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The MBS signal can be acquired using similar acquisition hardware as GPS receivers. However, there are differences arising from the time‐slotted structure of the MBS that requires a different acquisition sequence. The MBS signal search space (similar to GPS) consists of PRN, frequency, and code phase. One additional dimension in a TDMA system is slot alignment. The system‐wide preamble portion transmitted by every beacon simplifies the search in the frequency and slot time alignment dimensions so that the search can be completed using low search resources with a single preamble PRN.

The frequency dimension of the search is dominated by the receiver clock ppm uncertainty since Doppler (in contrast to GNSS systems such as GPS) is relatively small. For example, a moving object at 200 kmph directly in the direction of an MBS beacon will experience a Doppler of about ±175Hz (< 0.2 ppm). Just as in a GPS/GNSSS receiver, when external fine time assistance information (such as from the modem) is not available, search over the full code duration needs to be done in the MBS receiver.

As an illustration, the well‐understood GPS search space shown in Figure 39.12 is compared with the MBS search space shown in Figure 39.13. The GPS acquisition search space basically consists of three dimensions: code phase, frequency, and PRN. The code phase search space is defined by the 1 ms CA code, whereas the frequency search space is a combination of satellite Doppler, user Doppler, and receiver clock uncertainty, as shown in Figure 39.12. In assisted GPS, this search space is reduced, potentially, in all three dimensions through rough knowledge of user position, GPS time, and satellite ephemeris/almanac information [10].

Figure 39.12 GPS search space.

The MBS search space also consists of the same three dimensions. However, the search space is effectively reduced to two dimensions when using the preamble for initial acquisition. The optional modulation pattern on the preamble (see Section 9.2 of [8]) can be used to facilitate a more robust slot alignment.

The preamble acquisition enables coarse frequency and code phase acquisition, which reduces pilot/data PRN search requirements. Once the initial preamble acquisition has been performed, the beacon‐specific PRNs need to be searched. The search space in code phase and frequency is reduced to the intersection of the gray boxes in Figure 39.13 (a) and leads to a search space as shown in Figure 39.13 (b) for the beacon PRN search. Once a beacon is detected, the search space for other beacons can be reduced, since their relative ranges in a terrestrial system will always be below the code duration of 1 ms.

Once the beacon pilot/data signal acquisition is complete, the range measurements as well as the trilateration data can be extracted. Ranging is normally done using the pilot section with known modulation, but can also be done using the data section.

Estimating the TOA in terrestrial channels from the beacon is a different challenge when compared to a GPS satellite channel. The channel responses are quite complex due to blockage, diffraction, and reflection from a variety of obstacles creating a mix of LoS and NLoS paths. Figure 39.14 shows sample measured correlation functions measured at the receiver when using a direct‐sequence spread MBS transmission waveform of bandwidth 2MHz. The measurements were carried out in outdoor rooftop locations. The purpose of these figures is to illustrate various common channel scenarios in static outdoor terrestrial scenarios. In the figures, the red vertical line represents the TOA of the true LOS path, whereas the green line represents the TOA of the detected earliest path in the receiver. The x‐axis represents distance in meters, and the y‐axis represents the magnitude of the correlation function. Figure 39.14(a) shows the measured correlation function in the case where the LOS is clearly detectable so that the green and red vertical lines overlap each other. Figure 39.14(b) shows a correlation function for the NLoS scenario with a strong early NLoS path, and Figure 39.14 (c) shows a correlation function for the NLoS scenario with a weak early NLoS path. Note that in both cases the earliest path is not detectable, as shown by the green vertical line (representing the estimated TOA of the earliest detectable path) being to the right of the red vertical marker (true LoS TOA). Observe that in Figure 39.14(b), the earliest detectable path is actually stronger, whereas in Figure 39.14(c), the earliest detectable path is actually weaker.

Figure 39.13 (a) Shows the MBS preamble search space and (b) shows the MBS beacon search space after preamble detection.

Figure 39.14 (a) Shows a correlation function for a scenario with detectable LoS path, (b) shows a correlation function for the NLoS scenario with a strong early NLoS path, (c) shows a correlation function for the NLoS scenario with a weak early NLoS path.

Some additional examples of measured channel correlation functions are shown in Figure 39.15 The x‐axis represents the correlation lag in units of 122 ns (which corresponds to the time duration of a sample when using the sampling rate = 8 × 1.023 MHz chipping rate). From the various plots, a wide variety of channel spreads and types of channels is observed.

Note that there are cases where the earliest path is weaker than the multipath. In order to retain the channel information, a simple two/three tap early‐late‐prompt correlation will not suffice. A multi‐delay correlation function, as shown in Figure 39.15, is required from the receiver to facilitate accurate ranging.

The channel spread statistics help determine the width of the TOA detection correlation window required on the receiver. The choice of window size directly affects the receiver complexity. In order to help this analysis, the percentage of detectable paths within a certain delay (expressed in meters) relative to the signal peak can be analyzed. Note that the simplest way is to center the window using the signal peak as the center of the window. Figure 39.16 shows the channel spread statistics obtained using real measurements for different environments in the San Francisco Bay Area including suburban, urban, and dense urban. The results show that in the suburban environment, a correlation window that includes ±900 m includes 98% of the paths, whereas in a dense urban environment the same window includes only 90% of the paths. 100% percent of paths in all environments fit within the ±1800 m correlation window.

In order to get the best performance in a positioning system, the ranges should correspond to the LoS or the earliest arriving detectable path in the channel response to minimize range bias errors. The MBS system link budget and beacon network plan facilitate high‐resolution range determination to determine the earliest detectable path since the signals are designed to have higher SNRs as compared to GPS systems.