Design of Multichannel Sample Rate Convertor

The full utilization and practical realization of Multichannel sample rate convertor is restricted by increased power consumption and resource utilization of the interpolator and decimator design in the context of contemporary wireless broad band standards using. So we are trying to make all the multimedia devices compatible with all the wireless communication multiple standards. For that purpose we are about to develop sample rate converter which will provide the flexibility to change its sampling rate according to requirement of the different wireless multiple standards. The second challenge of resampler design is that the numbers of channels are limited. In such a case, we have to develop multichannel interpolator and decimator of high performance low power consumption with near optimal performance.


Introduction
The full utilization and practical realization of Multichannel sample rate convertor is restricted by increased power consumption and resource utilization of the interpolator and decimator design in the context of contemporary wireless broad band standards using. So we are trying to make all the multimedia devices compatible with all the wireless communication multiple standards. For that purpose we are about to develop sample rate converter which will provide the flexibility to change its sampling rate according to requirement of the different wireless multiple standards. The second challenge of resampler design is that the numbers of channels are limited. In such a case, we have to develop multichannel interpolator and decimator of high performance low power consumption with near optimal performance. Generally conventional interpolator and decimator implemented by using direct form FIR filter structure. The problem with Implementing Sample Rate Convertor using direct form architecture was that filter length linearly increases with the decimation and Interpolation rate. Therefore resource Utilization also increases; this in turn increases Power consumption, Area requirement and Delay of the sample rate convertor. To overcome these problem CIC FIR filter structure to implement sample rate convertor. CIC filters can efficiently perform either decimation or interpolation, with two complementary structures being employed to implement these functions. The problem with implementation of Sample Rate Convertor using CIC filter was that CIC filter was used only for narrowband signals. So it would not be used for implementation of sample rate convertor for large bandwidth. MAC architecture was an efficient solution developed as a sample rate convertor for large bandwidth signal.
MAC Architecture can also be used for increase bandwidth of the input signal. This application note deals with single MAC filters, as the low sample rates at which the FIR filters operate allow high clock-persample ratios, allowing many taps to be calculated in a single multiplier in each sample period. Limitation of MAC Architecture is not support for large change in sampling rate conversion but allow large bandwidth signal. Our purpose model CMFIR filter is an efficient solution of that problem. On CMFIR implement cascading of CIC and MAC FIR filter We apply genetic algorithm on coefficient of CMFIR filter to achieve desired frequency and magnitude response while having minimum linear phase; hence, reducing the time response, constant group delay, increasing bandwidth. Genetic optimization technique is also used for reducing the power consumption of multichannel sample rate convertor by optimization of coefficient of filter by scaling which are used in implementation of multichannel sample rate convertor design in FPGA implementation.

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Number of Input Channels limited the total filter length grows linearly with the decimation rate. So that resource Utilization also increases.

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We cannot change the sampling during the run time.

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Non Linear Phase response of sample rate convertor.

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Group Delay of sample rate convertor is very high.

1.
To design and optimize CIC FIR filter to prevent aliasing.

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To design and optimize MAC FIR filter to smoothen out the signal transitions.

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Cascading of CIC and MAC FIR filter to design and optimize CM FIR filter.

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To design and optimize suitable decimator and interpolator using CM FIR filter, delay and advanced units.

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Assembling of single channel sample rate convertor using decimator and interpolator designed in objective (d).

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To develop and optimize 8 channel sample rate convertor using multiplexer unit and single channel sample rate convertor.

8.
FPGA implementation of multichannel sample rate convertor and performance analysis.

Genetic Algorithms
Genetic Algorithm is very flexible, no problem specific, and robust. It can explore multiple regions of the parameter space for solutions simultaneously. Owing to the heuristic nature of GAs, arbitrary constraints can be imposed on the objective function without increasing the mathematical complexity of the problem. Multiple objective functions can be optimized simultaneously.
Gene: A single encoding of part of the solution space, i.e., either single bits or short blocks of adjacent bits that encode an element of the candidate solution.
Chromosome: A string of genes that represents a solution.
Population: The number of chromosomes available to test. Start with a population of candidate solutions Variation: Introduce variation by applying two operators: crossover and mutation Survival of the fittest: Use a fitness criterion to bias the evolution towards desired features. Representation:

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GAs on primarily two types of representations:

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Binary-Coded (genotype) GAs must decode a chromosome into a real value (phenotype), for evaluating the fitness value.

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Real-Coded GAs can be regarded as GAs that operates on the actual real value (phenotype).

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For Real-Coded GAs, no genotype-to-phenotype mapping is needed.
Selection: A proportion of the existing population is selected to bread a new bread of generation.
Crossover: It is a genetic operator that combines (mates) two individuals (parents) to produce two new individuals (Childs). The idea behind crossover is that the new chromosome may be better than both of the parents if it takes the best characteristics from each of the parents.
Mutation: It is a genetic operator used to maintain genetic diversity from one generation of a population of chromosomes to the next.

