The growing demand for wireless multimedia services requires reliable and high data rate data communication over a wireless channel. However, high rate data communications are significantly limited by Intersymbol Interference (ISI) because of the time dispersive nature of the wireless channel. Multicarrier systems have aroused great interest as a potential solution to the problem of transmitting data over wireless channels. An Orthogonal Frequency Division Multiple access (OFDMA) system is one of the widely used multicarrier systems. The principle of the OFDMA system is to split the transmission bandwidth into a number of orthogonal subcarriers. By adding a cyclic prefix to each OFDMA symbol, the Inter symbol Interference (ISI) can be removed.

MU-OFDMA allows a large number of users to share an OFDMA symbol. Two types of resource allocation schemes exist: fixed resource allocation and dynamic resource allocation. Fixed resource allocation schemes such as TDMA, FDMA assign an independent dimension such as time slot, subchannel to each user, but this is not optimal because it is fixed regardless of the current channel condition. On the other hand dynamic resource allocation allocates a dimension adaptively to the users based on the channel gains. Dynamic resource allocation makes full use of the multiuser diversity to achieve higher performance.

This Paper investigates the resource allocation problem in a multiple user OFDMA cellular network, and we focus on the downlink in which the base station is transmitting to mobiles. There are several mobiles in each cell. In the base station, all channel information is sent to the subchannel and power allocation algorithm through the feedback channels from all mobile users. The resource allocation made by the algorithm is forwarded to the OFDMA transmitter. The transmitter then selects different number of bits from different users to form an OFDMA symbol. The resource allocation is updated as fast as the channel information is collected. The resource allocation is to decide the allocation of subcarriers to each user within a cell, and the power allocation across the subcarriers in order to satisfy the data rate constraints of the users.

The problem is that ideally, the subcarriers and power should be allocated jointly to achieve the optimal solution. However, this poses an extremely heavy computational burden at the base station in order to reach the optimal solution. Furthermore, the base station has to rapidly compute the optimal subcarrier and power allocation as the wireless channel changes quickly in time.

The solution for this problem is to separate the subcarrier and power allocation and it also reduces the complexity required to obtain the optimal solution.

Here in this Paper it is assumed that the base station have perfect Channel State Information (CSI) of all the users in the cellular system (i.e., perfect knowledge of the instantaneous channel conditions of all the users in the entire network and the transmit powers of other base stations). This knowledge could be used in solving the resource allocation problem and this leads to a search for suboptimal solutions that are computationally efficient.

Multi user OFDMA adds multiple accesses to OFDMA by allowing a number of users to share an OFDMA symbol. Two classes of resource allocation exist, namely:

- Fixed resource Allocation
- Adaptive resource Allocation -

Fixed resource allocation schemes such as Time Division Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA), assign an independent dimension, eg. time slot or subchannel, to each user. A fixed resource allocation scheme is not optimal, since the scheme is fixed regardless of the current channel condition. On the other hand, dynamic resource allocation allocates a dimension adaptively to the users based on their channel gains. Due to the time-varying nature of the wireless channel, dynamic resource allocation makes full use of multiuser diversity to achieve higher performance.

Two classes of optimization techniques have been proposed in the dynamic multiuser OFDMA system, namely:

- Margin Adaptive (MA)
- Rate Adaptive (RA) ,

Two RA optimization problems have been proposed by researchers. Authors, Jang and Lee proposed the rate maximization problem . In , they proved that the sum capacity is maximized when each subchannel is assigned to the user with the best subchannel gain and power is then distributed by the water-filling algorithm. However, fairness is not considered in . When the path loss differences among users are large, it is possible that the users with higher average channel gains will be allocated most of the resources, i.e., subchannels and power, for a significant portion of time. The users with lower average channel gains may be unable to receive any data, since most of the time the subchannels will be assigned to users with higher channel gains.

In , Rhee and Cioffi studied the max-minproblem, where by maximizing the worst user's capacity, it is assured that all users achieve a similar data rate. Here it is assumed that , the max-minoptimization problem can only provide maximum fairness among the users. In most wireless systems of interest, different users require different data rates, which may be accommodated by allowing users to subscribe to different levels of service.

