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We propose an

Recently, with the fast increasing demand for high data rate and wide bandwidth in wireless mobile communication, the use of broadband signal transmission has become an important technique for next-generation wireless communication systems, for instance, 3GPP long-term evolution (LTE) and worldwide interoperability for microwave access (WiMAX) [

On the other hand, the measurement results of the broadband channel showed that the wireless multipath channel consists of only a few dominant active propagation paths whose magnitudes are nonzero, even though they have large propagation delays [

Other effective adaptive channel estimation algorithms, denoted as zero-attracting algorithms, have been reported by the combination of the CS theory [

In this paper, we proposed an

The remainder of this paper is organized as follows. In Section

In this section, a sparse multipath communication system shown in Figure

Typical sparse multipath communication system.

The APA adopts multiple projection scheme by utilizing past vectors from time iteration

For channel estimation, the APA is used to minimize

Here, the Lagrange multiplier method is employed in order to find out the solutions that minimize the cost function

It is worthwhile to note that the APA is a NLMS algorithm when the affine projection order

In this subsection, we briefly review the ZA-APA and RZA-APA. On the basis of the past studies, we know that the cost function of the ZA-APA is defined by combining the cost function

In order to get the minimization of (

Then, by multiplying

Substituting (

From the update equation (

Unfortunately, the ZA-APA cannot distinguish the active taps and the inactive taps of the sparse channel so that it exerts the same penalty to all the channel taps, which forces all the channel taps to zero uniformly [

On the basis of the conventional APA and the zero-attracting techniques used in the ZA-APA and RZA-APA, we proposed an

By calculating the gradient of the cost function

Then, by solving (

In order to avoid dividing by zero, which is a case for a sparse channel at initialization stage, we introduce a small positive constant into the denominator of the last term of (

By multiplying both sides of (

Taking (

From the discussion of the APA, ZA-APA, and RZA-APA and considering

Substituting (

In this section, we use the computer simulation to investigate the channel estimation performance of our proposed LP-APA over a sparse multipath communication system. The simulation results are compared with those of the previously proposed sparsity-aware algorithms including ZA-APA and RZA-APA as well as the standard APA and NLMS algorithms. Here, we consider a sparse channel

Typical sparse multipath channel.

In this paper, the following parameters are used to obtain the channel estimation performance:

In the proposed LP-APA, two more parameters,

Effects of

Effects of

Effects of affine projection order

We can see from Figure

Now, we turn to discuss the effects of the

Then, we show the channel estimation performance of the LP-APA with different value of

In view of the results discussed above for our proposed LP-APA, we choose

Performance of sparse channel estimation with different sparsity levels.

In this paper, we proposed an LP-APA to exploit the sparsity of the broadband multipath channel and to speed up the convergence of the standard APA. The LP-APA was realized by incorporating an

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was partially supported by “973” Basic Research Development Program of China (no. 6131380101). This paper is also supported by Pre-Research Fund of the 12th Five-Year Plan (no. 4010403020102) and Fundamental Research Funds for the Central Universities (HEUCFT1304).

_{0}-norm constrained affine projection algorithm and its applications in sparse channel estimation