Essay: Channel estimation filters

Abstract: In the process of channel estimation coding, channel estimation adaptive filters are more commonly used. In the process of adaptive filtration the selection of band processing is an important criterion. For the selected band the signals are estimated using mean square deviation (MSD). With the approach of channel estimation filtration normalized channel estimation adaptive filter (NCAF) is more effectively been used. In the process of NCAF two successive bands are processed for optimizing the MSD factor. The convergence of this estimation is however time taking under variant noise conditions. To optimize the convergence time, in this paper a recurrent NCAF approach is proposed. This proposed approach optimizes the estimation process based on recurrent channel estimation consideration, rather than two successive bands.
Keyword: Normalized channel estimation filtration (NCAF), mean square deviation (MSD), recurrent ‘NCAF.
I. INTRODUCTION
Applications have emerged with various new approaches, providing services in new emerging demanding market. Various technologies have emerged in recent past to cope with these demands, providing new and enhanced approaches for efficient services. In the area of high end services new technologies are now coding with high end coding algorithms to provide better quality. However, with the dynamic characteristic of channel variation the streaming data are degraded at a nonlinear manner. To achieve a proper estimation of such signal estimation new signal processing approaches are in greater demand. In recent past new filtration approaches were developed to minimize the processing or medium impact. To achieve the objective of filtration, processing the signal at finer channel estimation level were developed. In such coding the filtration are performed at individual lower resolution. A large group of applications utilizing channel estimation adaptive filtration is seen for acoustic echo cancellation [1, 2, 3, 4, 5], speech enhancement [6], signal separation [7], beam forming [8] etc. However the accuracy of such coding is dependent on the approach developed for such decomposition or its processing approach. To decrease the complexity of filter bank structures, the sampling rate can be reduced in the channel estimation. These filter banks are referred to as decimated filter banks, and are afflicted with three major types of distortions: amplitude, phase and aliasing effect. To eliminate these effects Several approaches based on channel estimation adaptive filtering have been recently proposed In these approaches, the underlying signals are decomposed into slightlyoverlapping frequency bands by passing through a filter bankand the output signals are decimated to give channel estimation signals. Now, the adaptations are carried out in each channel estimation, but the problem with this approach is the aliasing of the input signals,which arises because of the decimation. Several solutions tothis problem, such as oversampling [9] of the analysis bankoutputs, incorporating adaptive cross filters [10] between the adjacent channel estimations, and putting spectral gaps between the bands [11], have been recently proposed. In [10], it is pointed outthat in the -band adaptive filters with critical sampling, thecross filters can be avoided if the analysis filters are eitherideal filters, or the path impulse response is nonzero for thecoefficient indices that are multiples of and zero otherwise.Thus, the cross filters are unavoidable in practical applications.It has been found [10] that the convergence performance withthe cross filters is not better than that of full b and adaptive filter. The process of adaptive filter is optimized by the usage of converging the cost function. To achieve the convergence operation at faster rate normalized channel estimation adaptive filter (NCAF) [8] and its modified format of dynamic selection (DS-NCAF) [1] is proposed. These approaches are developed to minimize the least mean error by weight optimization process. However the proposed DS-SAF approach is observed to process for mean square deviations (MSDs) for successive bands only. This process hence does not consider the processing of relative deviation over the whole bands, with respect to the current observing band. This limitation results in lowering of estimation accuracy in single coding. To improvise the estimation accuracy with faster convergence property in this paper a new recurrent-DS-NCAF (R-DS-NCAF) approach is proposed. To outline the proposed work this paper is presented in 6 sections. In section 2 the conventional approach of filter designing for analysis and synthesis is presented. In section 3 the proposed approach of proposed filter design is presented. In section 4 the obtained experimental results were outlined. The conclusion made to the proposed work is outlined in section 5.
II. CHANNEL ESTIMATION ADAPTIVE FILTRATION (SAF)
For the adaptive coding of the signal, data are processed using channel estimation coding. A basic architecture for adaptive filter is shown in figure 1. The input signal to such filter is captured from a measuring unit and passed to analysis filter. This signal is initially processed using analysis filters and the processing residuals are processed using synthesis filter.
Figure. 1: Channel estimation adaptive filter architecture to identify an unknown system [2]
Such a filtration process could be depicted as a set of filter banks with decimation at analysis and up sampling with reverse filter banks at the synthesis side. Such operation of a filter bank is as shown in figure 2.
Figure. 2: Analysis and synthesis branch of a n-channel filter bank [2]
In this process the analysis bank decomposes a signal x[n] into K channel estimations, each produced by a branch Hz(k) of the analysis bank. After decimation and expansion by a factor N, the full band signal is reconstructed from the channel estimations in the synthesis bank by filtering with filters Gk(z) followed by summation. The analysis filters Hk(n) are derived from the real value of a low pass FIR filter p[n] of even length Lp. For the estimation of signal using such filtration cost optimization approached is used where the channel estimation are processed adaptively termed as channel estimation adaptive filter (SAF) [5].