The problem of rate maximization with fairness was (is) also widely studied in this paper. Rhee and Cioffi considered a rate maximization problem with the objective of maximizing the minimum rate among the users, for a given power budget. By allowing continuous allocation of subcarriers, it was shown that the problem is convex and the optimal assignment can be found using numerical methods. Subcarriers are allocated to users, one at a time, with the worst user (i.e., with the lowest achieved rate) getting the subcarrier with the highest channel to noise ratio.

In order to be able to support the higher data rates demanded by future generation systems, the efficient use of radio resources is paramount.

Two of the most promising candidate technologies that are envisaged for future generation wireless communication systems are Code Division Multiple Access (CDMA) and Orthogonal Frequency Division Multiple access (OFDMA) .In CDMA, all users share the available bandwidth and unique spreading codes are used to differentiate between users. The transmitted information is distributed across the available frequency spectrum by using these codes. Each user can be allocated one or more codes for data transmission. The resources that are allocated in a CDMA system are the spreading codes and transmit powers. Existing systems that use CDMA as the access technology include IS-95, CDMA2000 and UMTS.

OFDMA is a multi-carrier transmission technology in which the available bandwidth is divided into a number of non-interfering (orthogonal) narrow band subcarriers. Each user can be allocated one or more subcarriers for data transmission. The resources allocated in an OFDMA system are the subcarriers and the transmit powers. OFDMA has been widely deployed in commercial systems, including in digital audio/video broadcasting and wireless LANs. It has also been proposed as the access technology for future systems such as WiMAX .

Orthogonal Frequency Division Multiple access(OFDMA) can be thought of as a modulation technique as well as a multiple access scheme. It offers high spectral efficiency and diversity.

The basic idea of OFDMA is to split a high rate data stream into a large number of lower rate data substreams and modulate them onto a number of specially designed carrier frequencies called subcarriers. The data is transmitted simultaneously over these parallel subcarriers.

OFDMA overcomes most of the problems with both FDMA and TDMA. OFDMA splits the available bandwidth into many narrow band channels (typically 100-8000). The carriers for each channel are made orthogonal to one another, allowing them to be spaced very close together, with no overhead as in the FDMA example. Because of this there is no great need for users to be time multiplex as in TDMA, thus there is no over head associated with switching between users. The orthogonality of the carriers means that each carrier has an integer number of cycles over a symbol period. Due to this, the spectrum of each carrier has a null at the centre frequency of each of the other carriers in the system. This results in no interference between the carriers, allowing then to be spaced as close as theoretically possible. This overcomes the problem of overhead carrier spacing required in FDMA.

Each carrier in an OFDMA signal has a very narrow bandwidth (i.e. 1kHz), thus the resulting symbol rate is low. This results in the signal having a high tolerance to multipath delay spread, as the delay spread must be very long to cause significant inter-symbol interference (e.g > 500usec).

Figure 1 shows an example of an OFDMA signal spectra. With perfect synchronization at the receiver, the information on each subcarrier could be decoded successfully without the interference from other subcarriers.

Figure 2 shows the savings of bandwidth with OFDMA compared to a conventional system with the same subcarrier bandwidth. A saving of almost 50% of bandwidth can be achieved with OFDMA due to the overlapping of subcarriers.

Figure 3 shows the block diagram of a multiuser OFDMA system. The channel information from the different users is fed to the subchannel and power allocate on algorithm through feedback channels. After computing the subchannel and power, the resource allocation algorithm is then forwarded to the OFDMA transmitter. The resource allocation algorithm only decides the subchannel that should be allocated to each user and the power for that subchannel. The transmitter takes different bits from different users to form an OFDMA symbol. As the resource allocation algorithm is carried out together, it poses a computational burden at the base station as the wireless channel keeps on changing rapidly with time. This problem was explained in the previous chapter.

