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The spectrum of the multiband OFDM signal for a time-based ranging system, consisting of M bands.
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Context 1
... τ 1 , α 1 and τ 2 , α 2 denote the delay and gain of the LoS path and the reflection, respectively. Now, we consider that M OFDM signal bands are available for time delay estimation, as shown in Fig.1. First, we derive the CRLB based on a single band OFDM signal r m [n; θ] (e.g., obtained from the m-th band), which is written by ...
Context 2
... n denotes the sample index, i and N respectively denote the index of the subcarrier and the total number of subcarriers in each band, c i denotes the data modulated on the i-th subcarrier, f m denotes the central carrier frequency of the m-th band (see Fig.1). In addition, M denotes the total number of signal bands available in the signal spectrum, e denotes the complex additive white Gaussian noise (AWGN). ...
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Citations
... To the best of our knowledge, there is little literature refers to designing the multiband sensing system parameters at the transmitter for the purpose of improving the sensing performance limits. In [20], the authors proposed a sparse subbands selection methodology for ranging based on the performance bound CRB. However, it only involves subbands selection with fixed system parameters. ...
... From (37), we can observe that the FIM J η depends on the relative delay, e.g., τ 2 − τ 1 , rather than on the absolute delay, which agrees with the results of [20], but the phase distortions are not considered in their model. Besides, the FIM is irrelevant to the true values of phase distortion factors δ and ϕ. ...
Multiband sensing is a promising technology that utilizes multiple non-contiguous frequency bands to achieve high-resolution target sensing. In this paper, we investigate the fundamental limits and optimization of multiband sensing, focusing on the fundamental limits associated with time delay. We first derive a Fisher information matrix (FIM) with a compact form using the Dirichlet kernel and then derive a closed-form expression of the Cramer-Rao bound (CRB) for the delay separation in a simplified case to reveal useful insights. Then, a metric called the statistical resolution limit (SRL) that provides a resolution limit is employed to investigate the fundamental limits of delay resolution. The fundamental limits of delay estimation are also investigated based on the CRB and Ziv-Zakai bound (ZZB). Based on the above derived fundamental limits, numerical results are presented to analyze the effect of frequency band apertures and phase distortions on the performance limits of the multiband sensing systems. We formulate an optimization problem to find the optimal system configuration in multiband sensing systems with the objective of minimizing the delay SRL. To solve this non-convex constrained problem, we propose an efficient alternating optimization (AO) algorithm which iteratively optimizes the variables using successive convex approximation (SCA) and one-dimensional search. Simulation results demonstrate the effectiveness of the proposed algorithm.
... Also, to derive the FIM for the propagation delay, the complex gain is assumed to be known a priori. In [33], the FIM for the propagation delay in a two path channel has been derived as follows, ...
... Using the full model (27), Fig. 6(a) shows the corresponding scaling factor sin −1 (ϑ) in the standard deviation of the LoS gain estimator, which is derived from (31). When the measure of dependence |s(τ 2,1 )| = 1, the LoS component a 1 and the reflection component a 2 will be fully dependent, and sin(ϑ) = 0 (see (33)), then the complex gain will be poorly estimated. Using a larger virtual signal bandwidth can reduce the measure of dependence for close-in reflections. ...
This paper presents a methodology to design a sparse multiband ranging signal with a large virtual bandwidth, from which time delay and carrier phase are estimated by a low complexity multivariate maximum likelihood (ML) method. In the estimation model for a multipath channel, not all reflected paths are considered, and time delay and carrier phase are estimated in a step-wise manner to further reduce the computational load. By introducing a measure of dependence and a measure of bias for a multipath reflection, we analyse the bias, precision and accuracy of time delay and carrier phase estimation. Since these two indicators are determined by the signal pattern, they are used to formulate an optimization for signal design. By solving the optimization problem, only a few bands from the available signal spectrum are selected for ranging. Consequently, the designed signal only occupies a small amount of signal spectrum but has a large virtual bandwidth and can thereby still offer a high ranging precision with only a small bias, based on the low-complexity simplified ML method. Numerical and laboratory experiments are carried out to evaluate the ranging performance of the proposed estimation method based on sparsely selected signal bands. Relative positioning, in which we only measure a change in position, based on either the time delay estimates or the carrier phase estimates, is presented as a proof-of-concept for precise positioning. The results show that positioning based on only 7 out of 16 signal bands, sparsely placed in the available spectrum, achieves a decimeter level accuracy when using time delay estimates, and a millimeter level accuracy when using carrier phase estimates. Compared with the case of using all available bands, and without largely decreasing the positioning performance, the computational complexity when using the sparse multiband signal can be reduced by about 80%
... The platform has been tested and validated through indoor ToA ranging experiments in a corridor located at the TU Delft campus. More experimental results using this testbed can be found in [37] and [38]. In [37], a ranging system based on sparse selection of narrow signal bands is presented and validated using the testbed. ...
... More experimental results using this testbed can be found in [37] and [38]. In [37], a ranging system based on sparse selection of narrow signal bands is presented and validated using the testbed. This work aims at increasing the bandwidth occupancy efficiency using a CRLB constrained convex optimization to select the frequency bands. ...
For validation and demonstration of high accuracy ranging and positioning algorithms and systems, a wideband radio signal generation and acquisition testbed, tightly synchronized in time and frequency, is needed. The development of such a testbed requires solutions to several challenges. Tight time and frequency synchronization, derived from a centrally distributed time-frequency reference signal, needs to be maintained in the hardware of the transmitter and receiver nodes, and wideband signal acquisition requires sustainable data throughput between receiver and host PC as well as data storage at GB level. This paper presents a testbed for wideband radio signal acquisition, for validation and demonstration of high accuracy ranging and positioning. It consists of multiple Ettus X310 USRPs and supports high accuracy (<100 ps) time-deterministic, sustainable signal transmission and acquisition, with a bandwidth up to 320 MHz (in dual channel mode) and frequencies up to 6 GHz. Generation and processing of wideband arbitrary signal waveforms, is done offline. To realize these features, RFNoC compatible HDL units were developed for integration in the X310 SDR platform. Wideband transmission and signal acquisition at a lower duty cycle is applied to reduce the data offloading throughput to the host PC. Benchmarking of the platform was performed to demonstrate sustainable long duration dual channel acquisition. Indoor range measurements with synchronous operation of the testbed show a decimeter-level accuracy.
In integrated sensing and communication (ISAC) systems, communication signals are supposed to provide high-resolution sensing services. Toward this goal, multiband sensing has recently emerged as a promising technology that jointly utilizes multiple noncontiguous communication bands to improve the sensing performance of ISAC systems. In this article, we first introduce the multiband signal model in the presence of phase-distortion factors, discussing the challenges and benefits of multiband sensing to reveal its intrinsic properties. Then, we investigate the resolution limit and discuss a specific sensing algorithm design of multiband sensing technology, which is designed to leverage multiband gains to achieve high-resolution sensing performance. Finally, a series of open research topics is discussed, which may bring new insights for future research on multiband sensing for ISAC.
