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| Year : 2008 | Volume
: 25
| Issue : 4 | Page : 175-185 |
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Optimized Multi-User Resource Allocation Scheme for OFDM - MIMO System Using GA & OGA
P Malathi, PT Vanathi
Department of ECE, PSG College of Technology, Peelamedu, Coimbatore 641 004, Tamil Nadu, India
Correspondence Address:
P Malathi
Department of ECE, PSG College of Technology, Peelamedu, Coimbatore 641 004, Tamil Nadu
India
 DOI: 10.4103/0256-4602.42809
 Abstract | | |
The objective of the paper is to implement an OFDM - MIMO system and analyze its performance, and implement an optimized dynamic resource allocation scheme for maximizing the minimum user's capacity. Performance of the system can be vastly improved by properly allocating resources among the different users. The bits, sub-carriers, the power among the users, and power among the channels are dynamically allocated depending on the channel conditions in such a way that the error-free capacity of the minimum user is maximized. Keywords: OFDM, MIMO, Resource Allocation, Channel Capacity and Optimization Problem.
How to cite this article:
Malathi P, Vanathi P T. Optimized Multi-User Resource Allocation Scheme for OFDM - MIMO System Using GA & OGA. IETE Tech Rev 2008;25:175-85 |
| 1. Introduction | |  |
One of the most challenging issues for future wireless communications is to support a large number of users and ensure the fulfillment of Quality of Service requirements, given the limited availability of frequency spectrum. To solve this issue, intelligent resource management algorithms in both the physical layer and the medium access control layer are essential. Orthogonal Frequency Division Multiplexing (OFDM) is a very promising solution to provide a high-performance physical layer, thanks to its ability to combat inter-symbol interference (ISI). Recently, adaptive resource management for multi-user OFDM systems has attracted enormous research interest. Adaptive Resource allocation has been identified as one of the key technologies for providing efficient utilization of the limited total transmit power and maximize the total data rate in future wireless systems.
| 2. OFDM System | | |
This part of the paper gives an overview of the Orthogonal Frequency Division Multiplexing (OFD14) System. Section 2.1 introduces the history of OFDM system. Sections 2.2 and 2.3 outline the benefits of the OFDM system and its applications. In the next section, the transmitter model is presented and the functionalities of the various blocks of the system are briefed. In section 2.5, the receiver model is presented.
2.1 OFDM System History
The idea of combining parallel data transfer and FDM for high-speed communications was proposed in the 1960s. In 1970, Weinstein and Ebert introduced FFT-based OFDM. In 1989, OFDM was selected for high-speed modem and high-density recording. In the same year, Hirosaki introduced an equalization algorithm to suppress both ISI and ICI.
OFDM, now, is of great interest by researchers and research laboratories all over the world. Orthogonal frequency division multiplexing (OFDM) is a promising technique for the next generation of wireless communication systems [1] [2]. It has already been accepted for the new wireless local area network standards IEEE 802.11a, High Performance LAN type 2 (HIPERLAN/2), and Mobile Multimedia Access Communication (MMAC) Systems. Also, it is expected to be used for wireless broadband multimedia communications. The new standard specifies bit rates of up to 54 Mbps. Such high rate imposes large bandwidth, thus pushing carriers for values higher than UHF band. For instance, IEEE 802. I la has frequencies allocated in the 5- and 17- GHz bands.
2.2 OFDM Concept
OFDM can be seen as either a modulation technique or a multiplexing technique. One of the main reasons to use OFDM is to increase the robustness against frequency selective fading or narrowband interference. In a single carrier system, a single fade or interferes can cause the entire link to fail, but in a multi-carrier system, only a small percentage of the sub-carriers will be affected. Error correction coding can then be used to correct for the few erroneous sub-carriers. A classical parallel data system, the total signal frequency band is divided into N non-overlapping frequency sub-channels. Each sub-channel is modulated with a separate symbol and then the N sub-channels are frequency-multiplexed. It seems good to avoid spectral overlap of channels to eliminate inter-channel interference. However, this leads to inefficient use of the available spectrum. To cope with the inefficiency, the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping sub-channels, in which each carrying a signaling rate `b' is spaced apart in frequency to avoid the use of high-speed equalization and to combat impulsive noise and multi-path distortion, as well as to fully use the available bandwidth.