In this Paper, we study the resource allocation for an OFDMA cellular system in the presence of multipath fading. High data rate communication over wideband channels are significantly limited by inter-symbol interference (ISI) due to frequency selective or time dispersive nature of the channels. In a multiuser systems such as cellular systems, users experience ISI as a result of multiple copies (multipath) of the transmitted signal created by the objects (such building, cars, etc) around them. To combat ISI, multicarrier modulation techniques, including Orthogonal Frequency Division Multiple access (OFDMA) are among the possible solutions that have been suggested. OFDMA divides a broadband channel into narrow subcarrier (of the same width) such that the channel response on a particular subcarrier seems flat. Adding a guard band or cyclic prefix (CP), whose length equals the dispersion time of the channel, to the transmitted symbols, makes each of the subcarriers parallel independent additive white Gaussian noise channels. This setup allows the received signal to be ISI free.

The allocation of bits for a single user OFDMA system is briefly explained. It is assumed that the channel information for the subcarriers is known. Under the total power constraint a greedy algorithm, also known as the water-filling algorithm is applied to maximize the total bit rate. It could also be run for a fixed data rate constraint while minimizing total power. Effectively, the algorithm assigns bit rates to the subcarriers depending on their channel gain, giving higher bit rates to higher gain channels. A subcarrier may be assigned no bits if it is in deep fade or low gain. Users of multiuser OFDMA systems observe multipath fading but have independent fading parameters due to their different locations. The probability that a subcarrier appearing to be in deep fade for one user may not be in deep fade for other users is quite high. Hence, multiuser system creates channel diversity which increases with the number of users. Therefore, in multiuser OFDMA environment, the system needs to allocate bits as well as subcarriers to the users. There are two approaches to allocate these resources; fixed and adaptive allocation. Fixed allocations use Time Division Multiple Access (TDMA) or Frequency Division Multiple Access (FDMA) as multi-access schemes to allocate each user a predetermined time slot or frequency band for transmission. While applying fixed allocation the system neglects the channel diversity and does not use the deep faded subcarriers for other users which do not seem as deep faded to them. Discusses and compares these two fixed allocation schemes in much detail. To exploit the channel diversity and achieve higher bit rates authors of [5, 6, 7, 8, ] have suggest adaptive allocation of resources. They use the instantaneous knowledge of the channel for each user to allocate the subcarriers accordingly and then subsequently allocate the bits and transmit power for each subcarrier.

Resource allocation schemes for multiuser OFDMA systems can benefit by taking account of various forms of diversity such as frequency diversity and multiuser diversity. Frequency diversity refers to different subcarriers within a wireless link having different channel gains due to the frequency selective nature of the channel, while multiuser diversity refers to different users experiencing different channel conditions due to their different locations in the network. These diversities imply that a subcarrier that is in a deep fade for one user may not be in deep fade for the other users. By allocating the subcarriers to users based on the channel conditions the users see on the subcarriers, these diversities can be exploited.

Adaptive resource allocation strategies allow available resources to be used efficiently, by taking account of the channel conditions, and allocate, to each user, a subset of subcarriers which experience good channel conditions for that user. The users can transmit simultaneously, in parallel. In this context, Orthogonal Frequency Division Multiple Access (OFDMA) simplifies the location problem. OFDMA is defined as one in which users are assigned different subsets of the subcarriers so that the users are mutually orthogonal.

In a single user OFDMA system, the user has full access to all subcarriers. In this context, the resource allocation problem is to determine an appropriate transmit power allocation across the subcarriers. When the perfect channel state information (CSI) is available at the transmitter, the power allocation for the user across orthogonal subcarriers with additive white Gaussian noise can be obtained with the water filling method. Water filling finds the optimal power allocation across the subcarriers that maximizes the capacity for a given total power constraint.

When the power allocation is determined by the water pouring technique, power Pi allocated to subcarrier i satisfies Pi + σi2 = B where σi2 is the “effective” noise spectral density on subcarrier i (i.e., noise spectral density divided by the fading coefficient of subcarrier i) and the “water level” B is a constant that is the same for all subcarriers. The more the effective noise spectral density on a subcarrier is, the less the power allocated to that subcarrier will be. Since Pi is a non-negative quantity, if σi2 ≥ B, then Pi = 0, i.e., subcarrier i will not be used for transmission at all.

