A Site-Specific MIMO Channel Simulator for Hilly and Mountainous ...

2013 IEEE Military Communications Conference

A Site-Specific MIMO Channel Simulator for Hilly and Mountainous Environments

Jonathan S. Lu and Henry L. Bertoni NYU WIRELESS Center Polytechnic Institute of New York University Brooklyn, New York, U.S.A. [email protected] and [email protected]

arrival and departure of each multipath arrival (direct, ground reflected, terrain scattered and terrain diffracted) between all TX and RX antenna pairs. The total phase of a terrain scattered arrival for an antenna pair, is determined by the propagation path length and additional phase incurred by scattering. Because available terrain databases have resolution (> 30m) larger than the UHF wavelengths (< 1m) considered in this work, the total phase cannot be deterministically known. Thus, the additional phase is modeled with a uniformly distributed random variable [5] and the path length is found from the geometry of the antennas with the center of the terrain element. Note that even though the total phase of this arrival cannot be deterministically known, the relative phases of this arrival between all antenna pairs are known from the different path lengths. After determining the multipath information of all arrivals, our simulator forms the MxN channel matrix in time or frequency domain. To demonstrate the use of the proposed simulator, we investigate the feasibility of MIMO communications in rural environments using Monte Carlo simulations of 2x2 MIMO radio links in many different types of terrain. An overview of the SISO channel simulator is presented in Section II. The methodology of our MIMO channel simulator is given in Section III, along with closed form expressions for the tapped delay line coefficients and channel frequency response in terms of the channel impulse response. The setup and procedure of the Monte Carlo simulations using our MIMO channel simulator is given in Section IV. The results of the Monte Carlo simulations are analyzed in Section V.

Abstract— This paper presents a real-time site-specific MIMO channel simulator for communication links in rural environments. This simulator first predicts the delay, angle of arrival and departure, and amplitude of the individual multipath arrivals (direct, ground reflected, terrain diffracted, and terrain scattered) for a specified multiple antenna receiver and transmitter link. The predicted multipath characteristics are then used to compute the tapped delay line coefficients and/or frequency responses of the channel between each transmitter antenna and receiver antenna pair, which are the outputs of the simulator. To demonstrate the use of this simulator, Monte Carlo simulations of SISO and MIMO channel capacity for many databases are performed. Conclusions are drawn on the relationship between capacity, terrain roughness and other channel characteristics. Keywords— MIMO Channel Modeling, Mobile, Mountainous Terrain, Rural Propagation, Terrain Scattering

I.

INTRODUCTION

Scattering from terrain can result in a rich multipath radio environment for radio links located in hilly or mountainous terrain [1]. To efficiently predict the multiple-input-multipleoutput (MIMO) channel in rural terrain for UHF band (300 MHz – 3 GHz) military communications, a real-time sitespecific MIMO channel simulator, which accounts for the scattering from terrain, was created from our previously developed site-specific propagation single-input-single-output (SISO) simulator. Previously proposed empirical MIMO channel models [2],[3] simulate the time domain channel in the form of tapped delay lines. The SUI channel model A [2] is the only one to consider hilly terrain. It was developed from 1.9 GHz measurements [4] taken in flat to hilly terrain with light to heavy tree density for fixed wireless applications. The transmit antenna heights in these measurements ranged from 12 to 79 m while the receive antenna height was 2 m. Because of the high antenna heights, relatively gentle terrain and fixed links, this model may only apply to specific radio scenarios in which the line-of-sight (LOS) is dominant. Thus, we have developed a real-time channel simulator which can apply to a greater range of radio scenarios and terrain, while accounting for the sitespecific environment. For a MxN MIMO link, where the mobile transmitter (TX) has N antennas and the mobile receiver (RX) has M antennas, our proposed simulator utilizes the previously developed SISO simulator [1] to predict the local area amplitude, and angles of 978-0-7695-5124-1/13 $31.00 © 2013 IEEE DOI 10.1109/MILCOM.2013.135

II.

