NSGA-II Implementation for Resource Allocation in MIMO

One of the most challenging issues for future wireless communication systems is the provision of quality service (QoS) guarantees to users over the harsh wireless channels given the limited resource availability. The aim of this paper is to probe the problem of dynamic subcarrier and bit allocation in downlink of MIMO-OFDMA systems. Using Singular Value Decomposition, MIMO fading channel of each subcarrier is transformed into an equivale parallel SISO sub-channels. NSGA-II is handled which is a multi-objective Genetic Algorithm, for joint allocation of bits and subcarriers, in the downlink of MIMO-OFDMA system. NSGA intended for optimization problems involving multiple conflicting objectives. Here the two conflicting objectives are Rate Maximization and Transmit Power Minimization.


INTRODUCTION
Wireless communications has emerged as one of the largest sectors of the telecommunications, industry, evolving from a niche business in the last decade to one of the most promising areas for growth in the recent era.
The increasing demand for wireless mult services are in need of reliable and communications over a wireless chann channel capacities or transmission rate bandwidth with no additional power requirem employing multiple antennas (MIM transmitter and receiver is contributed by Spatial multiplexing.(OFDM) efficiently uses the spectrum @ IJTSRD | Available Online @ www.ijtsrd.com | Volume -2 | Issue -5 | Jul-Aug 2018 One of the most challenging issues for future wireless communication systems is the provision of quality-ofservice (QoS) guarantees to users over the harsh ited resource availability. The aim of this paper is to probe the problem of dynamic subcarrier and bit allocation in OFDMA systems. Using Singular Value Decomposition, MIMO fading channel of each subcarrier is transformed into an equivalent bank of II is handled objective Genetic Algorithm, for joint allocation of bits and subcarriers, in the OFDMA system. NSGA-II is intended for optimization problems involving multiple flicting objectives. Here the two conflicting objectives are Rate Maximization and Transmit Power dominated Sorting objective optimization, Wireless communications has emerged as one of the largest sectors of the telecommunications, industry, evolving from a niche business in the last decade to one of the most promising areas for growth in the wireless multimedia high-rate data s channel. High rate for the same power requirements by (MIMO) at the receiver is contributed by Spatial OFDM) efficiently uses the spectrum by spacing the channels closer, and ability to reduce ISI. The technologies has been rese hopeful applicant technique for wireless systems. Due to fading, a major portion of the a specific user would unde power will not be efficient to number of user increases the Multius creates channel. Adaptively each user provide a better performa fixed schemes and it is based condition which can, abuse mu The MIMO/OFDM system enjoys more freedom for efficient resource to the spatial parallelism and fr the channel.

MIMO-OFDMA
Multi-user MIMO-OFDMA is regarded as an important technology for increasing the flexibility and efficiency of wireless communication systems [2] the MIMO-OFDMA downlink system model from the base station (BS), all channel state information of each transmit and receive antennas is sent to the subcarrier and power allocation block through the feedback channels from all mobile users. allocation scheme is forwarded to the MIMO transmitter. The transmitter then loads each user's data onto its allocated subcarriers.
The resource allocation scheme is the channel information is composed and also the subcarrier and bit allocation information is guided to each user for the purpose of detection, through a separate channel [6].

Aug 2018
Page: 490 6470 | www.ijtsrd.com | Volume -2 | Issue -5 Scientific (IJTSRD) Journal II Implementation for Resource Allocation in MIMO-OFDMA closer, and it also has the The blend of these two earched for the most for the next generation the frequency-selective the subcarriers assigned to undergo severe fading and efficient to carry any data. As the of user increases the Multiuser system assigning resources to performance compared to and it is based on their channel multiuser diversity [2]. enjoys more degrees of urce allocation and it is due ism and frequency selectivity of OFDMA is regarded as an increasing the flexibility and efficiency of wireless communication systems [2].In OFDMA downlink system model from the base station (BS), all channel state information of each transmit and receive antennas is sent to the cation block through the feedback channels from all mobile users. The resource allocation scheme is forwarded to the MIMO-OFDM transmitter. The transmitter then loads each user's data onto its allocated subcarriers.
The resource allocation scheme is updated as soon as the channel information is composed and also the subcarrier and bit allocation information is guided to each user for the purpose of detection, through a International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470 Page: 491 MIMO exploits the space dimension to progress wireless systems capacity, range and consistency. It offers significant escalations in data throughput and link range without supplementary bandwidth or increased transmit power. MIMO achieves this goal by spreading the same total transmit power over the antennas to achieve an array gain that progresses the spectral efficiency (more bits per second per hertz of bandwidth).