2.2.1 Conventional FDM Technique
[Figure 1] illustrates the difference between the conventional non-overlapping multi-carrier technique and the overlapping multi-carrier modulation technique. To realize the overlapping multi-carrier technique, however, we need to reduce cross-talk between sub-carriers, which means that we want orthogonality between the different modulated carriers.
2.3 Advantages and Applications of Ofdm0 System
2.3.1 Advantages of OFDM System
- Immune to Frequency Selective Fading:
Each sub-channel is almost flat fading. To overcome multi-path fading, it uses a multi-carrier transmission scheme.
- Immunity to Delay Spread:
The tolerance is due to the cyclic extension. In practical system, the length of the guard period can be chosen depending on the multi-path delay spread immunity.
- High Spectral Efficiency:
The orthogonality of the sub-channels ensures that the available spectrum is utilized in a more efficient manner; more data that can be transmitted over a smaller bandwidth.
- High-speed Communication:
An OFDM system is an attractive technique for high-speed communication; it supports data rates up to 54Mbps.
- Is less sensitive to sample timing offsets than single-carrier systems are. It also provides good protection against co-channel interference and is impulsive.
- Easy Implementation:
It is simple to implement an OFDM System. Also, the equalization is very simple as compared to single-carrier systems.
2.3.2 Applications of OFDM
Digital audio broadcasting (DAB)
DAB is a successor of current analog audio broadcasting based on AM and FM. DAB offers improved sound quality comparable to that of a compact disc, new data services, and higher spectrum efficiency. DAB has four transmission modes using different sets of OFDM parameters; one important reason v 1 to use of for DAB is the possibility to use a single frequency network, which greatly enhances the spectral efficiency. In a single-frequency network, a user receives the same signal from several transmitters simultaneously. Because of propagation differences among transmitters, there is some delay between the arrivals of the signals. As long as the propagation differences between the two signals are smaller than the guard time of the OFDM signal, no ISI or ICI will occur. The DAB transmitted data consists of a number of audio signals, sampled at 48 KHz with an input resolution of up to 22 bits. The total data rate is approximately 2.2 mbps.
Terrestrial digital video broadcasting (DVB)
Terrestrial DVB uses OFDM with two possible modes, using 1705 and 6817 sub-carriers, respectively. These modes are referred to as 2 K and 8 K modes, respectively. They are the size of the FFT or IFFT needed to generate and demodulate all sub-carriers. The 2 K system is a simplified version which requires an FFT/IFFT that is only a quarter of the size needed for the 8 K system. Because the guard time is also four times smaller, the 2 K system can handle less delay spread and less propagation delay differences among transmitters within a single-frequency network. The FFT interval duration for the 8 K system is 896 ms, while the guard time can have four different values from 28 to 24 ms.
Magic WAND
The magic wand (wireless ATM network demonstrator) implemented a prototype, wireless ATM network based on OFDM modulation. This prototype has a large impact on standardization activities in the 5 GHz band. By employing OFDM-based modems, magic wand helps to gain acceptance for OFDM as a variable modulation type for high-rate wireless communication.
Some examples of current application using OFDM include GSTN (General Switched Telephone Network), cellular radio, DSL and ADSL modems, HDTV broadcasting, HYPERLAN (high performance local area network standard), and the wireless networking standard IEEE 802.11, WiLAN. Few members of OFDM forums are NOKIA, SAMSUNG, SIEIVIENS, MOTOROLA, SASKEN, PHILIPS, SOLECTEK, WIAN, and TCFI.
2.4 Importance of Orthogonality in OFDM
The orthogonal part of the OFDM name indicates that there is a precise relationship between the frequencies of the carriers in the system. In a normal FDM system, many carriers are spaced apart in such a way that the signals can be received using conventional filters and demodulators. In such receivers, guard bands have to be introduced between the different carriers, and the introduction of these guard bands in the frequency domain results in a lowering of the spectrum efficiency.
