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A discussion about which of the two factors, rich multipath (in NLOS) or signal-to-noise ratio (SNR) (usually in LOS), affects the Multiple-Input Multiple-Output (MIMO) channel capacity more is presented in this paper. This interesting discussion is investigated by performing simulations using simple circle scatterer model and WINNER II channel model. And the simulation shows that these two factors behave differently as the channel condition varyies. When the scatterer number in channel is low, the high receive SNR is more important to capacity. The multipath richness will have greater influence when the scatterer number exceeds a certain threshold. However, the channel capacity will not change much as the scatterers continue to increase.

Multiple-Input Multiple-Output (MIMO) is a hot research topic that has always attracted much attention in recent decades. When multiple antennas are deployed at both transmit side and receive side, the performance of communication system can be enhanced significantly.

The MIMO performance highly depends on the propagation environments and channel model structures. Two channel conditions, that is, NLOS (Non-line-of-sight) and LOS (Line-of-sight), are commonly used in propagation research. In general, if a strong LOS path exists in environment, it is called the Ricean channel. If there is no LOS path, the receive signal will follow Rayleigh distribution. In Rayleigh assumption, the multipath is scattered by the rich scatterers uniformly distributed around the receiver. And the multipath richness is important for MIMO system, for it will provide a large number of eigenvalues of MIMO channel. While in LOS scenario, generally the LOS path is stronger than scattering components and leads to a high receive SNR which will also contribute to MIMO capacity. But a high SNR associated with LOS often implies a low degree of scattering which, however, will cause the capacity loss again. This paper is going to talk about whether the rich multipath or high receive SNR is more important to MIMO capacity.

The discussions about which of these two factors is more important have started in the literature. Wallace and Jensen discuss the MIMO capacity variation with SNR and multipath richness using full-wave indoor finite-difference time domain (FDTD) simulations [

To avoid the Rayleigh channel model limitation that the scatterers’ distribution is ideal and does not agree well with the real case, the circle scatterer model and WINNER II channel models are used in this paper, for they can be manipulated flexibly and are much closer to the real case that the multipath is a kind of sparse in real channel. Although a general geometry-based stochastic model, consisting of two-ring and ellipse scatterers with single-bounce and double-bounce paths, is proposed in [

The paper is organized as follows. In Section

This model is aimed at generating multiple-point scatterers around the receiver. The scatterers can be placed in a circle with the receiver in the center. The receive signal consists of the waves scattered once by each point scatterer. The basic simulation idea is to calculate the complex envelop for each possible combination of transmit and receive antennas, like what Figure

Circle scatterer model.

The general representation of the complex envelop received at antenna

The WINNER II channel model is a geometry-based stochastic channel model, which can generate an arbitrary MIMO channel matrix for defined scenarios. It is ray-based double directional multilink and antenna-independent model for MIMO systems. The statistical distributions of channel parameters such as AoA (Angle of Arrival), DoA (Angle of Departure), delay spread, and delay values are obtained from channel measurements. In the simulation, the parameters are determined stochastically from the distributions for each channel sample. Fixed 20 rays compose a cluster, which is considered as a propagation path diffused in space domain. The channel impulse response coefficients are generated by combining contributions of all rays which are characterized by small scale parameters.

One single link of the WINNER II channel model is illustrated in Figure

WINNER II channel model.

The channel response for cluster

A MIMO system model can be expressed as

According to the information theory, the ergodic capacity is given by [

The channel also can be divided into several parallel independent subchannels by the method of SVD. The number of subchannels is the same as the number of singular values and the gains of these subchannels are related to the value of the singular values. Hence, the total channel capacity can be obtained by summing the capacities of all the subchannels. In that case, the ergodic capacity can be expressed as follows [

If the sum of

The power allocation strategy also affects the capacities of the subchannels. There are two strategies in common use, waterfilling algorithm and equal power allocation scheme [

In this section, based on the formula described above, the performance of MIMO capacity with different scatterer number, that is, different multipath richness, is investigated in simulations. Meanwhile, the effect of scatterer number on MIMO channel structure is shown as well.

The simulation of this model is depicted in Figure

Circle scatterer model setup.

The effects of NLOS and LOS with different Ricean

MIMO capacity comparison.

The reason of MIMO capacity change is that multipath richness and LOS power (also Ricean

Eigenvalues comparison in NLOS.

Eigenvalues comparison in LOS.

D2 scenario (rural moving networks) is used in the simulation. It represents radio propagation in environments where both the access point and the receiver are moving at very high speed in a rural area. A typical example of this scenario occurs in carriages of high-speed trains where wireless coverage is provided by the so-called moving relay stations (MRSs). Hence, There are two parts in D2 scenario: D2a (BS-MRS) and D2b (MRS-MS). WINNER II defines D2a as LOS case which has 8 clusters. The parameters in D2b scenario are not defined in WINNER II but it recommends using the parameters in D1 scenario (rural macrocell) instead. So, D2b is typically seen as NLOS case with 10 clusters. In the simulation, the distance between BS and MS is 500 m, and the height of BS and MS is 32 m and 1.5 m, respectively. The velocity of MS is limited at 55.56 m/s in LOS and 10 m/s in NLOS. The carrier frequency is 5.25 GHz and the wavelength is 0.057 m. The SNR is set to 20 dB as well. 4 × 4 antennas are used and they are separated by 1 cm at each side. In this scenario, Ricean

Figure

MIMO capacity comparison.

Figures

Eigenvalues comparison in LOS.

Eigenvalues comparison in NLOS.

Hence, in this WINNER channel model simulation, the path number (cluster number) does not affect the capacity as much as the former model.

In this paper, the effect of rich multipath and high receive power on MIMO channel capacity is investigated. A simple circle scatterer model and WINNER II channel model are used to simulate the channel matrix. From the simulation results, it can be seen when the scatterer number exceeds a certain threshold, the multipath richness prevails over the high receive SNR. When the scatterers are few, the high receive SNR is more important. However, the multipath richness will have little influence on capacity as the scatterers continue to increase.

The project is supported by the Program for New Century Excellent Talents under Grant NCET-09-0206, the National Natural Science Foundation of China under Grant 60830001, the Key Project of State Key Laboratory of Rail Traffic Control and Safety under Grants RCS2008ZZ006 and RCS2011ZZ008, Program for Changjiang Scholars and Innovative Research Team under Grant no. IRT0949, the Project of State Key Laboratory of Rail Traffic Control and Safety under Grants RCS2008ZT005 and RCS2010ZT012, Beijing Natural Science Foundation (4112048), and “the Fundamental Research Funds for the Central Universities” under Grants nos. 2010JBZ008 and 2011YJS010.