# Analysis of Dual-Band Direction of Arrival Estimation in Multipath Scenarios
## 2 Dual-Band DoA Approach  
DoA is a well-known technique commonly used for localization [17; 18] in many communication systems [19] such as WiFi [20], Bluetooth [21] and Ultra-Wide Band [22].  
Among all the possible approaches proposed to simplify the positioning infrastructure and improve accuracy, the DoA technique shows the advantage of combining the use of a limited number of nodes with a simple estimation algorithm.  
In particular, DoA approaches implementing the Space Division Multiple Access (SDMA) technique, based on phaseless Received Signal Strength Indicator (RSSI), represent efficient and effective solutions for indoor localization applications [23; 24]. The integration of RSSI measurement circuits in almost every legacy transceiver [25; 26] makes this approach really worthwhile.  
Among the various DoA estimation strategies available in the literature, the most effective are those based on Maximum-Likelihood (MLH) criteria [27; 28]. These well-known methods solve the estimation problem by comparing the power of the impinging signal vector with the predicted power distribution, estimated from the beam-set of the anchor antenna [29]. The calculated DoA becomes the one that minimizes a cost function based on the difference between the actual signal and the predicted one. This approach allows real-time estimations, even with ultra-low hardware resources, given the extremely reduced computational cost of the algorithm.  
Unfortunately, DoA approaches are heavily influenced by critical multi-path effects [30], since the angular distribution of signals may be widely different from that expected because of undesired signal contributions originating from the latter.  
Over the years, solutions to minimize these effects have been proposed and demonstrated. In particular, in previous papers [16; 31; 32], the authors have suggested a solution based on combination of Frequency Division Multiple Access (FDMA) approach along with RSSI-based DoA techniques. The results illustrated in those papers show an improvement in system performance with respect of complex real-life scenario, hardly affected by multi-path issues. Specifically, in [16] the authors shown, through a series of experiments, how a DoA approach based on two uncorrelated frequencies leads to a robust improvement of the DoA estimation.  
The idea behind the suggested dual-band DoA solution refers to the assumption that for any given scenario, it is well known that there is a very low probability for signals at two uncorrelated frequencies to be equally affected by multi-path. Unfortunately, the severity of these non-idealities cannot be determined a-priori. It is a matter of fact that it is difficult to fully demonstrate the real benefits of a dual-band approach making use exclusively of measurement-based experiments.  
The aim of this paper is to illustrate an analysis environment capable of correctly predicting the improvement introduced by the use of a dual-band system approach in a multi-path affected complex scenario, where the first line of multi-path is the one which downgrade the system performance harder than the other components. Consequently, the core of the proposed environment consists of modeling the first line effects by means of a full-wave simulation. Multipath effects are described making use of a two-ray reflection model exploited in [33]. The introduction of the present technique of analysis gives the system designer an effective a-priori method that reduces the on-site verification step. The use of rigorously modeled full-wave analysis within the simulation environment leads to an excellent agreement, in terms of performance improvements compared with the experimental results already shown in previous literature [16].