Luận án Location-aware multipath-based channel prediction for next generation wireless communication systems

Nội dung text: Luận án Location-aware multipath-based channel prediction for next generation wireless communication systems

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7. APPENDICES A. Description of channel measurement campaigns A.1. Measurement campaign 1 Frequency Domain Measurements - Vector Network Analyzer Frequency-domain measurements have been obtained with a Rhode & Schwarz ZVA- 24 VNA. The frequency range has been chosen as the full FCC bandwidth from 3.1 to 10.6 GHz (corresponding to a wavelength range of 9.67 cm to 2.83 cm), resulting in a delay resolution of 0.1333 ns and a spatial resolution of 4 cm. At the l-th trajectory position, a sampled version Hl[k] of the CTF Hl(f) with a frequency spacing of ∆f is measured. The VNA has been calibrated up to (but not including) the antennas with a through-open-short-match (TOSM) calibration. The FCC bandwidth has been measured for different discrete frequencies with a frequency resolution of 1.5 MHz.The transmit power has been set to 15 dBm. Measurement Post Processing For the VNA measurements, the major system influences on the measured CTF H(f) have already been removed by the previously mentioned TOSM calibration. This includes cables and connectors, but not the antennas, which are considered as part of the transmission channel. The necessary post-processing tasks reduce to a filtering of the signal to select a desired frequency band out of the FCC range and to downconvert the signal transformed to time domain to obtain a baseband signal. The filtering is done with a baseband pulse s(t) that covers the desired bandwidth. The CTF is measured at Nf discrete frequencies fk = k∆f +fmin, k = 0, , Nf 1, − where fmin is the lowest measured frequency. This sampled CTF H[k] corresponds to a Fourier series representation of the time-domain CIR h(τ) [121], which is periodic with a period of τmax. With f0 and fc denoting the lower band edge and the center frequency −1 of the extracted band, respectively, and using an IFFT with size NFFT = (∆f∆τ) , ⌈ ⌉ where ∆τ is the desired delay resolution, the time domain equivalent baseband signal is obtained as −j2π(fc−f0)t r(t) = IFFTN H[k]S[k] e . (A.1) FFT { } Here, S[k] is the discrete frequency domain representation of the pulse s(t) in the desired frequency range. This procedure is similar to [122]. 81
8. 6 uwin 4 A2 2 p rwin 0 ym −2 lwall lwin −4 −6 −8 A278 −5 0 5 10 15 20 xm (a) Overview of floorplan 5 4 A2 cpill 3 p 2 ym 1 pl 0 −1 −2 2 4 6 8 10 12 xm (b) Close-up of floorplan Figure A.1: Scenario floor-plan: a physical anchor is located at position a1 and an examplary VA is at position a . The gray grid with positions p indicates the measurement grid with 5 5 cm spacing; 2 ℓ × the red dot indicates its center position p, the actual mobile agent position used in the illustration. Blue lines depict specular reflections at wall segments. 83
9. 11 segment 1 10 segment 2 segment 3 segment 4 9 (1) segment 5 a5 segment 6 F E 8 D segment 7 C B A phys. anchor 7 VA 6 (1) a(1) D† a(1) a 5 4 p 1 2 4 C† -direction in meter y 3 B† 2 φk 1 (2) (2) (2) A† a a a4 1 2 C∗ 0 B∗ A∗ 1 − (2) a3 2 − 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1 − − − − − − − − − − − − − x-direction in meter Figure A.3: Floor plan of the evaluation scenario. Bold black lines denote walls, thick gray lines represent glass windows, other lines illustrate other materials. Two blue crosses represent the physical anchors; orange circles denote virtual anchors (VAs) which were considered in the experimental vali- dation. An agent moves along a trajectory segmented into seven parts indicated with distinct colors. Capital letters (with or without mark or ) refer to sub-segments of different materials along each ∗ † wall. 85
10. Figure A.5: Calibration setup for time domain measurements up to (but not including) the antennas. Hence, the influence of the device internal transfer functions and the measurement cables and connectors, combined in the transfer function Hsys,i(f) for the i-th RX channel, as well as the crosstalk between TX channel and i-th RX channel, Hcross,i(f), have to be compensated. For the further description, we will drop the channel index. To achieve this, two types of measurements are necessary. First, to determine the crosstalk, the TX antenna is unmounted and the TX port is terminated with a 50Ω match and the crosstalk signals are measured. Second, also the RX antennas are unmounted and TX and RX cables are connected. In this way, Hmeas(f) = Hsys(f) + Hcross(f) are measured. Using the measurement configuration with all the antennas as depicted in Figure A.5 yields Hmeas(f) = H(f)Hsys(f)+Hcross(f). Hence, a calibrated version of the radio channel transfer function is obtained as Hmeas(f) Hcross(f) H(f) = − . (A.2) Hsys(f) Hcross(f) − To avoid excessive noise gain, we use a thresholding on the time-domain representation of the denominator in (A.2) and set samples below the threshold to zero. The time domain signal is obtained by an inverse Fourier transformation. Finally, the time- domain signal within the desired frequency range around the center frequency fc can be computed using a suitable baseband pulse shape s(t) as  j2πfct −j2πfct r(t) = h(t) s(t)e e δ(t τshift) (A.3) ∗ ∗ − Here, τshift is a time shift that accounts for the delays of connectors in the calibration 87
11. C. Predicted Variance ∗ ∗ The predicted variance V[y(ϕk(p )) k, θk] at position p approximates the variance |D of the SMC amplitude values, which relates to the DMC term in (2.7) for position p∗. ∗ Assuming the Gaussian approximation to hold for αˆk(p ) , we have | | ∗ 1 ∗
    ∗
    2 V[ψ(ϕk(p )) k, θk] Sν(τk; p )Tp + N0 dk(p ) . (C.8) |D ≈ 2 ∗ 1 While the PDP Sν(τk; p ) decreases with delay τk = c dk(p), the squared distance ∗
    2 dk(p ) will be increasing, implying a counteracting effect. The left-hand side is independent of the distance. We can thus re-write the equation to illustrate the shape ∗ of the PDP as a function of τk at some angle ϕk, 2 S (τ ; ϕ∗)T [ψ(ϕ∗) , ] N . ν k k p 2 2 V k k θk 0 (C.9) ≈ τk c |D − This result indicates a reciprocal squared decay in contrast to the usually assumed exponential decay. On the other hand, from Appendix B, by neglecting measurement noise, we have:  2  2 E νk(p) + wk(p) E νk(p) = TpSν(τk; p) (C.10) | | ≈ | | So, the predicted variance obtained from GPR can be validated by comparing with the DMC power, c.f. equations (C.8-C.9). 89