TR Validation with TD-TLM Simulations

We introduce a three dimensional electromagnetic approach to the modeling of TR technique. Time-domain transmission line matrix (TD-TLM) method is used for the computation of the channel response in a rich scattering environment. The time reversed version of the computed channel response is used as the source signal of the transmitting antenna. The electromagnetic solution is repeated to study the characteristic of the TR scheme.

48 Validation of TR Scheme Channel Environment τ_dec,CIR^−40dB (ns) τ_{dec,T R}^{−40 dB} (ns) τ_dec,CIR^−30dB (ns) τ_{dec,T R}^{−30 dB} (ns)

residential LOS 114.5 174 79.6 94

residential NLOS 201.25 183.5 152.8 99.5

office LOS 126.6 101.75 74.37 31.75

office NLOS 118.12 114.75 93.75 52.25

industrial LOS 82.7 121.5 62.75 42.25

industrial NLOS 840.75 469 655.37 54.5

Table 2.2: Time Reversal characteristics with different measurement configurations

Normally, it is expected that k(r) to peak at the intended receiver location atro and decays rapidly with increasing the distance from it.

III. Simulationsetup and results

Fig. 1 shows the modeledenvironment. The dimensions are kept small to minimize the simulation time and memory. All faces are metalselected except the indicated face that is selected as absorbing boundary. The reason is to reduce the delay spreadof the signals and consequently short duration time. The chamber is fed by a vertically polarized bi-conicalantennalocatedatthe lower leftside,16cm overthe floor and20cmdistancefrom the walls. Theantennadimensionsareoptimizedto coverthefrequencyrangeof0.5-3GHzwithagood free-spaceimpedance matching.

Three-dimensional TD-TLM code is used for the solution of Maxwell equations in the propagation environment. The dimensions ofthegridsonthestructuredependingontheregionaredifferent selectedin order topreciselyconstructtheantennamodel and the chamber after thestructurediscretizing.Anarray of11x10ideal isotropic sensors is selected atthe height of30cmfrom the floor.

Theantennais excited byashortpulse withaspectrumthatcoversthefrequencyrangeof0.5-2.5GHzfor 1OdB bandwidth. The simulation is performed and the channelresponsebetween theTXantennaand the virtual sensors are computed. The received waveforms for allpolarization components onthe virtual locations are extracted. Inthissimulation, the total number of cells is 433878, the allocatedmemoryis 57Mbyte and the computation time is 15 minutes. Using time-domain solution based on TLM code has the features of fast computation time and small allocatedmemory.

Im Fig.1Geometryof the modeledenvironment,transmittingantennaand the virtualantennaarray

Examplesof the noise-free instantaneous powerdelay profile (PDP)at twodifferent locations at the center and thecornerof therectangular surface areillustrated inFig.2.As shown, the modeled environment is very dispersiveand the channel responsesaresignificantlydifferent. The transmittedsignalisvertically polarizedbut due to the reflection of thewave from the metallic walls and the chamber corners the received field at the rectangularsurface has allpolarization components. Wehave observed that the average power ofz-polarization componentis 2.5 and 1.5 timesmorethan the average power ofx-andy-polarizations,respectively.

Inthe second simulationstep,thecomputed z-polarizedwaveform at the center of therectangularsurface is selected for TR test. Thepreviouslydefined discretized model is used and theelectromagneticsimulationsare

repeated by introducing the novel waveform at the antenna excitation port. Fig.3 shows the received instantaneousPDP of theequivalent TRchannelatthe selected location. Asshown, theresponseof the TR systemiscompressedintime.Therefore, the complex task of estimatingalarge number oftaps atthe receiver is

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Figure 2.7: Simulation setup

2.2.3.1 Simulation Setup

Fig. 2.7 shows the modeled environment which has the dimensions of 1.8 m×1m× 0.75m. The dimensions are kept small to minimize the simulation time and memory.

In the selected environment, all faces are metallic except the indicated face that is selected as an absorbing boundary. Such an environment is selected to study the per-formance of TR scheme in the presence of both reflective and absorbing boundaries.

