Research On Subband-type Adaptive Filter Algorithms

Adaptive filter is very common in the signal processing field,because its coefficients could be changed over time,it can summarize the statistical properties of the signals gradually in the iterative process,thus adjusting the coefficient vector of the filter.When the identification system change again after the adaptive filter has realized optimal filtering,the adaptive filter still update the filter's coefficient to realize optimal filtering,which shows its strong tracking capability.The excellent flexibility and the strong self-learning ability make it easier to deal with non-stationary or less statistical properties or even uncertain signals.Therefore,it plays a critical role in communications,navigation,control,seismology,biomedical engineering and so on.Subband adaptive filter is a new research branch of the signal processing field since 1980 s.The fullband signal can be divided and decimated into the subband signals by the analysis filter bank,and then are reconstructed into output signal by synthesis filters bank.The unique feature makes it have decorrelation characteristic,thus speeding up the convergence rate of the traditional fullband adaptive filter when the input signal is highly correlated.However,each subband of the subband adaptive filter uses different adaptive filters,thus it will produce aliasing components in the output signal,making it obtain a higher steady-state error.The researchers Lee and Gan proposed a normalized subband adaptive filter in 2004,called multiband structure.The biggest distinguish between this kind of subband adaptive filter and the traditional subband adaptive filter is that the subband input signal share the same adaptive filter instead of separate adaptive filter,thus solving the aliasing components issue in the traditional subband adaptive filter.On the basis of this structure,Lee and Gan also presented a normalized subband adaptive filter algorithm based on the principle of minimal disturbance.It retains fast convergence speed and low steady-state error under the circumstance of the highly correlated input signal and has less computational burden.While similar to all fixed step-size filter algorithm,the normalized subband adaptive filter algorithm also need to make a tradeoff between fast convergence rate and low steady-state error.The iteration speed will slow down when the identified unknown system is sparse,and the normalized subband adaptive filter algorithm will suffer from severe performance degradation when dealing with impulsive interference.Therefore,some methods have been presented in this paper to improve these problems existed in the normalized subband adaptive filter algorithm.Since normalized subband adaptive filter algorithm needs to make a tradeoff between convergence speed and steady-state error,a normalized subband adaptive filter algorithm with combined step-sizes has been proposed by combining two independent adaptive filters with different step-sizes.And by letting the powers of the subband posterior error signals instead of those of the subband system noises,a variable step-size method has been introduced into an improved normalized subband adaptive filter algorithm which applied to the low signal-noise-ratio system.Since the performance of the normalized subband adaptive filter algorithm will degrade severely when encountered with the impulsive interference,two novel arctangent normalized subband adaptive filter algorithms have been presented due to the excellent robustness of the arctangent cost function against impulsive interference,and the proportionate scheme have been introduced to these two arctangent normalized subband adaptive filter algorithms to improve their performance in the sparse system.Since the performance of the normalized subband adaptive filter algorithm will degrade severely when identifying the sparse unknown system and is encountered with the impulsive interference,by combining the normalized logarithmic cost function and the L0-norm constraint of the estimated unknown vector,a L0-norm constraint normalized logarithmic subband adaptive filter algorithm has been proposed.Since the performance of the normalized subband adaptive filter algorithm will degrade severely when encountered with the impulsive interference,a L2-norm normalized subband adaptive filter algorithm has been proposed by means of the cost function which contains the L2-norm of all normalized subband error signals and gradient descent technique,and the variable control parameter method has been added to further accelerate the convergence rate.Besides,since these fixed control parameter algorithms require to make a tradeoff between convergence speed and steady-state error,an iterative mechanism based on the exponential function has been presented to update the control parameter recursively.A large number of simulations results have demonstrated that these improved algorithms obtain faster convergence rate,lower steady-state error,better tracking capability and stronger robustness against impulsive interference when compared with the traditional normalized subband adaptive filter algorithm.