Efficient near-field localization aided with reconfigurable intelligent surface using geometric dilution of precision

Figures & data

Figure 1. RIS-assisted network model.

Figure 2. Signal model for RIS-aided localization.

Figure 3. Considered system scenario.

Table

Algorithm I: Proposed Positioning System
Step One:
1. Create the sub-working areas.
2. Create different tile group combinations:
$L_s\left(n\right)=\left(\begin{array}{c}n\\ 3\end{array}\right)+\left(\begin{array}{c}n\\ 4\end{array}\right)+\dots \left(\begin{array}{c}n\\ \overline{n}\end{array}\right)$
where $\overline{n}=n-1$
3. Calculate the GDoP distribution for each combination.
Step Two:
1. Use LS calculations (14) to make an initial estimation for UE location.
${\overline{\mathit{p}}}_{\mathrm{UE}-I}=[\overline{x}\overline{y}\overline{z}{]}^T=({\mathit{A}}^T\mathit{A}{)}^{-1}{\mathit{A}}^T\mathit{B}$
2. Assign the appropriate tile combinations as:
$\mathrm{if}{\overline{\mathit{p}}}_{\mathrm{UE}-I}=[\overline{x}\overline{y}\overline{z}{]}^T$
$\mathrm{Find}{L}_s\left(n\right)=\arg \underset{L_s}{min}\left\{{\mathrm{GDoP}|}_{\mathit{P}={\overline{\mathit{P}}}_{\mathrm{UE}-I}}\right\}$
$\mathrm{end}$
3. Re-estimate UE position using the LS method in (14)

Figure 4. GDoP for 10–60% of total tiles, (a) to (f) respectively, from the largest SNR for ToA measurements in each wall.

Figure 5. GDoP for 10–60% of total tiles, (a) to (f) respectively, from the largest SNR for ToA measurements in each subdivided wall.

Figure 6. GDoP for some combinations use 5% of the tiles on each wall.

Figure 7. GDoP for some combinations use 7% and 3% of the tiles 1st and 2nd wall.

Table 1. Used notations and parameters.

Parameter	Description	Value
$N_e=N_r\times N_c$	No. of elements in the tile	$5\times 20=100$
$N_l$	Total no. of tiles in the RIS	100
$d$	Spacing between each two tiles	20 cm
$N_{\mathrm{sc}}$	No. of pilot symbols	512–1024
T	No. of OFDM pilot transmissions	40–128
$N_t$	Total no. of OFDM subcarriers	2048
$f_c$	Carrier frequency	28 GHz
$\mathrm{\Delta f}$	Subcarrier frequency interval	120 kHz
$P_{\mathrm{Sc}}=P_T/N_t$	Transmitted power per subcarrier	−5 dBm
$N_{\mathrm{tap}}$	No. of multipath taps	10
${\sigma }^2$	The noise power	−120 dBm
$F$	IDFT oversampling	8
B.W	System bandwidth	250 MHz

Figure 8. Empirical CDF of the estimation error for different percentages of selected tiles compared with the proposed GDoP method.

Figure 9. Average localization error vs number of symbols transmission for different percentages of selected tiles compared with the proposed GDoP method (a) The overall CDF curves; (b) enlarged view of CDF curves.

Figure 10. Bar chart for average localization error vs different percentages of selected tiles compared with the proposed GDoP for different number of symbol transmission (T).

Figure 11. The cumulative distribution functions of the GDoP.

Figure 12. Empirical CDF of the estimation error for different numbers of OFDM subcarrier numbers at 60% of the tiles compared with the proposed GDoP method.

Figure 13. Average localization errors for different numbers of OFDM subcarrier at 60%, 70% and 80% of the tiles for SNR method compared with the proposed GDoP method.