Accuracy Bounds for Array-Based Positioning in Dense Multipath Channels

Abstract

The accuracy of radio-based positioning systems will be limited by multipath interference in realistic application scenarios. This paper derives closed-form expressions for the Cramér–Rao lower bound (CRLB) on the achievable time-of-arrival (ToA) and angle-of-arrival (AoA) estimation-error variances, considering the presence of multipath radio channels, and extends these results to position estimation. The derivations are based on channel models comprising deterministic, specular multipath components as well as stochastic, diffuse/dense multipath. The derived CRLBs thus allow an evaluation of the influence of channel parameters, the geometric configuration of the environment, and system parameters such as signal bandwidth and array geometry. Our results quantify how the ToA and AoA accuracies decrease when the signal bandwidth is reduced, because more multipath will then interfere with the useful LoS component. Antenna arrays can (partly) compensate this performance loss, exploiting diversity among the multipath interference. For example, the AoA accuracy with a 16-element linear array at 10.166667emMHz bandwidth is similar to a two-element array at 10.166667emGHz, in the magnitude order of one degree. The ToA accuracy, on the other hand, still scales by a factor of 100 from the cm-regime to the m-regime because of the dominating influence of the signal bandwidth. The position error bound shows the relationship between the range and angle information under realistic indoor channel conditions and their different scaling behaviors as a function of the anchor–agent placement. Specular multipath components have a maximum detrimental influence near the walls. It is shown for an L-shaped room that a fairly even distribution of the position error bound can be achieved throughout the environment, using two anchors equipped with 2×2-array antennas. The accuracy limit due to multipath increases from the 1–10-cm-range at 10.166667emGHz bandwidth to the 0.5–1-m-range at 1000.166667emMHz.

Single-Anchor Positioning: Multipath Processing With Non-Coherent Directional Measurements

“…b(φ) 2 = |c | 2 = 1, we get b(φ) 2 = M . It is seen that an SINR gain by a factor of M is obtained, which is identical to the SINR gain obtained with conventional coherent processing [12], [13].…”

“…• Introduced time delays at antenna elements in relation to the mass point will be only considered in terms of a phase change, i.e., the time delay of the signal envelope will be neglected. This is usually referred to as the narrowband/wideband assumption 3 and it is fair to use since the envelope information is negligible with respect to the phase information, especially in practical situations [11], [13], [14]. We apply these assumptions to obtain the received signal at antenna m via convolution of the spreading function in (1) with the transmitted signal s(t) and antenna response b m (φ)e jζ (m) (φ) resulting in…”

“…COMPARISON TO COHERENT PROCESSING For a conventional antenna array with coherent processing, we obtain (cf. [11], [13])…”

“…Comparison to a uniform linear array with coherent processing and λ/2-spacing [13,Eq. (33)] reveals the same scaling with M and an increase by a factor of π 2 in broadside direction.…”

RadioWeaves for efficient connectivity: analysis and impact of constraints in actual deployments

“…Large intelligent surfaces theoretically provide excellent positioning accuracy. It has been proven however that multi-path components may impact the performance of single array-based systems, particularly near walls [20]. A central planar array typically is never well placed to determine all positions withing its coverage reliably.…”