It is possible, however, to arrange the carriers in an OFDM signal so that the side bands of the individual carriers overlap and the signals can still be received without adjacent carrier interference. In order to do this, the carriers must be mathematically orthogonal. Two conditions must be considered for the orthogonality between the sub-carriers.
- Each sub-carrier has exactly an integer number of cycles in the FFT interval.
- The number of cycles between adjacent sub-carriers differs exactly by one.
2.5 Transmitter Model
The transmitter for OFDM is designed in such a way that it must be able to combat the problems of strong signal variations and ISI caused by multi-path propagation. The input serial data stream is formatted into the word size required for transmission. An inverse Fourier transform is used to find the corresponding time waveform. Due to filter complexity and the need to control group delay distortion, 128-point IFFT is used.
2.5.1 Transmitter Structure
In the transmitter, the high-speed serial data to be transmitted is converted into parallel data. Then the transmitted data of each parallel sub-channel is modulated. The modulator used is one of the schemes suggested in the IEEE 802.1la standard. This modulated data are fed into an IFFT circuit and an OFDM signal is generated. The ISI is eliminated by a cyclically extended guard interval. The guard interval used is one-fourth of the actual signal. The signal before transmission is passed through a wave shaper. The wave shaper used here is to smoothen the signal. The block diagram of the transmitter and receiver sections are shown in [Figure 2] and [Figure 3] and its functions are explained in the following paragraphs.
2.5.2 Serial-to-Parallel Conversion
The transmitter first converts the input data from a serial stream to parallel sets. The data is then transmitted in parallel by assigning each data word to each sub-carrier in the transmission. Depending on the modulation scheme used, the input serial data stream is formatted upto the word size required for transmission.
2.5.3 Modulation
The data is modulated using one of the schemes recommended for OFDM system. Here, we have used Quadrature Phase Shin Keying (QPSK), 4 Quadrature Amplitude Modulation, 1G Quadrature Amplitude Modulation, and G4 Quadrature Amplitude Modulation.
2.5.4 Inverse Fast Fourier Transform (IFFT)
An inverse Fourier transform converts the frequency domain data set into sample of corresponding time domain representation of this data. Specifically, the IFFT is useful for OFDM because it generates samples of a waveform with orthogonal frequency components. Before performing the inverse fast Fourier Transform, the data set is arranged on the horizontal axis in the frequency domain. This symmetrical arrangement about the vertical axis is necessary for using the IFFT to manipulate the data. The N complex valued symbols x (n)., O ~ n ~ N-1 modulate N orthogonal carriers using the IDFT.
The real and imaginary parts correspond to the in-phase and quadrature parts of the OFDM signal. The OFDM signal is in fact the Inverse Fourier Transform of input symbols. The time discrete equivalent is the IDFT and this transform can be implemented efficiently by the IFFT.
By using an IFFT process, the spacing of the sub-carriers is chosen in such a way that at the frequency where the received signal is evaluated, all other signals are zero. Each sub-carrier has exactly an integer number of cycles in the interval T and the number of cycles between the adjacent sub-carrier differs by exactly one. This property accounts for the orthogonality between the sub-carriers. IIFT is the heart of the OFDM modulation technique.
2.5.5 Guard Interval Insertion (Cyclic Prefix)
One of the most important reasons to do OFDM is the efficient way in which it deals with the multi-path delay spread. By dividing the input data stream in Ns sub-carriers, the symbol duration is made Ns-time larger, which also reduces the relative multi-path delay spread, relative to the symbol time, by the same factor. To eliminate ISI almost completely, a guard time is introduced for each OFDM symbol such that the multi-path components from one symbol cannot interfere with the next symbol.
