]. Relaitis, A. Ravindran, and K. M. Ragsdell, Engineering ptimization, Methods, and Applications. ew Yor: Wiley, 983.

Impact of CSI on Radio Resource Management Techniques for the OFDMA Downlink

06 JOURNAL OF COMMUNICATIONS, VOL. 6, NO. 4, JULY 0 Impact of CSI on Radio Resource Management Techniques for the OFDMA Downlink Leonidas Sivridis, Xinheng Wang and Jinho Choi School of Engineering Swansea