Channel characteristics of MIMO–WLAN communications at 60 GHz for various corridors
- Shu-Han Liao^{1},
- Chien-Ching Chiu^{1}Email author,
- Chien-Hung Chen^{2} and
- Min-Hui Ho^{1}
https://doi.org/10.1186/1687-1499-2013-96
© Liao et al.; licensee Springer. 2013
Received: 27 June 2012
Accepted: 30 January 2013
Published: 2 April 2013
Abstract
A comparison of 4 × 4 multiple-input multiple-output wireless local area network wireless communication characteristics for six different geometrical shapes is investigated. These six shapes include the straight shape corridor with rectangular cross section, the straight shape corridor with arched cross section, the curved shape corridor with rectangular cross section, the curved shape corridor with arched cross section, the L-shape corridor, and the T-shape corridor. The impulse responses of these corridors are computed by applying shooting and bouncing ray/image (SBR/Image) techniques along with inverse Fourier transform. By using the impulse response of these multipath channels, the mean excess delay, root mean square (RMS) delay spread for these six corridors can be obtained. Numerical results show that the capacity for the rectangular cross section corridors is smaller than those for the arched cross section corridors regardless of the shapes. And the RMS delay spreads for the T-and the L-shape corridors are greater than the other corridors.
Keywords
MIMO–WLAN Corridors SBR/image Mean excess delay RMS delay spread1. Introduction
In recent years, there has been a growing interest in the development of potentially mass-producible wireless systems using millimeter waves, such as wireless local area networks (WLAN) systems [1]. To develop millimeter-wave wireless LAN systems, however, we need to know the reflection and transmission characteristics in millimeter-wave bands so that we can evaluate indoor multipath propagation characteristics and the interactions of millimeter waves with various objects. Many propagation characteristics have extensively been studied, and several models have focused on specific indoor environments [2, 3]. Lee and Bertoni [4] use a hybrid ray-mode conversion model for the L-bend and T-junction, respectively, for a 900-MHz signal in a 4-m wide tunnel.
Channel capacity of multiple-input multiple-output (MIMO) for wireless communications in a rich multipath environment is larger than that offered by conventional techniques [5–9]. Channel capacity of WLAN transmission or MIMO transmission has been discussed separately in many literatures. However, there are only few papers dealing with channel capacity of MIMO–WLAN transmission. In [10], the feasibility of dual-polarized antennas in the MIMO system has been validated for indoor scenarios.
This article addresses basic issues regarding the wireless LAN systems that operate in the 60-GHz band as part of the fourth-generation (4G) system [11]. The 60-GHz band provides 7 GHz of unlicensed spectrum with a potential to develop wireless communication systems with multi Gbps throughput. The IEEE 802.11 standard committee [12], one of the major organizations in WLAN specifications development, established the IEEE 802.11ad task group to develop an amendment for the 60-GHz WLAN systems.
All wireless systems must be able to operate in a multipath propagation channel, where object in the environment can cause multiple reflections to arrive at the receiver. In general, effective antenna selection and deployment strategies are important for reducing bit error rate in indoor wireless systems [13, 14]. In general, the transmission quality is estimated with strength of power in the narrowband communication system. Besides, a prior knowledge of the characteristics of the channel is necessary for understanding how the signal is affected in the environment. Therefore, many techniques of channel calculation have been developed in recent years. Especially, using ray-tracing method to obtain impulse response is extensively applied [15–17]. The different values of dielectric constant and conductivity of materials for different frequencies are carefully considered in channel calculation.
The remainder of this article is organized as follows. In Section 2, system description and channel modeling are presented. Several numerical results are included in Section 3. Section 4 gives the conclusion.
2. System description
2.1. Channel modeling
The two steps described in the following two subsections are used to calculate the multipath radio channel.