The guard period allows time for multi-path signals from the previous symbol to die away before the information from the Current symbol is gathered. The most affective guard period to use is the cyclic extension of the symbol. If a mirror in time of the end of time symbol waveform is put at the start of the symbol as the guard period, this effectively extends the length of the symbol, while maintaining the orthogonality of the waveform. This ensures that delayed replicas of the OFDM symbol always have an integer number of cycles within the FFT interval. The transmitter first converts the input data from a serial stream to parallel sets. The data is then transmitted in parallel by assigning each data word to each sub-carrier in the transmission. Depending on the modulation scheme used, the input serial data stream is formatted into the word size required for transmission. Due to the cyclic prefix, the transmitted signal becomes periodic. Usually, the Guard Interval is selected to have a length of one-tenth to a quarter of the symbol period leading to an SNR loss of around 1 dB. The total symbol duration is
T total = T g + T s
where T g - Guard Interval.
T s - Actual symbol.
Each symbol is made of two parts that consist of active symbol and guard interval. The whole signal is contained in the active symbol, the last part of which is also repeated at the start of the symbol. When the guard interval is longer than the channel impulse response or the multi-path delay, the effect of 1ST can be eliminated. The ratio of the guard interval to the useful symbol duration is application-dependent. T g is usually smaller than T S /4.
2.5.6 Additive White Gaussian Noise
AWGN channel is assumed to corrupt the signal by the addition of White Gaussian Noise. When the transmitted signal, white Gaussian noise, and received signal are defined as s ( t ), n ( t ), and r ( t ), respectively, the received signal is given by
r(t) = s(t) + n(t)
where n ( t ) is a sample function of the AWGN process.
The white Gaussian noise represents the ultimate `randomness'. White noise has infinite average power and as such it is not physically realizable. The utility of a white noise process is parallel to that of an impulse function or delta function in the analysis of linear systems. We may observe the effect of white noise only after it has been passed through a system with a finite bandwidth. As long as the bandwidth of a noise process at the input of a system is appreciably larger than that of the system itself, then we may model the noise process as white noise.
2.6 Receiver Model
The mobile communication is affected by the multi-path propagation and fading. The transmitted signal travels in several paths to the receiver. As the propagation time over the multiple paths is different, the signal at the receiving antenna consists of several multi-path components spreading out in time over an interval of several milli-seconds. The ionosphere is a turbulent medium so that an individual propagating mode suffers modulation in magnitude and phase in a random manner. This gives rise to a spreading of signal in frequency. The total received signal is thus a composite of a number of components, each with different time delays and independent fading patterns.
2.6.1 Receiver Structure
The received signal is filtered by a pulse-shaping filter, which is assumed to sufficiently smoothen the signal. The cyclically extended guard time is removed, which reduces the complexity of FFT. An FFT circuit is applied to the signal to obtain the Fourier coefficients of the signal. The BER depends on the level of the receiver's noise. In OFDM transmission, the orthogonality is preserved and the BER performance depends upon the modulation scheme on each sub-channel. Therefore, if QPSK is used, the BER under AWGN channel is given as 1/2 erfc (Eb/No).
The OFDM receiver mirrors the operation of the OFDM transmitter. Time domains and frequency domain signals are treated as complex. The adjacent channel interference is prevented and the receiver time samples are converted to the frequency domain by a forward FFT. The relatively long period of the OFDM waveform makes the system resistant to delay spread.
In the receiver, the reverse process of what was done in the transmitter is clone. The guard interval block is removed, the data is converted into parallel data, and Fast Fourier Transform is applied. On the transformed data, demodulation is done and then converted into serial data.
| 3. MIMO Transmission | | |
Multiple antennas can be used at the transmitter and receiver, an arrangement called a Multi input Multi output (MIMO) system. A MIMO system takes advantage of spatial diversity that is obtained by spatially separated antennas in a dense multi-path scattering environment. Advantages of MIMO systems are:
- Achieve higher data rates through very high spectral efficiency the wireless communication channel
- Exploits multi-path propagation
- Longer range through spatial diversity
- Increased reliability
- Compatible with legacy waveforms and standards
- Spectrally benign
- Spatially benign
- No specialized antennas are required
- Mitigates effects of interference; the combination of OFDM with MIMO is regarded as a promising solution for enhancing the specification of Fourth generation wireless communication system.
| 4. Orthogonal Genetic Algorithm (OGA) | | |
4.1 GA Performance
Genetic Algorithm is commonly used for optimization problem. To find an optimal point, we start with some randomly selected points in the solution space (population of solutions), evaluate the fitness of each point, perform some genetic operations (crossover, mutation) on the population, form a new population based on the fitness values of the individuals (reproduction), and proceed as such until the best solution (specified condition) is reached.