In the context of multiple user OFDMA networks, the resource allocation involves assignment of subcarriers to users and selecting the transmit powers to be used on the allocated subcarriers. It is possible to perform the multiuser resource allocation by using water pouring based techniques. Jang and Lee solved a data rate maximization problem for a multiuser OFDMA network, by assigning each subcarrier to its best user (i.e., the user with the highest channel gain), and then running water filling among the subcarriers assigned to each user individually.

However, these water filling based approaches do not, in general, guarantee fairness among users. The users that are further away from the base station or with a bad channel quality will be disadvantaged.

In order to support the individual rate or quality of service (QoS) requirements, these requirements need to be included into the resource allocation optimization problem. Such resource allocation problems in the literature can be broadly classified into two categories, based on the optimization objectives. The objective in the first category of work is to minimize overall transmit power given individual user quality of service (QoS) requirements (e.g., data rate requirements).The body of work in the second category aims to maximize the throughput under a power constraint with some fairness criteria (e.g., proportional fairness among the users). Both categories of problems are combinatorial in nature due to the discrete nature of the subcarrier allocation.

Consider an OFDMA system with M users and Nc subcarriers. User m has a data rate requirement of R m . Let Gm (i) be the channel gain, pm (i) be the transmission power, σ2m (i) be noise spectral density for user m on subcarrier i. Then, the signal to-noise ratio (SNR) on subcarrier i at receiver m is gm(i) = Gm (i)pm (i) / σ2m(i). The transmission rate rm (i) of subcarrier i for user m is a function of the SNR, that is rm (i) = fm (gm (i)). Function fm (i) is monotonically increasing and fm (0) = 0.Note that if subcarrier i is not allocated to user m then pm (i) = 0 and rm (i) = 0. The power minimization problem is to determine a subcarrier allocation to users and a power allocation for the subcarriers that minimize the total transmit power while satisfying the user rate requirements:

Where N is the total number of subchannels, K is the total number of users, B is the total bandwidth, Pk,n is the power allocated to user k's subchannel n, αk,n is the channel gain in user k's subchannel n, Sk is the set of subchannels that are assigned to user k, N0 is the power spectrum density of additive white Gaussian Noise, Pmax is the total power constraint. Notice that Sk are mutually exclusive since we do not allow a subchannel to be shared by different users.

The rate optimization shown above is a non-convex problem and combinatorial in nature, making it computationally intractable. Hence, various suboptimal approaches have been proposed to solve it in the literature. Wong *et al. * applied a Lagrangian Relaxation (LR) to this problem. They relax the problem to allow time sharing of subcarriers between users. With this relaxation, the problem can be turned into a convex problem. This relaxed problem is solved with an iterative search algorithm based on Lagrangian techniques.With the relaxation that sharing a subchannel is allowed, the solvers in the optimization tool need to perform matrix decomposition and inversion to find the optimal solution efficiently. Once the solution to the relaxed problem is found, discrete subcarrier allocation is obtained by assigning each subcarrier to the user who has the largest time share on that subcarrier. Then, using the assigned subcarriers, single user bit loading (power allocation) is applied to each user. Firstly, the iterative search algorithm takes a large number of iterations to converge, and the accuracy and the rate of convergence are highly dependent on the choice of the step size. Secondly, some users may be disadvantaged with the quantization method used. These operations are not practically in real-time implementation of dynamic resource allocation algorithms. Thus suboptimal algorithms that balance the computation requirement and performance are always of interest. In this Paper, the optimization problem is solved by allocating subchannel allocation and power allocation sequentially.

The first step of the algorithm is the bandwidth allocation, which determines the number of subchannels to be allocated to each user based on the average SNR of the users. The second step then allocates the required number of subcarriers (determined by the first step) to users, by applying a greedy approach considering the channel quality of the individual subcarriers. In this step, the algorithm examines the subcarriers, assigning one subcarrier at a time to the user who has the highest SNR on it and has not yet received the required number of subcarriers. The subcarrier allocation produced by this algorithm is not unique, and depends on the order in which the subcarriers are considered. Once the subcarrier allocation is determined, the bit loading on the subcarriers is done using a greedy water-filling algorithm.