2.1.1. Frequency responses for sinusoidal waves by SBR/image techniques
The SBR/image method can deal with high-frequency radio wave propagation in the complex indoor environment [18, 19]. It conceptually assumes that many triangular ray tubes are shot from the transmitting antenna (TX), and each ray tube, bouncing, and penetrating in the environment is traced in the indoor multipath channel. If the receiving antenna (RX) is within a ray tube, the ray tube will have contributions to the received field at the RX, and the corresponding equivalent source (image) can be determined. By summing all contributions of these images, we can obtain the total received field at the RX. In real environment, external noise in the channel propagation has been considered. The depolarization yielded by multiple reflections, refraction, and first-order diffraction are also taken into account in our simulations. Note that the different values of dielectric constant and conductivity of materials for different frequencies are carefully considered in channel modeling.
where p is the path index, N_{ p } is the total number of paths, f is the frequency of sinusoidal wave, θ_{ p } (f) is the p th phase shift, and α_{ p } (f) is the p th receiving magnitude. Note that the transmitting and receiving antenna are modeled as a WLAN antenna with simple omni-directional radiation pattern and vertically polarized. The channel frequency response of WLAN can be calculated from Equation (1) in the frequency range of WLAN.
2.1.2. Inverse fast Fourier transform and hermitian processing
The frequency response is transformed to the time domain by using the inverse fast Fourier transform (IFFT) with the Hermitian signal processing [30]. By using the Hermitian processing, the pass-band signal is obtained with zero padding from the lowest frequency down to direct current (DC), taking the conjugate of the signal, and reflecting it to the negative frequencies. The result is then transformed to the time domain using IFFT [31]. Since the signal spectrum is symmetric around DC. The resulting doubled-side spectrum corresponds to a real signal in the time domain.
Using ray-tracing approaches to predict channel characteristic is effective and fast, and the approaches are also usually applied to MIMO channel modeling in recent years [26, 32]. Thus, a ray-tracing technique is developed to calculate the channel matrix of MIMO system in this article.
2.2. System description
where X, Y, and W denote the N_{ t } × 1 transmitted signal vector, the N_{ r } × 1 received signal vector, and the N_{ r } × 1 zero mean additive white Gaussian noise vector at a symbol time, respectively, H is the N_{ r } × N_{ t } channel matrix and h_{ ij } is the complex channel gain from the j th transmitting antenna to the i th receiving antenna.
where U and V* are the N_{ r } × N_{ r } and N_{ t } × N_{ t } unitary matrices, D is a N_{ r } × N_{ t } rectangular matrix whose diagonal elements are non-negative real values and other elements are zero and the symbol * in Equation (4) stands for the conjugate transpose or Hermitian operation.
Note that there is no adding or subtracting of any signal power in the system, because $\stackrel{\u02c6}{V}$ and $\stackrel{\u02c6}{U}$ are both unitary matrices.
where I is an appropriately sized identity matrix. SNR_{ t } is the ratio of total transmitting power to noise power. N_{ t } is the number of transmitting antennas. B is the bandwidth of the narrowband channel and the symbol * in Equation (6) stands for the conjugate transpose. The equation is especially effective to calculate MIMO capacity in a mathematical software package, since the channel capacity needs CSI for the receiver only.
where BW is the total bandwidth of WLAN and N_{ f } are the numbers of frequency components.
where ‖·‖_{ F } denotes the matrix Frobenius norm, Tr{·} denotes the matrix trace, and λ_{ k } are the eigenvalues of the eigenmatrix R_{ H }. Eigenmatrix can provide information about the relative strengths of the independent transmission modes supported by the MIMO. It is well known that high spatial correlation between sub-channels can reduce the number of significant eigenvalues of eigenmatrix. In other words, just one significant eigenvalue exists with perfect correlation between sub-channels, and N_{ m } significant eigenvalues exist with perfect independence between sub-channels. As a result, the number of significant eigenvalues determines the spatial degrees of freedom and the corresponding channel capacity.
where ${\overrightarrow{\lambda}}_{k}$ is the eigenvalue vector. If total transmitting power is spread equally between all the transmitting antennas, then a system that has highest channel capacity is the one with all the singular values equal. In other words, the eigenvalues are identically equal to P_{ H }/N_{ m }, a uniform power allocation strategy optimizes the channel capacity of MIMO-NB system. Furthermore, a channel matrix is said to be well conditioned if its condition number is close to 1, and the elements of the vector ${\overrightarrow{\lambda}}_{k}$, here are close to each other. As a result, a well-conditional channel matrix can facilitate communication.
