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The downlink performance and capacity of distributed antenna systems (DASs) with multiple receive antennas are investigated in multi-input multi-output (MIMO) fading and multicell environment. Based on the moment generating function and performance analysis, an exact closed-form expression of DAS ergodic capacity is derived, and it includes the existing capacity expression as a special case. Moreover, a simple closed-form approximate expression of ergodic capacity is also derived by using the Taylor series, and it has the performance result close to the exact expression. Besides, the outage capacity of DAS is analyzed, and an exact closed-form expression of outage capacity probability is derived. All these expressions can provide good theoretical performance evaluation for DAS. Simulation results corroborate our theoretical analysis.

As a promising technique for future wireless communications, the distributed antenna system has received considerable attention in recent years. It can significantly improve the system capacity and cell coverage and reduce power consumption in comparison with traditional centralized antenna systems, and thus it has become one of the key technologies in next generation mobile communication systems such as 3G-LTE (long term evolution) and IMT-advanced [

Although, in all these studies, the DAS capacity is well analyzed, only limited work has been carried out for DAS in the multicell environment. Especially, the capacity analysis of DAS with multiple antennas at the mobile station (MS) for multicell environment is not provided in the existing literature. Motivated by the above reasons, in this paper, we will address the downlink capacity study of DAS with multiple receive antennas in the multicell environment and focus on the derivation of accurate capacity expressions of DAS in multi-input multi-output (MIMO) Rayleigh fading channel. By using the moment generating functions (MGF) and Taylor series expansion, the exact and approximate closed-form expressions of ergodic capacity for DAS are derived, respectively. Besides, the outage capacity of the system is analyzed, and the corresponding outage probability is derived. As a result, an exact closed-form expression of outage probability is achieved. For a given outage probability, a practical iterative algorithm based on Newton’s method for finding the outage capacity is proposed. Based on these theoretical expressions, the downlink capacity performance of DAS can be effectively evaluated. Moreover, the derived exact capacity expression avoids the error in the existing theoretical expression. Computer simulation shows that our exact expressions can match the simulation result very well, and the approximate expression is also close to the exact one.

The notations we use throughout this paper are as follows. Bold upper case letters denote matrices.

In this paper, we consider the distributed antenna systems with multiple receive antennas in a multicell environment. The main processing modules are centralized at a central unit and are connected with distributed antennas (DAs), and each of these DAs is also called an access point (AP). Through coaxial cables, fiber optics, or radio links, all the APs are connected with a home base station (BS) [

The transmitters from home BS and six APs and the receivers from MS construct a macroscopic MIMO fading channel, and channel matrix of the

Let the transmitted signal vector be

In this section, we will give the downlink capacity analysis of the DAS in a multicell environment. The ergodic capacity at a given location of the target mobile station can be expressed as^{(0)} and can be given by a diagonal matrix

Using (

Substituting (

Utilizing the equality

Let

Using

To further simplify the calculation in (

Substituting (

In this section, we will give the outage capacity analysis of the DAS in a multicell environment and derive the corresponding outage probability. Since the channel capacity is a random variable, it is meaningful to consider its statistical distribution. A useful measure of statistical characteristic is the outage capacity [

Substituting (

Using the incomplete Gamma function

This is an exact closed-form expression of outage probability of DAS in the multicell environment, which is shown to match the simulation well. For a given outage probability

In the following, we express solving the outage capacity from (

There are many methods such as bisection for finding the root of a strictly monotonic function. We propose to use Newton’s method to find the root iteratively because it has the quadratic convergence rate. Newton’s method is described as follows:

In addition, the proposed analysis method for the downlink capacity can be easily extended to the uplink case by the appropriate transformation and mathematical calculation, and correspondingly, closed-form expressions of ergodic capacity and outage probability of DAS uplink can be derived, respectively. Thus, some similar results can be obtained. Here, we no longer give specific details due to much more similarities.

Simulation results are provided to evaluate the effectiveness of the derived capacity expressions. We set the pathloss exponent

Figure

Ergodic capacity versus the normalized distance from the home BS.

In Figure

Comparison between exact and approximate ergodic capacity.

In Figure

Outage probability versus the normalized distance from the home BS.

Figure

Outage capacity versus the normalized distance from the home BS.

We have studied the downlink performance and capacity of DAS in MIMO fading and multicell environment. The MGF and PDF of SINR of the system are derived. Based on these results, exact and approximate closed-form expressions of the ergodic capacity of DAS are obtained, respectively. The exact expressions include the existing expression with single receive antenna as a special case and correct minor error of the latter. Moreover, according to the outage capacity analysis of the system, an exact closed-form expression of outage probability is also derived. Newton’s method is proposed to find the outage capacity value for a given outage probability. Computer simulation shows that the derived theoretical expressions can match the simulation results well, and the application of multiple receive antennas can obviously increase the system capacity. Thus, these expressions provide good performance evaluation for DAS in the multicell environment and avoid the conventional need for numerical integration or Monte Carlo simulation.

The authors would like to thank for the anonymous reviewer and Associate Editor for their valuable comments and suggestions, which greatly improve the quality of this paper. The work was supported in part by National Natural Science Foundation of China (61172077), Doctoral Fund of Ministry of Education of China (20093218120021), Fundamental Research Funds for the Central Universities (NS2012075), National Key Project of Chinese Ministry of Science and Technology (2009ZX03003-006-03), and Shanghai Municipal Natural Science Foundation (10ZR1436000).