RURAL ENVIORNMENT SISO CHANNEL SIMULATOR

In this section we provide an overview of the previously developed SISO channel simulator for rural environments [1]. This simulator is used to predict the local area RMS voltage amplitudes ap, angles of arrival and departure, and initial propagation delays Rp/c of the p = 0,1, .. P arrivals. Here c is the speed of light. A. Vertical Plane Model The Terrain-Integrated Rough Earth Model (TIREM) [6] is used to predict the received power from rays lying in the vertical plane (VP) containing the TX and RX. For line-ofsight (LOS) links, the dominant waves in the vertical plane travel along the direct and ground reflected paths.

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σ (θ1 , θ 2 ) = γ cos m (θ1 ) cos m (θ 2 ) ,

On non-LOS (NLOS) links where one or more ridges separate the TX and RX, radio waves diffract over the ridges. For one diffracting edge, TIREM uses Bullington’s approximation to the 4-Ray diffraction expression [7]. For multiple edges, the Epstein-Peterson method is used [8]. In both LOS and NLOS cases, waves scattered from the troposphere and surface waves are also accounted for [6]. At the higher frequencies and shorter ranges of interest here, these latter effects are not of importance. The RMS voltage amplitude a0 of the VP contribution is found by taking the square root of the TIREM predicted power. The delay of this VP arrival R0/c is also returned by TIREM. Note that in the case of LOS, there may be two rays, but the arrival time will be nearly equal since the separation between the antennas is usually large compared to the antenna heights relative to the ground. Parameters used for TIREM in our simulations are: Earth’s surface conductivity = 0.01S/m; Surface humidity near the antennas = 7.5 g/m3; Surface refractivity = 289; Relative permittivity of earth’s surface = 15; Polarization is VV.

and is seen to satisfy the symmetry condition. In this study we have chosen m = 1 and  = 0.1 (-10 dB) as in [1]. The value of  is independent of frequency when the wavelength is on the order of the surface roughness, or smaller [5]. Thus, aside from the weak frequency dependence associated with diffraction, the ratio of the scattered power to VP power will be nearly independent of frequency in the UHF band where wavelength is less than the expected surface roughness. C. Terrain Visibility Algorithm To apply the bi-static equation (1) to a radio link, we have developed an efficient visibility (viewshed) algorithm to search for the terrain elements visible to both the TX and RX viewshed algorithm. A detailed description of our algorithm can be found in [1]. To increase processing speed of the algorithm by taking advantage of fast integer operations, we approximate the TX and RX locations by their nearest terrain points (correcting for the effect of this assumption on delay and path length is discussed below). Along with “pre-treating” the terrain database, computation time of the terrain scattered contributions and vertical plane contributions is on the order of a mili-second.

B. Terrain Scattering Model For NLOS cases in mountainous or hilly environments, radio waves are expected to be very weak after diffracting over the mountains or hills between the TX and RX. In these cases, scattering from terrain elements visible to both the transmitter and receiver may give significant contributions. Terrain surfaces in hilly and mountainous areas are rough for frequencies in the UHF band. Thus incident radio waves on a terrain surface element are scattered into many directions in addition to the specular direction. For the case when P terrain surface elements have LOS with both TX and RX, the RMS voltage amplitude ap as a result of scattering from the pth terrain element is [5],[9]-[11]

ap =

Pt

λ 2 σ Ap . (4π ) 3 R p21 R p2 2

(2)

III.

RURAL ENVIORNMENT MIMO CHANNEL SIMULATOR

In this section, we present the methodology of our MIMO channel simulator for rural environments using the outputs of the SISO channel simulator discussed in Section II. This MIMO channel simulator predicts the MxN channel matrix in time domain and frequency domain when given the positions of a transmitter array (TX) with N antennas and a receiver array (RX) of M antennas in a terrain database. Also presented in this section are expressions for SISO and MIMO wideband channel capacity. These expressions are used later in our Monte Carlo simulations.

