alt="Schematic illustrations of (a) the MBS preamble search space and (b) shows the MBS beacon search space after preamble detection."/>
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.
39.1.4.3 Position Calculation
The MBS system facilitates accurate 3D position computation. Since the MBS is a network of tightly synchronized beacons, trilateration can be done using pseudoranges determined from time‐stamped TOA measurements from the beacons and the beacon coordinates available from the beacon data.
The range equation in 3D space from the receiver to the transmitter is given by
(39.1)
The location of the transmitters is given by (xi, yi, zi), and the unknown location of the mobile units is given by (X, Y, Z) in some local coordinate frame. The pseudorange measurement has a receiver time bias additive term as well, so that the usual pseudorange measurement equation can be written as
(39.2)
where c is the speed of light, and Δt corresponds to the receiver time bias. Traditionally, a minimum of four pseudorange measurements would be required for 3D trilateration to solve for the four variables: X, Y, Z, and receiver time bias. In a terrestrial network, estimating the Z coordinate through trilateration is error prone due to limited VDOP. When the z‐axis is available through barometric techniques, a minimum of three pseudorange measurements is sufficient for 3D trilateration.
There is another aspect of trilateration that is quite different for a terrestrial system of beacons when compared to a GPS satellite system. In a GPS system, traditionally, the trilateration problem is linearized to a weighted least squares (WLS) problem. The linearization works well due to the large distance of the satellites relative to the receiver. In the terrestrial system, the case of when a receiver is close to a beacon has to be carefully considered. In such conditions, locally linearized algorithms can suffer from position divergence. In general, the best estimate of the receiver location when altitude aiding is available can be obtained as the set of (X,Y,Z,Δt) that minimizes the objective function
Figure 39.15 Sample channel responses from MBS beacons.
Figure 39.16 Channel spread statistics.
(39.3)
39.1.5 Assisted Mode of MBS
The Assisted GPS (A‐GPS) concept was developed to improve the sensitivity and time to fix of a GPS receiver when compared to a stand‐alone GPS receiver. See [10] for an explanation of the A‐GPS concept. A‐GPS facilitates improved sensitivity by providing assistance in the form of ephemeris/almanac information to the receiver so that decoding is no longer required. In addition, assistance, in the form of a coarse/fine GPS time estimate and rough receiver position, enables the receiver to compute the list of visible satellites, rough satellite Doppler frequency, and code phase, thereby significantly reducing its acquisition search space.
Analogous to the assisted mode of GPS, an assisted mode can be considered for MBS as well. In A‐MBS mode, beacon information such as the almanac, any corrections, and atmospheric information may be transmitted over a cellular/other side channel. A list of visible beacons (based on the rough user position) can also be provided to the receiver to help reduce the PRN search space.
39.1.6 MBS System for Time and Frequency Synchronization
The advent of 5G networks and indoor small cells for cellular coverage/capacity enhancements has spurred the need for indoor time (phase) and frequency synchronization solution on a wide‐area basis in a scalable manner. Today, time/frequency is distributed directly via a GPS module attached to a small cell or a Grand Master, whose primary source is GPS. The Grand Master distributes time over an Ethernet or fiber‐optic