SYSTEM MODEL
The system under deliberation is downlink of a MIMO-OFDMA system, with K users and N subcarriers. At the transceiver the perfect channel state information is assumed. Then each subcarrier composed of a narrowband channel with M antennas at both the receiver as well as the transmitter, which can be modeled by M× M channel matrix and it is of H = [hi,j], where hi,j is the gain of the channel at the receive antenna i from transmit antenna j.The SVD of H is then written as: Where U and V are the unitary matrices, V denotes the transpose conjugate of V, and ⋀ is a diagonal matrix. The elements of ⋀=diag([λ ….λ ]) are real and they are arranged as λ ≥….≥λ ≥0.The SVD analysis is shadowed by the breakdown of channel matrix H into a number of self-governing orthogonal excitation modes, and it is known as eigen-modes of the channel.
The transmit preceding and receiver shaping convert the MIMO channel into R (R is the rank of the matrix H) parallel SISO channels with input and output Since from the SVD,it has,  (λ , , ≥….≥λ , , ≥0).

OPTIMIZATION PROBLEM
The transmit power for the k th user and the m th Eigenmode of the n th subcarrier must be equal to: Where , , is the bits allocated for unit channel gain. The overall transmit power is given by Where the subcarrier allocation indicator , is defined as ρ , = 1, if the nth subcarrier is allocated to kth user 0, otherwise Problem is framed to maximize the minimum data rate among entire users subject to the constraint that the total power cannot exceed a given value. The power objective is modified little and assumes that the total available transmission power is limited to a certain range with a typical value P T .Second objective to bring the total power as close as possible.
The multi-objective optimization problem is: R K denotes the transmit bits per OFDM symbol for the k th user, D is a set of available bits in the adaptive modulation, D max denotes the maximum value in the set D. Constraint C 2 takes care of the fact that one user is assigned with one subcarrier only.

NSGA-II
Non-dominated Sorting Genetic Algorithm is to use to progress the adaptive fit of a population of candidate solutions to a Pareto front which is inhibited by a set of objective functions [9]. The algorithm uses an evolutionary process with for evolutionary operators that include selection, genetic crossover, and genetic mutation. The population is sorted into a hierarchy of sub-populations based on the ordering of Pareto dominance. Similarity between members of each subgroup is evaluated on the Pareto front, and the resulting groups and similarity measures are used to endorse a various front of non-dominated solutions. NSGA-II algorithm includes the following steps to be employed:

Population initialization
The number of individuals in the population P and the number of generations G are initialized and can be varied for different runs of the algorithm. Each individual is created by generating 0's and 1's randomly.

Evaluate the objective functions
For each individual the fitness values of the objective function are calculated.

5.3
Non-dominated sorting Based on non-domination the population is sorted into fronts and each individual is assigned a rank. After the completion of non-dominated sorting the crowding distance is assigned.The non-dominated sorting algorithm is done by following steps: Step 1: From the main population P each individual p is made to do the following:  Initialise Sp= ɸ {set of individual being dominated by p}  Initialise Np=0{ no of individual that dominates p}.  Consider individual p in population P  If p dominates q then S p is S p = {q U Sp}  Else Np=Np+1 Step 2: If Np=0 (no individual dominates p and it belongs to first front).Set p rank =1.First front update is made with addition of p to the set(F 1 ={ p U Fi }).
Step 3: Intialize front counter i=1 (Carry out for the entire individual in main population P)  For each individual q in Sp  Nq=Nq-1 (Nq is domination count)  If Nq=0 then  q rank = i+1  update Q ={ Q U q } Step 4: If Fi not equal to 0 then Q=0{set for storing individual in i+1 front} For each individual p in Fi Step 5: Increment the front counter Fi = Fi + 1 Step 6:Set Q in the next front Fi=Q.

Crowding distance calculation
In addition to fitness value for each individual crowding distance is calculated. The crowding distance is calculated as: Step 1: For each front Fi, in a non-dominated set I, l is the number of solution Step 2: For all the individuals, initialize the distance to 0 i.e. ,Fi(dj) = 0, j corresponds to j th individual in Fi.And for each objective function m Step 3: Based on the objective m sort the individuals in front Fi (I=sort(Fi,m)).
Step 4: Boundary solution is assigned to infinite distance and for each individual in front Fi(I(d1) = ∞ and I(dl) = ∞).By this for all other points the boundary points are always selected. For j = 2 to (l-1) Step Based on the rank and crowding distance parents are selected from the population by using binary tournament selection.

Crossover and Mutation
Crossover is the mechanism by which design characteristics between any paired individuals are exchanged to form two new (child) individuals and single point crossover the data beyond the point in either organism string is swapped between the two parent organisms.
Mutation is a genetic operator used to maintain genetic diversity from one generation of a population of chromosomes to the next. The probability of mutation is given as P m and it is usually 100 times less than P c, where P c is the probability of crossover.

Generation of New Population
The new population is filled up by taking the best individuals from the combined population based on rank and crowding distance.

CONCLUSION
NSGA-II has been proposed for subcarrier allocation in MIMO-OFDM system for the multiuser and simultaneous bit-loading .The solution generated by the algorithm is found to be suitable for different sets of users and subcarriers taking multiple conflicting objectives into the algorithm and it guarantees fairness among the users by means of optimizing the rate.