برآورد کانال پراکنده. ℓ 1-منظم سازی ℓ 1-منظم سازی. برنامه ریزی خطی. حداقل انحراف مطلق. برابری. نویز ضربه ای
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|25419||2013||11 صفحه PDF||سفارش دهید||6596 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Signal Processing, Volume 93, Issue 5, May 2013, Pages 1095–1105
In this paper, an algorithm for sparse channel estimation, called ℓ1-regularizedℓ1-regularized least-absolutes (ℓ1-LAℓ1-LA), and an algorithm for equalization, called linear least-absolutes (LLA), in non-Gaussian impulsive noise are proposed. The proposed approaches are based on the minimization of the absolute error function, rather than the squared error function. By replacing the standard modulus with the ℓ1-modulusℓ1-modulus of complex numbers, the resulting optimization problem can be efficiently solved through linear programming. The selection of an appropriate regularization parameter is also addressed. Numerical results demonstrate that the proposed algorithms, compared with the classical methods, are more robust to impulsive noise and have a superior accuracy.
In many wireless communication and localization applications, e.g., high definition television (HDTV) terrestrial transmission  and , underwater acoustic communication systems , and geolocation , it is necessary to estimate the multipath propagation channels with a large delay spread but with a small number of non-zero taps. Such channels, an example of which is given in Fig. 3(a), have a long but sparse impulse response. The large delay spread makes estimating the channels of this type a challenge task. The estimation performance can be improved if the sparse structure of the channels is taken into account. The sparse channel estimation can be viewed as a sparse representation problem. However, finding the sparsest solution, which leads to an ℓ0-normℓ0-norm minimization problem,1 is an NP-hard combinatorial optimization problem. To deal with this intractable problem, one appealing method is basis pursuit (BP)  or Lasso , which replaces the ℓ0-normℓ0-norm by the ℓ1-normℓ1-norm. The BP method results in an ℓ1-regularizedℓ1-regularized least-squares (ℓ1-LSℓ1-LS) problem , which can be solved with polynomial-time complexity . The performance of the ℓ1-minimizationℓ1-minimization based approach is satisfactory when the channel response is sparse  and . Many existing channel estimation methods and equalizers explicitly or implicitly assume that the ambient noise is Gaussian , , , ,  and . The ℓ1-LSℓ1-LS based channel estimation approaches and zero-forcing (ZF) equalizer use the squared error function, which is optimal in white Gaussian noise. However, the noise components in practice often exhibit non-Gaussian properties . One important class of non-Gaussian noise frequently encountered in many practical wireless radio systems is the impulsive noise (also referred to as burst noise or outliers) ,  and . The channel estimation and equalization by minimizing the squared error function is no longer optimal and the performance will degrade in the presence of impulsive noise. Several techniques for sparse representation in impulsive noise are available  and . These sparse signal recovery methods adopt some robust statistics  instead of the quadratic residual error function (ℓ2-normℓ2-norm of the residual vector). In , a sparse reconstruction method based on ℓ1-minimizationℓ1-minimization employing a Lorentzian norm  constraint on the residual error is proposed. This method is more robust to outliers by the use of Lorentzian norm instead of the ℓ2-normℓ2-norm of the residual vector. Despite its good performance in impulsive noise, the Lorentzian norm will lead to a non-convex optimization problem. Finding the global minimum of such a non-convex optimization problem is not easy. In , it was proposed to replace the quadratic error function with Huber's penalty function  to achieve robustness to impulsive noise. In addition, an iterative procedure is proposed in  to solve the resulting minimization of Huber's function with an ℓ1-regularizationℓ1-regularization term. In each iteration, it requires the solution to an ℓ1-LSℓ1-LS problem. Therefore, the computational complexity of the robust sparse reconstruction algorithm in  is high. Moreover, this algorithm for real-valued problems cannot be directly applied to channel estimation and equalization, where complex baseband signals are used. In this paper, we propose a new channel estimation and equalizer design criterion based on the minimization of the absolute error function with an ℓ1-normℓ1-norm regularization term. We refer to the proposed channel estimation method and the equalizer as the ℓ1-regularizedℓ1-regularized least-absolutes (ℓ1-LAℓ1-LA) and linear least-absolutes (LLA), respectively. By using the ℓ1-modulusℓ1-modulus of complex numbers instead of the standard modulus, the channel estimation and equalization problem is recast into a linear programming that can be efficiently solved. The ℓ1-LAℓ1-LA based channel estimation algorithm and LLA equalizer are more robust to impulsive noise than the classic methods. The remainder of this paper is organized as follows. Section 2 introduces the signal model and the channel estimation problem in the presence of impulsive noise. In Section 3, we detail the ℓ1-LAℓ1-LA based sparse channel estimation algorithm and the LLA equalizer that are robust to impulsive noise. A number of numerical simulations are performed to compare the performance of the ℓ1-LAℓ1-LA algorithm and LLA equalizer with those of other representative methods in Section 4. Finally, conclusions are provided in Section 5.
نتیجه گیری انگلیسی
We have proposed two algorithms, ℓ1-LAℓ1-LA sparse channel estimator and LLA equalizer, in the presence of non-Gaussian impulsive noise. The corresponding ℓ1-LAℓ1-LA and LLA algorithms replace the squared-error by the absolute error, which results in a different criterion for channel estimation and equalizer design. Linear programming can be applied to solve the resulting optimization problem efficiently. Simulation results under impulsive noise with generalized Gaussian distribution demonstrate that the proposed ℓ1-LAℓ1-LA and LLA are more robust to impulsive noise and outperform the conventional methods in terms of estimation accuracy and symbol error rate.