4.1.1 Initialization of Population
GAs start with a random population of individuals. To start with, the solution has to be coded into a fixed-length binary string. There are a number of ways to implement the coding of solutions. Bit string encoding is the most classical approach used because of its simplicity and trace-ability.
4.1.2 Genetic Operators
Crossover and mutation functions are the basic genetic operators.
Crossover
Crossover is the randomized exchange of genetic material between strings with the possibility that good strings can produce better ones. This produces two new individuals. There are various crossover processes, the simplest being the single-point crossover. The portions of the string beyond the crossover point are exchanged to form two new strings. The other types of crossover techniques are multi-point crossover, uniform partial mapping etc.
Mutation
Mutation is the random alteration of a gene in the chromosomal string. In binary coding, this simply means changing a 1 to 0 and vice versa.
By itself, mutation may introduce unnecessary alterations in the search space, thus randomizing the search totally. But when used sparingly with selection and crossover operators, it is an insurance policy against premature loss of important solutions. Thus, mutation is needed because even though reproduction and crossover effectively search and recombine existing solutions, occasionally they may become overzealous and lose some potentially useful genetic material (ones and zeros at particular locations). Mutation is used to maintain the diversity in the population. The probability of mutation is generally set to be very low when compared to the probability of crossover.
Significance of P c and P m
The crossover and mutation operators are the sources of the explorations. In order to explore, they must disturb some of the chromosome on which they operate. The higher the value of the P c , the quicker are the new solutions introduced into the population. However, as P c increases, the solutions can be disrupted faster. Typical values of P c range from 0.5 to 1. Similarly, P m also affects the quality of the population. Large values of P m transform the GA into a purely random search algorithm, while some mutation is required to prevent the premature convergence of the GA to sub-optimal solutions.
Consider randomly generated two initial population parent strings. Apply Simple GA steps to generate first iteration new population string. Parent strings
are
t1 = 0011001011
t2 = 1011101001
Resultant first generation new population strings are
O1 = 1011100011
O2 = 1001010111
It is the same number as the number of parent string. Similarly, the same procedure can be repeated four times, if g max = 4. At the end, Simple GA generates eight new population strings.
4.2 OGA Performance
There are more number of possibilities to sample the parent strings for crossover. Orthogonal GA produces an orthogonal array to perform a rational and representative sampling. Let L m ( p q ) denote an orthogonal array, where ` L ' denotes Latin square. Orthogonal array crossover operation can be defined as L m ( p q ), where p parents are divided into q factors, and the resulting m is the number of combination of levels to be tested; and then select ` j ' of them to be offspring strings. The details can be given as
Inputs: p parents strings
Outputs: m new generation strings
Selected Outputs: j offspring strings
(Satisfy the constraints of the problem)
Orthogonal design is incorporated into the crossover operation and has a statistically sound method to sample the genes from multi-parents for crossover. The resulting operation is called orthogonal crossover. For example, the orthogonal array L 4 (2 2 ) that samples the genes from two parents for crossover has two factors, i.e., we divide each parent into parts and it generates four combinations of output. Then choose GA operators; P c is maximum in the range of 0.5 to 1 and has a very low value of P m for mutation for the resulting strings.
By increasing the value of ` p ' - parent and ` q ' - crossover point, the numbers of resultant combination strings are also increased.
OGA STEPS:
Step 1: Randomly and independently generate n parent strings.
Step 2: Sample orthogonal array L ( p ) generated from p parent strings using orthogonal array crossover.
Step 3: Perform mutation with small probability in produced m binary output strings and execute the check-and-repair operation.
Step 4: Evaluate the fitness for every string and sort. Remove the duplicate strings, and then select j of them to be offspring strings.