3. Numerical results
Dielectric properties of concrete materials measured at 60 GHz
Materials | Relative permittivity | |||
---|---|---|---|---|
Real | Imaginary | Conductivity | Tan loss | |
ε' | ε'' | σ | Tan(δ) | |
Concrete | 6.4954 | 0.4284 | 1.43E+00 | 6.60E–02 |
The transmitting and receiving antennas in these six different corridors are both short dipole antennas and vertically polarized. The positions of transmitting antenna (TX) for these corridors are shown in Figures 4, 5, 6, and 7 with the fixed height of 1.5 m. There are 270 receiving points for each corridor. The locations of receiving antennas in these six different corridors are distributed uniformly with a fixed height of 1 m. The distance between two adjacent receiving points is 0.25 m.
A three-dimensional SBR/image technique has been presented in this article. This technique is used to calculate the WLAN channel impulse response for each location of the receiver. Based on the channel impulse response, the number of multipath components, the root mean square (RMS) delay spread τ_{RMS}, and the mean excess delay τ_{MED} are computed.
where $G={\displaystyle \sum _{n=1}^{N}{\left|{a}_{n}\right|}^{2}}$ is the total multipath gain.
By Equations (10) and (11), we can obtain the RMS delay spreads and MED.
In this article, the capacity versus SNR_{ t } for these six corridors is calculated. Here, channel capacity is the average information rate over the ensemble of channel realizations. There are 270 receiving points for each corridor. In truth, the capacity in Equation (7) can be calculated by equal transmitting powers in these six different corridors. SNR_{ t } is the ratio of total transmitting power to noise power for 270 receiving points. As a result, the channel realizations for various receiving locations are combined into one ensemble with 270 samples.
MIMO can dramatically increase channel capacity not only due to the beamforming gain and diversity gain, but also MIMO spatial multiplexing technique makes full use of multipath fading. Furthermore, a channel matrix is vitally interrelated to calculate the received power. As a result, the capacity can be increased substantially in straight shape corridors with rectangular and arched sections.
Parameters of multipath channel for the six different geometrical configurations of corridors
Shapes | τ_{MED}(ns) | τ_{RMS}(ns) | ||
---|---|---|---|---|
Mean | Standard deviation | Mean | Standard deviation | |
Rectangular straight | 0.83 | 0.35 | 1.65 | 0.54 |
Arched straight | 0.97 | 0.45 | 1.46 | 0.42 |
Rectangular curved | 1.68 | 1.59 | 1.90 | 0.54 |
Arched curved | 1.76 | 1.51 | 1.47 | 0.49 |
L-shape | 4.48 | 5.06 | 2.59 | 0.73 |
T-shape | 5.60 | 5.37 | 2.47 | 0.78 |
The τ _{ RMS } and τ _{ MED } for these six corridors with 10 and 50 reflections
Shapes | τ_{MED}(ns) | τ_{RMS}(ns) | ||
---|---|---|---|---|
Mean (10 reflections) | Mean (50 reflections) | Mean (10 reflections) | Mean (50 reflections) | |
Rectangular straight | 0.83 | 0.845 | 1.65 | 1.668 |
Arched straight | 0.97 | 0.989 | 1.46 | 1.475 |
Rectangular curved | 1.68 | 1.702 | 1.90 | 1.928 |
Arched curved | 1.76 | 1.785 | 1.47 | 1.491 |
L-shape | 4.48 | 4.516 | 2.59 | 2.629 |
T-shape | 5.60 | 5.645 | 2.47 | 2.515 |
4. Conclusions
Comparison is made of 4 × 4 MIMO–WLAN communication characteristics for corridors of different shapes and cross sections. The frequency dependence on materials utilized in the structure on the indoor channel is accounted for in the channel simulation. The MED and RMS delay spread for six different channels are computed by the SBR/image method and inverse Fourier transform. Numerical results are given for the capacity varying with channel shapes and cross sections. Furthermore, we find that the capacity for the rectangular straight and arched straight corridors is greater than corridors of other shapes. The capacity for T-shape corridor is smallest among all shapes. The RMS delay spread for arched straight corridor is smaller than those corridors regardless of the shapes. It is found that the RMS delay spread for the T-shape corridor is the largest. Besides, the RMS delay spread for arched cross section corridors are less than those for rectangular cross section corridors regardless of the shapes.
Declarations
Authors’ Affiliations
References
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