1 Introduction
2 Proposed localization method
2.1 CSI from MIMO-OFDM receivers as location information
2.2 Proposed algorithm
2.2.1 Obtaining an effective CFR
2.2.1.1 Obtaining a reflection-rich CFR for contiguous subcarriers
2.2.1.2 Obtaining parameters of sinusoids
2.2.1.3 Transforming a reflection-rich CFR
2.2.2 Search for the best location
2.3 Some remarks
2.3.1 AOA-based localization
2.3.2 Effect of MT velocity
2.4 CRLB for two-dimensional systems with linear-type arrays
3 Numerical results and discussions
3.1 Multipath propagation model
Model D | Model E | ||
---|---|---|---|
First-tap k-factor (dB) | NLOS |
\(-\infty \)
|
\(-\infty \)
|
LOS | 3 | 6 | |
RMS delay spread (nm) | NLOS | 50 | 99 |
LOS | 47 | 95 | |
Maximum delay spread (nm) | NLOS | 390 | 730 |
LOS | 390 | 730 |
3.2 Common assumptions and search method
3.3 Selection of algorithm parameters
3.4 Implications of σ 0 and CSI interpolation
3.5 Comparison with other methods
3.6 Effect of infrastructure conditions
M=2 |
M=4 | ||
---|---|---|---|
B (MHz) | 40 | 3.9 m; 13.79 % | 2.8 m; 9.90 % |
80 | 2.0 m; 7.07 % | 1.8 m; 6.36 % | |
160 | 1.2 m ; 4.24 % | 1.1 m ; 3.89 % |
4 Recommendations for further study
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Validation with real measurements: In this paper, the localization performance of the proposed algorithm was evaluated on the basis of statistical indoor channel models specifically obtained for benchmarking data communication systems. It is much more relevant to evaluate the performance on the basis of real measurements or a statistical indoor channel model specifically obtained from real measurements for benchmarking AOA-based localization systems. Therefore, performance validation with real measurements is very important.
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Other super-resolution methods: Estimating the frequencies of all the sinusoids in the CFRs plays a major role in obtaining an effective CFR for the proposed algorithm. Although the MPM is used in this paper because it directly addresses the problem of interest, we believe that other super-resolution methods should also be studied in this regard.
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Using a priori knowledge in estimation: In this paper, estimating the parameters of all the sinusoids in the CFRs plays a major role in obtaining an effective CFR. Such estimation has been performed without considering a priori knowledge about the parameters, i.e., their statistical models. Note that such knowledge may be used to improve the estimation performance in general, as discussed in [16]. Applying such knowledge to the proposed algorithm is an interesting direction for further study.
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Optimal parameters for the algorithm: In this paper, the values of the algorithm parameters L and ρ were selected for simply demonstrating the basic working performance of the proposed algorithm. Actually, the optimal values could depend on variable conditions of the radio channel and infrastructure. These effects are also worthy of further study.
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Problem of NLOS: In addition to bandwidth availability and multiple-antenna configuration, an essential requirement for the proposed algorithm to work is the availability of LOS in the radio channel. In this regard, the availability required is just sufficient for triangulation. This requirement is the same as for the ultrawideband-based localization regime [19, 20]. Several methods for mitigating the problem of LOS availability have been presented in the literature. These methods are based on the detection of channel condition. By applying the detection of channel condition, we may simply ignore an AP if the detection result declares unavailability of LOS. We could then expect performance degradation on the basis of the results shown in Fig. 9, or encounter an outage if the number of usable APs is less than two. We note that the signal processing results obtained using the proposed method are employed as observation data for the detection of channel condition. However, a detailed study of such detection is beyond the primary scope of the present paper and it is therefore recommended for future work.
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AOA bias induced by diffraction: In the present study, the effect of diffraction caused by building components, such as walls, is ignored. If not properly managed, this effect may degrade the performance of the proposed algorithm by introducing a bias into the AOA of a direct path, as well as the performance of the ultrawideband-based localization regime by introducing a bias into the time of arrival of a direct path. Therefore, further investigation is required to efficiently mitigate such a bias.
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MT velocity effect: As discussed in Section 2.3.2, a detailed analysis of the effect of MT velocity on the localization performance should be carried out in a future study.
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Simple way to obtain the effective CFR: Note that a n,m obtained using the proposed algorithm by solving (13) is an estimation of \(\phantom {\dot {i}\!}g_{\textit {\text {n,q}}}e^{-j\phi _{\textit {\text {n,m,q}}}}\). Therefore, according to (7), a 0,m is also an estimation of G m,q . Then, it might be better to save computation by using a 0,m as G m,q , instead of obtaining G m,q from (16). This issue also requires further investigation in order to observe its possible effects on the localization performance.