Recently, the scatter cluster models which precisely evaluate the performance of the wireless communication system have been proposed in the literature. However, the conventional SAGE algorithm does not work for these scatter cluster-based models because it performs poorly when the transmit signals are highly correlated. In this paper, we estimate the time of arrival (TOA), the direction of arrival (DOA), and Doppler frequency for scatter cluster model by the modified multiple signal classification (MUSIC) algorithm. Using the space-time characteristics of the multiray channel, the proposed algorithm combines the temporal filtering techniques and the spatial smoothing techniques to isolate and estimate the incoming rays. The simulation results indicated that the proposed algorithm has lower complexity and is less time-consuming in the dense multipath environment than SAGE algorithm. Furthermore, the estimations’ performance increases with elements of receive array and samples length. Thus, the problem of the channel parameter estimation of the scatter cluster model can be effectively addressed with the proposed modified MUSIC algorithm.

It is important to estimate the spatial/temporal parameters, such as directions of arrival (DOAs), path delays, frequencies, and so forth, embedded in the receive signals in radar, sonar, and wireless communication systems. It also finds applications in source localization, accident reporting, cargo tracking, and intelligent transportation. For example, a precise estimation of DOAs and frequencies of rays in wireless communication channels can helpfully provide better channel information so as to enhance the performance in terms of coverage, capacity, and quality of service (QoS) considerably and increase resistance against interferences. On the other hand, an effective channel model must rely on a realistic characterization of the probability distribution of the relevant channel parameters. So the validation of channel parameter is a prerequisite to ensure that these models reproduce the critical features of the propagation environment, that is, in delay, direction, Doppler, and polarization.

Recently, various high-resolution methods have been proposed in mobile channel to estimate some of the parameters of impinging plane waves, that is, their complex amplitude, relative delay, incidence azimuth, incidence elevation, and Doppler’s frequency. These methods can be grouped into three of the categories [

Unfortunately, the computational burden of the SAGE algorithm is high due to the necessity of nonlinear and multidimensional optimization procedure. Since Swindlehurst proposed several computational efficient algorithms for the estimation of the delays of a multiray channel and solved the spatial signatures (or DOAs) as a least square problem [

With the development understanding of the wave propagation phenomena, the ray model is not suitable to interpret the parameter estimation results of a channel parameter estimator. This is due to the limited resolution of any wireless channel system. A number of radio channel models based on scatter clusters have been proposed in the literature. Many such models which are referred to as cluster delay line (CDL) models simplify the scattering environment and thereby precisely evaluate the performance of the communication system.

However, the SAGE algorithm did not work for the scatter cluster model because the transmit signals are highly correlated. In this paper, we present a low-complexity, yet high-accuracy, MUSIC-based algorithm, which combines the techniques of temporal filtering and of joint DOA and frequency with two-dimensional (2D) searching. Except for this, there are several other advantages of modified MUSIC algorithm compared with SAGE algorithm, such as the reduction of computation, reduced complexity.

This paper is organized as follows. Section

We consider a wireless communication system with

Using the general relation,

The frequency array response matrix

Because the rank of correlation matrix is the number of cluster and not the number of ray, the conventional MUSIC algorithm does not work for scatter cluster model directly. So we make some modification based on the conventional MUSIC algorithm. The flow chart of the modified MUSIC algorithm is illustrated in Figure

The flow chart of the our modified MUSIC algorithm.

Despite the conventional MUSIC algorithm constructs a spatial correlation matrix, the proposed algorithm is based on the decomposition of the theoretical temporal correlation matrix

Note that the number of the incoming paths is assumed to be known a priori; otherwise, we may estimate

The column vectors of

Using the orthogonality property between the signal and the noise subspaces, the T-MUSIC algorithm estimates the path delays by

After searching

By applying the T-MUSIC, the resulting delays are estimated. Based on the delay estimates, we define the temporal filtering matrices as

Note that

After applying the temporal filter, we can jointly estimate DOAs and Doppler frequencies of each delay cluster. However, the signals included a delay cluster are coherent, the matrix becomes singular, so that some of its eigenvalues are zero. This means that part of the signal subspace is indistinguishable from the noise subspace. As a result, the observed noise subspace is no longer orthogonal to the signal subspace and the MUSIC algorithm fails. So, to overcome these problems, we use a technique called spatial smoothing (SS) to allow the MUSIC algorithm to be applied to the coherent signal case [

The basic idea is to form covariance matrices from subsets of the array, which is equivalent to partitioning the original covariance matrix. If there are

Then we can jointly estimate DOAs and frequencies in one delay cluster by the spatial correlation matrix

Similarly, after eigen decomposition of

In this section, we conduct simulations to assess the proposed MUSIC algorithm. Assume narrow-band signals that are transmitted through 7 rays and received by a ten-element

Figure

Delay clusters estimation using our algorithm.

Joint DOA and Doppler’s frequency estimation of first cluster using our algorithm.

As illustrated in Figures

In this part, we hereby make a brief comparison for the algorithmic costs in contrast with the modified MUSIC algorithm and SAGE algorithm. Table

The complexity for algorithms.

Algorithm | Complexity |
---|---|

Modified MUSIC algorithm | |

SAGE algorithm |

When the number of ray estimated is small, it is proved that the SAGE algorithm can achieve coverage within 6–10 iterations through simulation analysis. The complexity of SAGE algorithm is less than that of the modified MUSIC algorithm.

On the contrary, the SAGE algorithm achieves coverage within 20 iterations when the wireless scatter environment is dense multipath. So, the complexity of SAGE algorithm is larger than that of the modified MUSIC algorithm.

From Table

To compare the estimation performance of both algorithms, we present 300 Monte Carlo’s simulations to assess the angle estimation performance of our algorithm in specular model and define root mean squared error (RMSE) as

The RMSE of DOA estimation performance with Modified MUSIC algorithm and SAGE algorithm in specular models.

Through the simulation, it is found that the iteration step shows sharp fluctuation for scatter cluster model using the SAGE algorithm. The major reason which leads to the failure of SAGE algorithm in the scatter clusters model is the searching procedure in the M step of SAGE algorithm that does not identify the peak caused by the signals which have same delays.

As mentioned above, the modified MUSIC algorithm is proved to be applied for the cluster models. However, the estimation performance depends on the mean of correlation matrix which substitutes for the expect of the correlation matrix in the practice. So, the number of receive antennas and sample length make a great part in the accuracy of estimation.

Figure

The DOA estimation performance with different elements of receive array.

The DOA estimation performance with different samples.

As to the conventional SAGE algorithm does not work for these scatter cluster models, in this paper a modification channel parameter method was proposed which combines the temporal filtering techniques and the spatial smoothing techniques based on the conventional MUSIC algorithm. The synthetic channel was then adopted in simulation to evaluate its performance. We come to a conclusion that the modified MUSIC algorithm takes less time than the SAGE algorithm and has less complexity than the SAGE algorithm in dense multipath environment. The results indicated that this method could fulfill parameter estimation with high resolving capability. It is demonstrated that the estimation performance grows with the number of array elements and the sample rate.

This work is supported by the National Science and Technology Major Project of the Ministry of Industry and Information of China (2009ZX03007-003) and the National Natural Science Foundation of China (61101223).