The two main steps of the resource allocation algorithm are described in detail below:

A suboptimal sub channel allocation algorithm is first carried out based on the max-min method assuming equal power equal distribution across all subchannels. The channel to noise ratio for user k in subchannel n is defined as Hk,n=(h2k,n/N0(B/N)) where B is the total bandwidth available at the base station and N is the total number of users There is a set of subchannels assigned to each user . The suboptimal resource allocation algorithm can be described as follows:

- First all the capacities of all users are initialized to zero
- Next for each user, the subchannel with maximum gain is found out and based on this maximum value, capacity of that particular user is found out. Thus after this step we get the capacity of each user.
- The third step is to find out the minimum user based on the capacity.
- For the found minimum user, the subchannel has to be found out with the maximum gain.
- Lastly for the found minimum user and subchannel , the capacity of the minimum user has to be found out

The principle of the suboptimal subchannel algorithm is for each user to use the subchannels with high channel to noise ratio as much as possible. At each iteration the user with the lowest proportional capacity has the option to pick up which subchannel to use. The subchannel allocation algorithm is suboptimal because equal power distribution is assumed for all users. After this subchannel allocation, only coarse proportional fairness is achieved. The goal of maximizing the sum capacity while maintaining proportional fairness is achieved by the power allocation method.

After the sub channel allocation the optimal power distribution is carried out. A two step procedure has to be taken to get the optimal power distribution. First a set of nonlinear equations has to be solved in order to get the power distribution among users. Then to a particular user, the greedy water-filling algorithm is adopted to maximize the capacity.

Suppose N subchannels are assigned to a user. The power allocation scheme is equivalent to finding the maximum of the cost function.

Where pi, αi are respectively the power and the channel gain for the ith subchannel. Ptot is the total power allocated to the user. We also assume that αi's are in the descendingorder: αM ≥ αM-1 ≥ . . . ≥α1

Given the total power constraint, this optimization problem is solved by obtaining the Lagrangian optimization problem.

The above equation shows how to calculate the optimal power for the first subchannel. The power of the other subchannel can be calculated by equation (4). There is one condition that needs some discussion: if the summation in the right side of equation (5) is larger than Ptot, p1 will be negative value, which is not possible since all the power value should be non-negative. The negative value for p1 indicates that the gain in the 1st sub channel is so poor that it should not be used. With the total power for single user and the total power constraint, the capacity ratio constraints are expressed as nonlinear equations

The proposed resource allocation algorithm to be designed and implemented has two main steps: first is the subchannel allocation and the second step is the power allocation.

In this chapter, we will study how the proposed algorithm is implemented.

- The number of subchannels is initialized as N=64
- The bandwidth B is initialized as 1 MHz
- The total power available at the base station is taken as 1 W
- The number of users is taken as 8 and 16. Simulations are carried out for both the number of users.
- The number of channels is initialized as 5
- The sample number is taken as 1
- The parameters for finding the subchannel and power allocation for TDMA are also initialized.

- First arandom signal is generated with the user number, sample number and Doppler frequency as inputs.
- Next the gain of the signal which is generated is found out.
- The function for the subchannel allocation is called and the required parameters are given. This function calculates the maximum capacity and assigns that to the minimum user. It returns the capacity and the subchannel allocation for all users
- Next the function for the power allocation is called. This computes the power distribution among users using a set of non-linear equations.
- The condition that satisfies the water filling algorithm is checked for each user. If the condition fails, there would be no water-filling taking place in that subchannel.
- The power distribution for a single user is found out by the water filling algorithm. As per the water filling algorithm, more power is put into the subchannel with higher channel gains.
- After the subchannel and power allocation, the capacity of each user is found out
- With the help of the same water-filing algorithm, the capacity of each user according to the sum-capacity maximization method is found out.
- The capacity of the non-adaptive methods such as TDMA is calculated using specific functions.
- The capacity of the largest user and smallest user is also found out for comparison with other methods.
- Comparisons are done between the capacity achieved by the proposed resource allocation algorithm and capacity achieved by the sum-capacity maximization method. Capacity achieved by TDMA method is also compared.
- Graphs are plotted for showing the variations of the capacity with respect to the rate constraints.
- he max-min method is also implemented in a similar way. The subchannel allocation method is same as given above , the only difference is that in this method equal power distribution is considered.
- omparisons are done with the proposed method to the max-min method. The capacities of both these adaptive methods are compared with the non adaptive TDMA method.

