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A new generation method for spatial and temporal correlated multiple-input multiple-output (MIMO) Nakagami fading channel is proposed, which has low complexity and is applicable for arbitrary fading parameters and prespecified correlation coefficients of different subchannel. The new scheme can be divided into two steps: (1) generate independent Nakagami fading sequences for each subchannel based on a novel rejection method; (2) introduce the temporal and spatial correlation based on the relationships between Rayleigh, Gamma, and Nakagami random processes. The analysis and simulation results show that the proposed simulator has a good agreement with the theoretical model on fading envelope distribution, spatial-temporal correlation characteristic.

In the past decades, more and more attentions have been given to MIMO system for its high channel capacity [

A number of methods for generating independent Nakagami fading channels are available in the literature. Yip and Ng’s method [

Yip and Ng’s method and the decomposition method are also suitable for generating temporal correlated Nakagami fadings with specific values of

In this paper, we propose a new framework for generating the correlated MIMO Nakagami fading channels which possess (1) arbitrary and different

The rest of the paper is organized as follows. In Section

Throughout the paper, we use

A flat fading MIMO system equipped with

MIMO system with

The probability density function (PDF) of Nakagami distribution was given in [

Following [

In general, the correlated Nakagami MIMO channel simulation is to generate

The rejection/acceptance technique is a universal generation method for nonuniform RVs, which is summarized as follows [

Find a hat function

Generate a RV

If

The main difficulty of this technique lies in finding a hat function which is close to the required distribution and satisfies the inequality. In this paper, we adopt a new truncated Gaussian distribution function as the hat function for arbitrary

An important measure for the quality of the rejection algorithm is the acceptance probability or rejection efficiency which involves the closeness between the Nakagami PDF and the hat function. Figure

Rejection efficiency of the new method.

For stationary random processes, the TCC of the samples is well approximate with the TCC of their statistical ranks [

The Nakagami envelope autocorrelation function is given by [

According to the definition of autocorrelation coefficient, we obtain

It is difficult to get the accurate relationship expression between

The absolute error between

Thus, we can rearrange the Nakagami sequence to match the statistical rank of the Rayleigh sequence in order to introduce the desired temporal correlation (see Figure

Introducing temporal correlation.

We introduce the spatial correlation for

Introducing spatial correlation.

The decomposition method assumes that the linear summation of independent Gamma RVs follows Gamma distribution. In the following, we will analyze the simulation error caused by this assumption. Firstly, the

The exact PDF of

The straightforward transformation

Finally, the theoretical expression for absolute error of simulated Nakagami PDF is obtained as^{6} samples of the Nakagami RV are generated by four independent Gamma RVs with different parameters sets of

Comparison of the absolute error of Nakagami PDF.

To illustrate the behavior of the proposed channel simulator, we consider a MIMO system with

The

A plausible model for the angle of arrival (AOA) of the receiving signals is Von Mise distribution, which is defined as [

In the simulation, 10^{6} samples of each subchannel are generated based on the proposed scheme. Figure

The PDFs of simulated subchannel fading envelope.

We next look at the spatial and temporal correlation coefficients of the above outputs. In the simulation, we assume that four subchannels experience almost the same no-isotropic (

The TCCs of simulated subchannel fading envelope.

In this paper, a new framework for simulating the spatial and temporal correlated MIMO Nakagami fading channels was proposed. It can be applied on arbitrary fading parameters and prespecified spatial-temporal correlation coefficients with a satisfactory accuracy. Moreover, the new simulation method is low complexity and applicable for large-scale and real-time channel simulation scenarios. The most complex part of this simulator is to generate

This work is supported by National Nature Science Foundation of China (no. 61102068), the Aviation Science Foundation of China (no. 2009ZC52036), Nanjing University of Aeronautics and Astronautics Research Funding (no. NP2011036 and NS2011013), and China Postdoctoral Science Foundation funded project (no. 20110490389).