Steps of genetic algorithm
The genetic algorithm loops over an iteration process to make the population evolves ( Figure 1). Each consists of the Following steps: 1. Selection: The first step consists in selecting individuals for reproduction. This selection is done Randomly with a probability depending on the relative fitness of the individuals so that best ones are often Chosen for reproduction than poor ones.

Methodology to Develop Multichannel Sample Rate Convertor Approach
A multichannel sample rate convertor based solution is proposed to make all the multimedia devices compatible with all the wireless communication multiple standards. The Multichannel sample rate convertor time response must be included in the requirements. On one hand, the time domain requirement where both a high speed and accurate system response are needed. On the other hand, the frequency domain requirements (DC, sub-synchronous and harmonic components elimination) which are the magnitude response within small bandwidth including sharp frequency edges as well as an approximately constant group delay in this band are required too. Usually the best optimum value of all the objective functions of this multichannel sample rate convertor design can be obtained for some values of design variables. A compromise or a trade-off between the objective functions must be made to achieve a satisfactory multichannel sample design [1,2].
The considered CMFIR multichannel sample rate convertor

Transfer function of multichannel sample rate convertor
The two basic building blocks of a CIC filter are an integrator and a comb. CIC filters can efficiently perform either decimation or interpolation, with two complementary structures being employed to implement these functions. Decimation requires a cascade of a number of integrator units, followed by a down-sampling stage and finally a cascade of the comb filter units. Conversely, interpolation cascades several comb filters with an up-sampler and several integrators. A comb filter running at the high sampling rate, f s , for a rate change of RM is an odd symmetric FIR filter described by [3].
The second equality corresponds to a comb is given by: Comb followed by an integrator Taking Z transform of the equation To generate parameterizable, high-performance and area-efficient filter modules utilizing the Multiply-Accumulate (MAC) architecture. Multiple MACs can be used in achieving higher performance filter requirements, such as longer filter coefficients, higher throughput, or increased channel support. Output of the MAC FIR filter is given by: Taking Z Transform: Cascaded multiple architecture finite impulse response (CMFIR) filter will be implemented by cascading of CIC filter and MAC architecture. The CMFIR filter (CMFIR) is an interpolating and decimator low-pass FIR filter. It provides a further increase in sample rate, reducing the resources requirements on the CIC and limiting the number of stages required, while also providing moderate pass band filtering of the QPSK modulated signal (although this requirement is less stringent where an effective QPSK modulator with good pulseshaping properties has been used).
Final Response of CMFIR Filter:

Magnitude response objective function
The amplitude and the phase responses of multichannel Sample rate convertor are given by: Where w is the frequency and x is a column vector with 2M + 2N + 1 components, that is in Cartesian form [2].

Group-delay and phase response objective function
The group delay is derived from the phase relation, as given in equation (11), and is defined as GD(x,,w) = (dØ(x,w))/(d(w)) Where is Ø(x,w) the phase response of the filter [4].

Genetic Algorithm Implementation Methodology
The design flow is highlighted in below ( Figure 2). Here are the steps that we follow:

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Given set of design specification, program them into MATLAB.

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Create an ideal response, group delay of the desired multichannel sample rate convertor.

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Use the order estimation function provided by MALTAB for each type of multichannel sample rate convertor.

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Design the GA multichannel sample rate filter using MATLAB multichannel sample rate convertor function.

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Compare the response, phase response, group delay of our design with the ideal multichannel sample rate convertor [2].

Optimization of power dissipation
The coefficient optimization is done in two phases: In the first phase, all the coefficients are scaled uniformly. The advantage of such an approach is that it does not affect the sample rate convertor characteristics in terms of pass band ripples and stop band attenuation and phase response. The sealing results in the same gain/ attenuation ratio.
In the second phase of optimization one coefficient is perturbed in the each iteration. In case of requirement to retain the linear phase characteristics, the coefficients are perturbed in pairs (Ai and An-1-i) so as to preserve coefficients symmetry. The selection of coefficient for perturbation and the amount of perturbation has the direct impact on overall optimization quality. Various strategies can be adopted for coefficient perturbation. The strategies adopted here include 'Genetic Algorithms'. The Genetic Algorithms are the evolutionary algorithm which generates the random numbers and selects the best fit value according to the fitness function and search the whole space to find the global value [5][6][7].

Results and Discussion
The above line graph in Figures 3-5 lists the difference between the power (total, static, dynamic ) consume in different fractional sample convertor which are implemented with different architecture of FIR filter. Here we have analyzed static power consume in all the available structure of fractional sample rate convertor, CMFIR filter with genetic algorithm provide minimum power consumption. The above line graph lists in Figures 6-10             available for data transfer of different fractional sample convertor which is implemented with different architecture of FIR filter. Here we have analyzed bandwidth available for data transfer all the available structure of down sample rate convertor, CMFIR filter with genetic algorithm provide maximum bandwidth for data transfer. The above line graph in Figure 11 lists the difference between the Group delays of different fractional sample convertor which are implemented with different architecture of FIR filter. Here we have analyzed the group delay of all the available structure of sample rate convertor, CMFIR filter with genetic algorithm provides required maximum samples or minimum, constant group delay in second [8].