Consider the orthogonal array L 9 (3 2 ). (three parent strings are divided into two parts, resulting in nine output strings). Let the parent strings be
t1 = (00001 11101)
t2 = (10100 10110)
t3 = (1011110010)
Using p-to-m orthogonal array crossover operation, produce nine strings based on orthogonal array L 9 (3 2 )
O1 = (0100111101)
O 2 = (1000110111)
O 3 = (0000110011)
O 4 = (1010011111)
O 5 = (1010010111)
O 6 = (1010110011)
O 7 = (1011111101)
O 8 = (1011110110)
O 9 = (1011110011)
Execute mutation, check and repair operation, and evaluate the fitness function of the string and then remove the duplicate strings. The resulting strings are considered as best output offspring. This technique is used to solve the optimized allocation explained in the next resource section.
| 5. Resource Allocation | | |
Performance of the system can be vastly improved by properly allocating among the different users. In this chapter, a resource allocation scheme algorithm for maximizing the minimum capacity is discussed. In section 5.2, the optimization problem is stated. In the next two sections, the complexity issue is analyzed and the suboptimal scheme for achieving the maximum capacity is discussed.
5.1 Introduction
The block diagram of Multi-user OFDM resource allocation is shown in [Figure 4]. Two classes of r allocation schemes exist: fixed resource allocation [6] and dynamic resource allocation [7],[8]. Fixed resource allocation schemes, such as time division multiple c (TDMA) and frequency division multiple access (FDMA), sign an independent dimension, e.g., time slot o sub-channel, to each u. A fixed resource allocation scheme i is not optimal since the scheme i is fixed regardless of the current channel edition. On the other hand, dynamic re-allocation allocates a dimension adaptively to the users based on their channel gains. Due to the time-varying nature of the wireless channel, dynamic allocation makes full use of multi-user resource diversity to achieve higher performance.
Two classes of optimization techniques have been proposed in the dynamic multi-user OFDM literature: margin adaptive (MA) [7] and rte adaptive CRAB [8], [9] The margin adaptive objective to achieve the overall transmit power given the constraints on the data rate r bit error rate (BER). The rate adaptive objective is to maximize each user's error- free capacities with a total transmit power restraint. These optimization problems are nonlinear and hence computationally intensive to solve. In [8], the nonlinear optimization problems were transformed into linear optimization problem with integer variables. The optimal solution can be achieved by integer programming.
Two rate adaptive optimization problems have been proposed by researchers. Recently, Jang and Lee proposed the rate maximization problem [6]. In [6], they proved that the sum capacity maximized when each sub-channel is assigned to the user with the best sub-channel gain and the power is then distributed by the water-filling algorithm. However, fairness i is not considered in [6]. When the path loss differences among e is large, it is possible that the users with higher average channel gains will be allocated most of the resources, sub-channels, and power, for a significant portion of time. The users with lower rage channel gains may be unable to receive any data; and most of the time, the sub-channels will be assigned to the user with higher channel gains. Here, the algorithm is in such a way that fairness to all users is considered. The resources allocated i is in such a way that the minimum user's capacity is maximized.
5.2 Optimization Problem
Throughout this paper, we assume a total of K users in the system sharing N sub-channels; with total transmit power constraint P total . The objective is to optimize the sub-channel and power allocation in order to achieve the highest sum error-free capacity under the total power constraint. Here, the sum capacity is the objective function and it is ensured that each user is able to meet his target data rate, given sufficient total available transmit power.
Mathematically, the optimization problem considered in this paper is formulated as
where K is the total number of users; N is the total number of sub-channels; N o is the power spectral density of additive white Gaussian noise; B and P total are the total available bandwidth and power, respectively; P k,n is the power allocated for user k in the sub-channel n ; H k,n is the channel gain for user k in the sub-channel n ; P k,n can only be the value of either 1 or 0, indicating whether sub-channel n is used by user k or not. The fourth constraint shows that each sub-channel can only be used by one user. The capacity for user k , denoted as R k , is defined as
5.3 Complexity Analysis
The optimization problem in 5.2 is generally very hard to solve. In a system with K users and N sub-channels, there are KN possible sub-channel allocations, since it is assumed that no sub-channel can be used by more than one user. For a certain sub-channel allocation, an optimal power distribution can be used to maximize the sum capacity, while maintaining proportional constraints. The optimal power distribution method is derived in the next section. The maximum capacity over all K N sub-channel allocation schemes is the global maximum and the corresponding sub-channel allocation and power distribution is the optimal resource allocation scheme. However, it is prohibitive to find the global optimizer in terms of computational complexity. A sub-optimal algorithm reduces the complexity significantly while still delivering performance close to the global optimum.
