Channel Model

A suitable propagation channel model is important for numerical analysis. It models how the transmit signals propagate through the air space. Thus, we follow the channel model to characterize radio effects in the 3GPP LTE-A environment [22] and introduce each parameter in the following section.

3.1.1 Spatial Channel Model

The spatial channel model (SCM) is widely used in LTE-A systems simulation [25, 26]. In the early years, the International Telecommunication Union Radiocommu-nication Sector (ITU-R) channel model was developed for the International Mobile Telecommunications-2000 (IMT-2000) systems. However, the ITU-R channel model is not well-defined due to the renewed parameters, such as bandwidth, frequency

band. Moreover, the ITU-R model is not suitable for the MIMO systems since it does not model the spatial correlation between antennas. Hence, SCM has been de-veloped to model the channel more correctly. As we know, SCM characterizes the spatial correlations as well as the multi-path fading. In the following, we discuss the formulations and parameters of SCM briefly.

The urban-macro scenario is adopted in our SCM simulations [22]. The macro-cell usually serves a large area, and hence the probability of experiencing a line-of-sight (LOS) environment tends to zero. Therefore, the LOS component can be neglected.

Assume that there are N paths with each consisting of M subpaths in each link from the BS to the user. We introduce each parameter in Fig. 3.1:

θ_BS : the angle between the LOS and the BS array broadside.

θ_{U ser} : the angle between the LOS and the user array broadside.

δn,AoD : the angle between the LOS and the n^th (n = 0, 1, 2, ..., N − 1) path.

δ_n,AoA : the angle between the LOS and the n^th (n = 0, 1, 2, ..., N − 1) path.

∆_n,m,AoD : the offset of the m^th (m = 0, 1, 2, ..., M − 1) subpath within the n^th path relative to δ_n,AoD.

∆_n,m,AoD : the offset of the m^th (m = 0, 1, 2, ..., M − 1) subpath within the n^th path relative to δn,AoA.

θ_V : the angle between the user movement direction and the user array broadside.

θ_n,m,AoA : θ_n,m,AoA = θ_{U ser}+ δ_n,AoA + ∆_n,m,AoA. θ_n,m,AoD : θ_n,m,AoA = θ_BS+ δ_n,AoD+ ∆_n,m,AoD.

Assuming Nt transmit antennas at BS and Nr receive antennas at user, we can

Figure 3.1: SCM parameters of the user and base station. where P_nis the power of the n^th path, θ_n,m,AoD is the angle between the m^th subpath within the n^th path and the BS array broadside, θ_n,m,AoA is the angle between the m^th subpath within the n^th path and the user array broadside, M is the number of subpaths per path, k is the carrier wavelength in meters, ds is the distance from the first antenna to the s^th antenna at the BS in meters, d_u is the distance from the first antenna to the u^thantenna at the user in meters, ψ_n,m is the phase of the m^thsubpath within the n^th path with uniform distribution in the interval [0^◦, 360^◦], V is the user

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speed, and θ_V is the angle between the user movement direction and the user array broadside.

Note that (3.1) is defined in the time domain. In order to apply the OFDM system, we must transform the time domain channel response into frequency do-main. Let N_{F F T} denote the fast Fourier transform (FFT) size. The SCM for the k^th subcarrier in the frequency domain can be formulated as

H^SCM(k) =

Each element of H(k) can be written as H^u,s(k) = F F T [

h^u,s,1(t), h^u,s,1(t), ..., h^u,s,N(t)]

, (3.4)

where H^u,s(k) denotes the channel response coefficient from the s^th transmit antenna to the u^th receive antenna in the k^th subcarrier, F F T denotes the FFT function with size N_{F F T}, and h^u,s,n(t) was shown in (3.2).

3.1.2 Radio Environments

Directional antenna pattern, path-loss model, and shadowing model are considered in our radio environment. A horizontal antenna pattern is defined for each fixed sector in 3GPP LTE-A systems [22]. It can be shown as

A^dB_s,b,u(ϕ) =− min

where ϕ_s,b,u is the angle between the beam direction of the s^th BS and the u^th user in the b^th sector, ϕ_3dB is 70 degrees, and A_m is 25 dB. Note that ϕ_3dB denotes the 3 dB power attenuation angle. Figure 3.2 shows the antenna pattern in simulation.

Figure 3.2: Horizontal antenna pattern for the 3GPP macro-cell.

Pathloss is the power attenuation when transmitting signals through the space. The pathloss model is usually represented as the difference between the transmit signal power and the receive signal power in decibels. The path-loss model has been defined for the macro-cell in [22] :

P L^dB_s,b,u = 128.1 + 37.6log₁₀(d_s,b,u), (3.6) where P L^dB_s,b,u is the power-loss term between the s^th BS and the u^th user in the b^th sector, and d is the distance from the s^th BS to the u^th user in the b^th sector in kilometers. The shadowing effect is caused by obstacles. It is modeled by the log-normal distribution with zero mean and 8 dB standard deviation.

For simplicity, we describe our following channel model in the single-carrier case. It can be extended to the multi-carrier case in the same way. Let Hs,b,u ∈ C^Nr×Nt denote the overall channel response including the spatial channel model and radio

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effects. Thus, we can derive the overall complex baseband channel response as H_s,b,u= H^SCM

√

η_s,b,uA_s,b,u(P L_s,b,u)⁻¹ , (3.7) where H_s,b,u is the channel response from the s^th BS to the u^th user in the b^th sector, H^SCM ∈ C^Nr×Nt is the SCM matrix shown in (3.3), η_s,b,uis the log-normal distribution shadowing with zero mean and 8 dB standard deviation, A_s,b,u = 10(^AdBs,b,u/¹⁰), and P L_s,b,u= 10(^{P LdBs,b,u}/¹⁰).