In this section, simulations have been done to compare with the performance of the proposed algorithm with other methods such as the sum capacity maximization method and the max-min method . The proposed algorithm is shown to perform close to the optimal solution but with reduced complexity. With this algorithm the rate constraints can be configured at the base station i.e rate allocation among users is flexible. The proposed algorithm is also compared with the static TDMA method. Simulations are carried out in MATLAB 7.

Results shows that the capacity does not vary with the rate constraints for the static TDMA method but with the proposed resource allocation algorithm, the capacity is distributed more fairly among users than the sum capacity maximization method. Also the proposed algorithm with optimal power allocation achieves more capacity than the method with equal power distribution

The proposed resource allocation algorithm is compared with the sum capacity maximization method . In these simulations for 8 users, it is assumed that the user 1 has average channel power 10 db higher than the rest of the seven users. For 16 users, it is assumed that the average channel power for the first four users is 10 db higher than the rest of the twelve users.

Figure 4 shows the capacity distribution versus gamma set index for 8 users. From the figure it can be seen that the capacity achieved by the proposed algorithm varies as the rate constraint changes. Also we can see that the capacity distribution using the sum capacity maximization method and static TDMA cannot be changed by varying gamma set values, because there is no fairness control mechanism in these systems.

Figure 5 shows the sum capacity distribution among 8 users. With the proposed subchannel and power allocation algorithm, it can be seen that the capacity is distributed very well among users according to the rate constraints. The proposed method achieves performance close to the optimal solution. However for the sum capacity maximization method, since user 1 has more channel gains, this particular user achieves a significant part of the sum capacity. But for the rest of the other users with lower channel gains may be unable to receive any data, since most of the time the subchannels will be assigned to the users with higher gains. Static TDMA allocates a fixed capacity for each user, since all users get equal opportunity to transmit.

Figure 6 shows the capacity distribution versus gamma set index for 16 users. The simulation parameters are same as 8 user system, the only difference being that the first four users have channel power 10 db higher than the rest of the users. It should be noticed that higher sum capacity is achieved by the sum capacity maximization method in this 16 user system, since more users with higher channel power are in this system.

Figure 7 shows the capacity distribution among the 16 users. From this figure, it can be seen that higher capacity is achieved by the first 4 users by the method in because of their higher channel gains. The users 5-16 get very small portions of the sum capacity, since the subchannels and power are allocated to the users with higher channel gains.

Figure 8 shows the capacity versus number of users for the two adaptive and static TDMA schemes. From the above figure, it can be seen that the adaptive resource allocation algorithm achieves significant gain over the non-adaptive TDMA. In addition, it is also seen that the proposed method with optimal power allocation achieves higher capacity than the scheme with equal power distribution. This increase in the capacity of the proposed method when compared with the max-min method in is only due to the optimal power allocation because both these methods adopt the same subchannel allocation

OFDMA represents a successful approach to mitigate ISI from wireless communication. Multiuser systems create channel diversity which increase with the number of users in the system. Exploiting the channel diversity in a multiuser OFDMA system increases the performance of the system. Due to the varying conditions of the channel between the transmitter and receiver, it is essential to adaptively allocate the subcarrier, bit and power levels based on instantaneous channel knowledge. This work presents the various adaptive allocation algorithms with different constraints and their simulation results. In the end a qualitative analysis of the various methods including fixed and adaptive schemes is presented.

The proposed method is compared with the other methods such as sum capacity maximization method and the max-min method . Results show that the capacity is well distributed among users with respect to the rate constraints than the sum capacity maximization method. It is also shown to achieve more capacity than the adaptive method with equal power distribution.

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