III. NORMALIZED-SAF (NCAF)
The SAF operation is based on the LMS-type adaptive filter. The converged of such filter is based on the optimization of this LMS function, wherein weight functions are used to optimize the mean error. To converge the cost function faster in [8] a Normalized SAF (NCAF) is proposed. In this approach the convergence speed is increased by increasing the number of channel estimation filters while maintaining the same level of steady-state error. However, it suffers from huge complexity when used in adapting an extremely long unknown system such as acoustic echo cancellation application. To overcome this problem in [1] a dynamic selection based NCAF (DS-NCAF) scheme is proposed. This approach sorts out a subset of the channel estimation filters contributing to convergence performance and utilizes those in updating the adaptive filter weight. This approach dynamically selects the channel estimation filters so as to fulfill the largest decrease of the successive mean square deviations (MSDs) at every iteration. This approach reduces the computational complexity of the conventional SAF with critical sampling while maintaining its convergence performance. The operational approach for the conventional DS-SAF approach [1] is as outlined.
In a SAF system the desired signal d(n) that originates from an unknown linear system is defined by,
where w0is an unknown column vector to be identified with an adaptive filter, v(i) corresponds to a measured noise with zero mean and variance ??v2 , and u(n) denotes a row input vector with length M defined as;
In the process of converging faster, the Normalized SAF (NCAF) [8] approach was proposed. A basic architecture for such coding is as shown in figure 3.
Figure 3. NCAF filter architecture [1]
In this approach the desired d(n) signal and output signal y(n) are partitioned into N channel estimations by the analysis filters H0(z), ‘ Hn-1(z) . The resulting channel estimation signals are then critically decimated to a lower sampling rate relative to their demanded bandwidth. The original signal d(n) is decimated to k signals and the decimated filter output at each channel estimation is defined as;
yi,D(k) = ui(k)w(k),
Where, ui(k) is a 1 x M row such that,
and
denotes the estimated weight value and the decimated channel estimation error is then defined by,
Where is the desired signal at each band. In the process of NCAF the weight optimization is defined as,
Where ?? is the step size.
This weight is used to optimize the band selection process where in it takes a large computation to converge for the optimization. To overcome this issue in [1] a MSD based weight optimization is proposed. In this DS-NCAF approach the largest decrease of the MSDs between successive iterations is used.
Hence the weight error vector is then defined as, . The weight optimization is then defined as,
Using this weight vector and taking the expectation a MSD is computed which satisfies the absolute expectation as,
E
Where
Defines the difference of MSDs between two successive iterations.However the convergence is optimized taking consideration of two successive observations only. In the process of signal estimation the disturbance v(i) is randomly distributed over the whole signal and two successive observation may not extract the overall impact over the whole period. This leads to the residual errors in the estimates due to current observation u(k) over u(k+1)’. u(n). Hence to achieve this objective a recurrent ‘DS-NCAF (R-DS-NCAF) approach is proposed.
IV. RECURRENT-DS-NCAF(R-DS-NCAF)
In the process of defining recurrent DS-NCAF approach, the estimate is observed over a period of ‘n’ sub channel data, hence the absolute estimation is then defined as,
Wherein integrating the estimate, over ‘n’ observation period accumulates the estimation for ‘n’ channel estimations. The frequency response of these ‘n’ channel estimations, then defined by, Hn(f), for n= 0,1,”’, N-1. The set of N sub signals, simultaneously effected at a given time instant ‘T’ is defined by, an = [a0(T),a1(T),”’,aN-1(T)] ,where F = 1/T is the dispersion rate.
The estimates for all these sub-signals, considering the line parameters is then defined as,
where signal for the kth channel estimation at ‘Tc’period is the sum of all dispersed signal ‘hn’ frequency deviated from original frequency by a factor of kTc.
The estimate factor is then defined by,
Where ‘i,n is defined as the observatory factor, and s(kTc) is the multipath signal defined with hn frequency response with Tc delay factor. The recurrent estimates over the n-sub channels are then used for signal estimates for DS-NCAF to recover the filter output. In the process of R-DS-NCAF, the integration over the n-sub channels results in the estimate accumulation of finer band information’s in comparisons to the usage of two successive band considerations. The modified architecture for the proposed R-DS-NCAF unit is as shown below.
Figure 4. R-DS-NCAF architecture
The recursive comparison of the weight updated decomposed bands, are fed to each band and the selective bands with lower MSD is evaluated. The estimated error components are processed to retrieve the original information. The system is evaluated for variant noise density and iteration counts. The obtained experimental results are as outlined below.
V. EXPERIMENTAL RESULTS
The proposed channel estimation coding for successive and recurrent estimates is evaluated for different noise density. The frequency response of such filter is observed in Figure 5.
Figure 5. Test sample
A test sample in a sinusoidal format is taken, at a frequency of 5.5KHz, with 1024 samples. The observed input sample is as shown in figure 5. This input signal is process with additive Gaussian noise, and adaptive filtrations are applied to estimate the signal. The measuring parameter of Mean square deviation (MSD) and convergence time is computed. The developed approach is evaluated over different values of decomposition, computation and channel parameters. To observe the effect of band decomposition effect, a variation in the level of decomposition ‘N’ is observed for N=4 and N=8 at noise variance ”?? of 0.8, setting updating step ”?? to 1.0 and estimation iteration to 200. The decomposed band at N=4 is shown in figure 6.
Figure 6. Decomposed bands for Noise free signal at N=4
The decomposition is then carried out over the noise effected signal and the bands obtained for N=4 is as seen in figure 7. The decomposed band reveals the noise variations at different bands.