5.4 Sub-Channel and Power Allocation
Ideally, sub-channels and power should be allocated jointly to achieve the optimal solution in 5.2. However, this poses a prohibitive computational burden at the base station in order to reach the optimal allocation. Furthermore, the base station has to rapidly compute the optimal sub-channel and power allocation as the wireless channel changes. Hence, lowcomplexity sub-optimal algorithms are preferred. Separating the sub-channel and power allocation is a way to reduce the complexity because the number of variables in the objective function is almost reduced by half.
5.4.1 Sub-Optimal Sub-Channel Allocation
In the sub-optimal sub-channel allocation algorithm, equal power distribution is assumed across all sub-channels. H k,n is defined as the channel state information for user k and n is the set of sub-channels assigned to user k . The algorithm can be described as:
Step 1: Assume equal power distribution to all sub-channels.
Step 2: Initialization (Enforce zero initial conditions).
Set R k = 0,
~k = o for k - 1, 2 ... K and
A = [1, 2 ... N].
Step 3: For k = 1 to K (Allocate best sub-carrier for each user).
a) Find n satisfying H k,n > H kJ
for all j in A.
b) Let SZ k = ~k U { n},
A = A - { n} and update R k
Step 4: While A is not equal to o (Then iteratively give lowest rate user first choice)
a) Find k satisfying Rk < Ri for
all I , 1 < I < k ,
b) For the found k, find n
satisfying Tin > Hk, ~ for all j c
A
c)
For the found k , n let 0 k = 0 k U { n}, A = A -{ n}, update R k
The principle of the sub-optimal sub-channel algorithm is for each user to use the sub-channels with high channel-to-noise ratio as much as possible. Using GA and OGA, at each iteration, the user with the lowest proportional capacity has the option to pick which sub-channel to use. The sub-channel allocation algorithm is sub-optimal because equal power distribution in all sub-channels is assumed. The goal of maximizing the sum capacity while maintaining proportional objective is achieved by the power allocation in the next section.
5.4.2 Power Allocation for a Single User
In this section, the optimal power distribution strategy for a single user k is given. When the single user power is allocated P k,tot , without loss of generality, it can be assumed that H k ,1 < H k z < H k 3 ...
From the above equation, power distribution can be achieved for a single user k on sub-channel n. By defining P k,tot as the total power allocated for user k , P k,tot can be expressed as
The proposed optimization problem considers maximizing the sum capacity while maintaining proportional power allocation among users for each channel realization. In the sub-optimal algorithm, sub-channel and power allocation are carried out separately. The power allocation is done using Orthogonal Genetic Algorithm to a determined sub-channel scheme that is developed.
| 6. Simulation Results | | |
6.1 BER Performance of the System
For comparison, the BER of the system was calculated and plotted for different modulation schemes (these are the modulation schemes recommended in the IEEE 802.11 a standard). These graphs are generated using MATLAB.
For comparison purposes, the Eb/No versus BER graph is plotted for different modulation schemes is shown in [Figure 5]. It is evident from the graph that the QPSK modulation scheme is better suited for OFDM transmission in terms of Bit error ratio performance. For QPSK, 1 IN 10 3 is obtained at 8 dB, whereas for 16PSK, it is achieved at 10.5dB. From this, we can conclude that in terms of BER performance, QPSK modulation is better suited for OFDM transmission.
The capacity of a multi-carrier system can be vastly improved by employing MIMO architecture. From [Figure 6], it can be seen that there is a significant increase in the capacity of the system as more antennas are used.
