RESUMO DAS OPERACIÓNS REALIZADAS POLOS CENTROS. Exercicio 2009

Tapped-delay line (TDL) channel models

Propagation channel models are aimed to realistically represent the physical channel.

In this sense, the multipath CIR is typically modelled defining a tap for each physical ray. Every tap is determined by a complex amplitude and a time delay. In mobile communications, the standard multipath models for single-antenna transmission are the so-called tapped-delay line (TDL) models [Pro00]. Indeed, the LTE technology adopts specific TDL models inherited from second- and third-generation mobile communications, i.e. GSM and UMTS, based on the ITU-R M.1225 [ITU97] recommendation and the 3GPP TS 05.05 [3GP11] specification for GSM. But, they are extended to be applied with the wide bandwidth of LTE signals. The TDL models are based on several multipath re ections characterized by fixed taps delays tk, relative average power RPk for every tap, and Doppler spectrum. Their channel impulse response is defined as

hc(t) =

Lc−1

X

k=0

hkδ (t− t^k− t^ǫ) , (3.5.1)

where L_cis the number of taps of the channel, h_k is the complex gain for the k-th path, t_k is the tap delay relative to the first tap (i.e. t0 = 0), and tǫ is the time delay introduced by the channel (i.e. the time delay of the first arriving ray). The channel coe cients hk

of these models are typically time-varying with a Rayleigh distribution, and following a classical Jakes Doppler spectrum S(f ),

S(f )∝

s 1

1− (f/fD)², for f ∈ [−fD, f_D] , (3.5.2) being fD the maximum Doppler shift. Considering the highest speed to be supported in LTE as v = 500 km/h [3GP06] and a carrier frequency fc = 2 GHz, the maximum Doppler shift expected is fD = fc· v/c ≃ 927 Hz, being c the speed of light. Thus, the 50% coherence time is computed using Clarke's model [Rap02], and results in

Tcoh,50% = r 9

16π · 1

fD ≃ 0.46ms. (3.5.3)

Particularly, the 3GPP consortium agreed, in [R4-07], on the use of the Pedestrian A and Vehicular A channels from [ITU97], and the Typical Urban (TU) channel from [3GP11], in order to model three reference environments characterized by a low, medium and large delay spread, respectively. Nevertheless, they were designed for a 5 MHz op-erating bandwidth, and an apparent periodicity appears in their frequency correlation properties for higher bandwidths [Sor05]. Thus, the LTE standard has adopted since 2007 an extension of the ITU and 3GPP models by following the procedure described in [Sor05], resulting in the Extended Pedestrian A (EPA), Extended Vehicular A (EVA) and Extended Typical Urban (ETU) channel models. The main parameters of these models, i.e. fixed delay t_k and relative average power RP_k, are specified in Annex B of TS 36.101 [3GP14a] and TS 36.104 [3GP12c], and shown in Table 3.2. These specifications also define maximum Doppler shifts for each model to represent low, medium and high mobile conditions, e.g. EPA 5 Hz, EVA 5 Hz, EVA 70 Hz, ETU 30 Hz, ETU 70 Hz, and ETU 300 Hz. Finally, the TDL models can be applied to multiple antenna schemes by introducing spatial correlation matrices, as it is discussed in [R4-06], resulting on a simple LTE MIMO channel model.

Geometric-based stochastic channel models (GSCM)

The LTE channel can also be modelled with geometric-based stochastic channel models (GSCM). These are more complex models based on the geometry between base station, mobile station and scatterers following a stochastic construction, as is shown in Figure 3.12. The GSCM models are widely adopted for MIMO channel modelling, e.g. COST

Table 3.2: LTE tapped-delay line channel model parameters.

Tap EPA channel EVA channel ETU channel k tk (ns) RPk (dB) tk (ns) RPk (dB) tk (ns) RPk (dB)

1 0 0.0 0 0.0 0 -1.0

2 30 -1.0 30 -1.5 50 -1.0

3 70 -2.0 150 -1.4 120 -1.0

4 90 -3.0 310 -3.6 200 0.0

5 110 -8.0 370 -0.6 230 0.0

6 190 -17.2 710 -9.1 500 0.0

7 410 -20.8 1090 -7.0 1600 -3.0

8 1730 -12.0 2300 -5.0

9 2510 -16.9 5000 -7.0

259 channel model [Mol06], COST 273 channel model [Cor06], COST 2100 channel model [Ver11], 3GPP spatial channel model (SCM) [3GP03], or the WINNER channel model [Ky•o07]. Indeed, the ITU-R M.2135-1 [ITU08] recommendation for the evaluation of IMT-Advanced systems is based on the WINNER channel model, which is able to operate on bandwidths from 5 MHz to 100 MHz. According to this recommendation, the deployment scenarios are classified as indoor hotspot, urban micro-cell, urban macro-cell and rural macro-cell. Depending on the scenario selected, large-scale parameters, such as delay spread, angle spread or shadow fading, are randomly generated following the distributions specified in Table A1-7 of [ITU08]. Then, the small-scale parameters, such as delay, power, AoA and angle of departure (AoD), are randomly distributed for each cluster of propagation rays (i.e. rays with similar delay and directions). Both large- and small-scale parameters are fixed during each channel segment (i.e. the so-called drop). Finally, the time-variant channel realisations of a drop are generated according to the random initial phases of the scatterers. Using the MATLAB software described in [Hen07], the power-delay profile (PDP) density is computed for WINNER B1 and C2 scenarios, as it is shown in Figure 3.13, by using 1000 realisations and NLoS propagation conditions.

Limitations of current channel models

Given the previous two examples of channel models, the LTE (i.e. EPA, EVA and ETU) and the WINNER channel models are compared in Table 3.3. The TDL and GSCM models represent the most typical channel models of current literature. Nevertheless,




Figure 3.12: Scheme of the geometry-based stochastic channel model [Ses11, p.443].

0 50 100 150 200 250

Path gains PDP density

0

0 500 1000 1500 2000 2500 3000

0

Path gains PDP density

0

Figure 3.13: Example of power-delay profile density of the WINNER B1 and C2 scenarios.

they are designed for communications purposes, and do not cover important features for positioning applications. First, the time-delay o set between the base station and the user is not considered in these models, thus the bias produced in NLoS conditions is not modelled. And second, the channel impulse response is not time-continuous, thus the time evolution of the CIR is not completely implemented. Recently, extensions of the WINNER channel model are being studied to jointly model satellite and terrestrial scenarios including these missing features, such as the quasi deterministic radio channel generator (QuaDRiGa) described in [Bur14] and developed under ESA MIMOSA activity (see [Ebe13]), or as proposed by Wang et al. in [Wan12b].