(1)

A. Channel Inpulse Response The (i, j) element of the time domain channel matrix is the baseband channel impulse response hij(t |c) between the ith RX antenna and the jth TX antenna. hij(t |c) can be approximated as a sum of impulses [12], [13] by treating each of the VP and the terrain scattered arrivals to arrive at distinct time intervals.

Here the TX and RX antennas are assumed to be isotropic (Antenna Gain = 1). Also, Rp1 and Rp2 are the distances in meters from the pth terrain element to the TX and RX antennas, respectively. They correspond to a propagation delay Rp/c = (Rp1 + Rp2)/c. The area of the pth terrain element is Ap and its normalized scattering coefficient is . Propagation paths that undergo two or more scatterings, or scattering plus diffraction are expected to be significantly weaker and are not considered. The bi-static scattering coefficient  of a surface element is dependent on the directions (1, 1) to the TX and the directions (2, 2) to the RX, the surface roughness compared to the wavelength, as well as the dielectric constant of the material. In order to satisfy reciprocity, the dependence of  on the two sets of directions must be symmetric. Measurements conducted on surfaces whose statistics are isotropic have found that  is nearly the same for both horizontal and vertical polarizations of the electric field, and the total scattered power depends on the angles 1,2 from the normal, but is independent of the azimuthal angles 1,2 [5]. The generalized Lambert’s Law is commonly used for the scattering coefficient. It is given by

P

hij (t ,τ | ωc ) = ¦ a p e p e jθ

− jωcτ ijp

e

jω p t

δ (τ − τ ijp ) .

(3)

p =0

Here p = 0 refers to the VP contribution from TIREM and p = 1,2, …, P refer to the terrain scattering contributions. Also, ap is the RMS voltage amplitude of the pth multipath ray, p is the additional phase caused by diffraction/scattering in radians, p is its Doppler frequency shift in Hz, and ijp is the propagation delay from the ith RX antenna to the jth TX antenna in seconds. c is the carrier frequency in Hz. As discussed previously, the phase p is modeled as a uniform random variable having values on the interval (0, 2]. This random distribution of the phase has been reported in [5].

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To determine the values of ap, p and ijp, the SISO channel simulator discussed in Section II, is fed the TX and RX positions inside a database. The simulator then returns ap, gridpoint to gridpoint delay Rp/c, and arrival and departure angles for each of the P + 1 multipath as if RX is located at its nearest grid-point and TX is located at its nearest grid-point. The amplitude ap is the square root of the power Pr(p) of the th p multipath and is the same for each TX-RX antenna pair (i, j). This approximation is valid because the separation of TX antennas and separation of RX antennas are all small relative to the multipath distances from the TX to RX. Furthermore, ap is assumed to be frequency independent over the UHF band as discussed in Section II.B. The delay of the pth multipath ray from the grid point nearest the TX array to the grid point nearest the RX array is Rp/c. To determine the delay ijp traveled by the pth multipath ray, we need to simply account for the additional delays caused by the distance offset ‫ݎ‬Ԧ௝ ȉ ݇ሬԦ௣்௑ Ȁห݇ሬԦ௣்௑ ห traveled by the ray from the jth TX antenna to the TX grid-point and the distance offset th ‫ݎ‬Ԧ௜ ȉ ݇ሬԦ௣ோ௑ Ȁห݇ሬԦ௣ோ௑ ห from the RX grid-point to the i RX as seen in th Fig. 1. Here ‫ݎ‬Ԧ௝ is a vector from the j TX antenna to the TX grid-point and ‫ݎ‬Ԧ௜ is a vector from the RX grid-point to the ith RX antenna. ݇ሬԦ௣்௑ Ȁห݇ሬԦ௣்௑ ห and ݇ሬԦ௣ோ௑ Ȁห݇ሬԦ௣ோ௑ ห are unit vectors in the direction of propagation that contain the angle of departure and angle of arrival information of the pth multipath ray output by the SISO simulator, respectively. Thus

τ ijp =

G G G G G G R p + r j