6.2 Multi-User Resource Allocation Scheme
Performance of the system can be vastly improved by properly allocating resources among different users. The algorithm presented here allocates the resources (sub-channel and power) among users in such a way that the minimum user's capacity is maximized. In all simulations presented in this section, the wireless channel is modeled as a frequency selective channel consisting of Rayleigh multi-paths. The total available bandwidth and transmit power are 1 MHz and 1 W, respectively.
In the proposed algorithm, based on the channel state information H~,k, the number of sub-carriers that are allocated to each user is presented in [Figure 7]. Select the total number of sub-carrier to be 64, and it is distributed among 16 users based on the proposed algorithm.
Once the sub-carrier allocation is fixed, the optimal bit and power allocation algorithm to every user is applied. The proposed algorithm distributes the total transmit power P er of 1W, among the user depending on T . That is, the sum of power of each user is equal to P tot , as shown in [Figure 8]. The Flowchart for Sub-channel and Power Allocation is shown in [Figure 12].
This power allocated P k,tot for each user is distributed among the channels using the Orthogonal Genetic Algorithm. After the allocations of resources are completed, the minimum user's capacity for this dynamic resource allocation scheme is calculated for a fixed noise power of 0.018 watts.
The throughput bits per sub-carrier versus average SNR is plotted in [Figure 9] for both adaptive and non-adaptive techniques; and it shows that the proposed adaptive technique improves throughput bits per sub-carrier as compared to the fixed technique.
After the allocation of resources are completed, the minimum user's capacity obits/sec/Hz~ is calculated for P tot = 1W and Bandwidth = 1MHz. [Figure 10] compares the minimum user's capacity of the proposed algorithm with the non-adaptive or fixed resource allocation of TDMA. For example, in the cast of 12 r '' user, user capacity is doubled as compared to the TDMA scheme. That is, 0.35 obits/sec/Hz~ for TDMA and 0.70 obits/sec/Hz~ for the proposed adaptive resource allocation scheme. The same concept of minimum user's capacity for different values of P ST is evaluated for 16 users in [Figure 11].
The simulation results have shown the promising results in terms of the minimum user's capacity for several values of P ST ; and the capacity is doubled as compared to the TDMA scheme by appropriate allocation of the resources obit, sub-carrier, and powers among users.
| 7. Conclusion | | |
OFDM appears to be a highly suitable modulation technique for many digital communication applications. OFDM is found to be extremely efficient in mitigating problems plaguing high-speed communication, such as multi-path fading, ISI, and noise interference. By making use of a set of orthogonal sub-carriers closely inter-spaced increased the bandwidth efficiency. Enhancements such as the use of guard periods lead to improved bit error rates. BER performance of the system, for the different modulation schemes suggested in IEEE 802.11a standard, was compared. The use of MIMO architecture is found to improve the performance of the OFDM system. The deployment of MIMO architecture improved the capacity of the system considerably.
A dynamic resource allocation scheme for maximizing the minimum user's capacity was presented and implemented. The performance of this resource allocation scheme is compared with the TDMA scheme. The simulation results indicated that the minimum user's capacity in the resource allocation scheme is almost doubled as compared to the TDMA scheme.[10]
Authors
 P. T. Vanathi received her B.E. Degree in Electronics and Communication Engineering from PSG College of Technology, Coimbatore in 1985 and M.E. Degree in Computer Science from the same institution in 1991. She has completed her Ph.D. in Signal Processing. She is a Professor in Electronics and Communication Engineering department with 20 years of teaching experience at PSG College of Technology, Coimbatore. She is a member of ISTE and IETE. Her areas of interest are Speech Recognition, Network Security, Wireless Mobile Communication, and Signal Processing. She has published about 40 papers in journals, National and International Conferences. E-mail: 
 P. Malathi received her M.E. Degree in Applied Electronics from Coimbatore Institute of Technology, Coimbatore in 2001. She is doing her Ph.D. at PSG College of Technology, Coimbatore. She is an Associate Professor in Electronics and Communication Engineering department at Sri Ramakrishna Institute of Technology, Coimbatore. She has the teaching experience of 12 years and the member of IEEE, ISTE and IETE. Her areas of interest are OFDM, MIMO, WLAN, PLC, and Wireless Mobile Communication. E-mail: 
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12]
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