Furthermore, such a selection also reduces the delay spread of the signals and conse-quently the simulation time. The chamber is fed by a vertically polarized bi-conical antenna located at the lower left side, 16 cm over the floor and 20 cm distance from the walls. The antenna dimensions are optimized to cover the frequency range of 0.5−3 GHz with a good free space impedance matching. To simulate the receiver, an array of 11×10 ideal isotropic sensors is selected at the height of 30 cmfrom the floor.

Three-dimensional TD-TLM code is used for the solution of Maxwell equations in the propagation environment. The transmitting antenna is excited by a short pulse

0 20 40 60 80 100 120 0

0.5 1 1.5 2

Time (ns)

PDP

(a)

0 20 40 60 80 100 120

0 0.5 1 1.5 2

Time (ns)

PDP

(b)

Figure 2.8: Normalized PDP of the CIR with TD-TLM simulation at a) corner of the rectangular surface b) center of the rectangular surface

with a spectrum that has a 10dB bandwidth of 0.5−2.5GHz. The channel response between the transmitting antenna and the receiving virtual sensors are simulated.

The received waveforms for all polarization components on the virtual locations are extracted. The simulation uses 433878 number of cells and has an allocated memory of 57M B. The simulation time is in the order of 15 minutes. Time-domain solution based on TLM code has the features of fast computation time and small allocated memory.

2.2.3.2 Simulation Results

The noise-free instantaneous power delay profile (PDP) at two different locations, i.e.

at the center and the corner of the rectangular surface is shown inFig. 2.8. It can be seen that the modeled environment is very dispersive and the channel responses are significantly different. The transmitted signal is z-polarized but due to the reflection of the wave from the metallic walls and the chamber corners, the received field at the rectangular surface has all polarization components. We have observed that the average power of z-polarization component is 2.5 and 1.5 times more than the average power of x- and y-polarizations respectively.

In the second simulation step, the computed z-polarized waveform at the center of the rectangular surface is selected for TR simulation. The model achieved in the last step is used and the electromagnetic simulations are repeated by introducing the novel waveform at the antenna excitation port. Fig. 2.9 shows the received instantaneous PDP with the TR scheme at the selected location. As expected, the simulated TRR is quite compressed in time.

To compare the characteristics of the simulated TRR, total excited signal power for the simulation of the CIR and TRR is normalized to a constant. A FG of 14 dB is observed for the simulated environment. The SSR of the time compressed signal is 6 dB. Fig. 2.10 shows the instantaneous PDP of the TR channel at the

in-1140 116 118 120 0.2

0.4 0.6 0.8 1

Time (ns)

Normalized PDP

Figure 2.9: Normalized PDP of the TRR with TD-TLM simulation

1000 105 110 115 120

0.02 0.04 0.06 0.08 0.1

Time (ns)

Normalized PDP

X−polarization Y−polarization Z−polarization Scaled by 0.1

Figure 2.10: Normalized peak power with the TR scheme in a square surface with TD-TLM simulation

tended location for different polarizations, x, y and z. For the sake of comparison, the PDP of z-polarization is scaled by 0.1. As shown, the peak power with the intended polarization (z-polarization) is extremely large than the other polarization compo-nents. This result shows the possibility to imply polarization diversity in multiple antenna configuration for example, TR multiple-input single-output (TR-MISO) or TR multiple-input multiple-output (TR-MIMO) systems.

Spatial focusing is another inherent property of the TR scheme. This means that the spatial profile of the power peaks at the intended location and decays rapidly away

−16

Figure 2.11: Normalized PDP with the TR scheme with TD-TLM simulation for x, y and z polarizations

from it. To illustrate this property, the received peak power is computed as a function of space. The intended signal is at the center of the rectangular surface. The signal for the intended signal is transmitted and the received signal is measured over whole of the rectangular surface. Fig. 2.11 shows the 2-D plot of the normalized received peak power (normalized to the peak power at the intended receiver) over the given surface. As shown, the maximum spatial focusing gain is generated at the intended location and the gain decreases non-symmetrically in x and y-axis directions away from it. The focusing zone is more concise in x-axis direction compared to y-axis direction due to the presence of two metallic walls of the chamber in x-axis direction which make large number of reflections. On the other hand, in y-axis direction, the reflections are limited by the absorbing boundary. This find may be applicable to determine the field angle of arrivals in multi-path propagation environments.

2.3 Semi Measurement Approach for TR