target="_blank" rel="nofollow" href="#ulink_d981697a-aad5-52fa-a3f2-6f53fac577fd">(40.5)The least squares solution applied to Eq. 40.5 gives
(40.6a)
(40.6b)
Note that due to the transmitter clock frequency instability, the actual field period may differ from the nominal one, which is thus estimated as part of the calibration process. In Eqs. 40.5 and 40.6c, the scaling by the number of measurements N is to ensure numerical stability of the solution when N becomes very large. Similar equations can be formulated for periodic pseudoranges [23].
Two field test examples with ATSC‐8VSB [23, 29] and one example with DVB‐T [9] are presented next. The test environment with ATSC‐8VSB signals is in the San Francisco Bay area shown on Google Earth in Figure 40.17. The test site is in Foster City; DTV transmitters are located around the Bay at Sutro Tower, Mount San Bruno, Monument Peak, and Mount Allison, respectively; and one CDMA cell tower is along SR92 near the San Mateo Bridge across the Bay. The first test example with ATSC‐8VSB shows the effect of fast fading on mobile ranging, and the second test shows the effect of clock errors on the range bias and their possible calibration.
Mobile Test 1: Slow and Fast Fading. Severe Rayleigh fading occurs for mobile users in urban environments [42, 83], creating “holes” in data streams, which cannot be easily corrected by conventional coding schemes. Only 1 out of 313 segments per data field (about 24 ms) contains pseudorandom (PN) codes that can be used for timing and ranging. Such a low‐duty cycle (0.3%) requires specially designed correlators and code tracking loops for mobile users, particularly when low‐quality clocks are used in both transmitters and receivers. Although subject to Rayleigh fading, tracking of the PN codes is less devastating for DTV‐based ranging than for DTV viewing. In the latter case, interruption prevents continuous reception of ATSC‐8VSB signals, and the picture quality becomes unacceptable to mobile users. In ranging, however, agile acquisition and reacquisition schemes can coast through the “holes” with instantaneous recovery after complete signal losses.
A mobile test was designed and conducted to help better understand mobile fading and its effect on our software DTV receiver. On the roof and sides of a minivan, we placed seven magnetic‐mounted antennas and connected to seven radio channels (Ch1–Ch7) of our data acquisition system. As shown in Figures 40.18(a) and (b), a small patch antenna, marked “1,” is connected to Ch1 for GPS. A whip antenna, marked “2,” is connected to Ch2. The remaining five antennas, marked “3” through “7,” are identical and are connected to Ch3 through Ch7, respectively. Ant3 is placed in the middle section on the right‐hand side (the passenger side), while Ant4 is placed horizontally above the right rear wheel. Ant5 repeats the placement of Ant3 but on the left‐hand side (the driver side). Ant6 is similar to Ant4, but placed far to the left. Ant7 is in the middle on the back.
Figure 40.17 Test environment with ATSC‐8VSB signals on Google Earth.
Figure 40.18 Test setting for study of mobile fading.
The mobile test lasted about 70 s, in which all channels were tuned to the station centered at 653 MHz. In this run, the van was initially stationary for 10 s and then moved for 10 s. It next stopped for 10 s and moved for 10 s. It repeated the stop and move sequence for 10 s each before finally stopping for the last 10 s.
Figures 40.19(a)–(g) show the correlation peak, peak to average ratio, code delay error, carrier phase error, TOA error, and pseudorange as a function of the field number for all six DTV antennas (from left to right, Ant2 and Ant3 on the top, 4 and 5 in the middle, and 6 and 7 on the bottom of each subplot in Figure 40.19), respectively. It is clear from the figures that the signal strength at stop has less variations than in motion, but the peak value during the stops is not necessarily larger. There are peaks and dips during motion. When transitioning from stationary to moving and back to stationary, the signal level could be either high or low, depending on the particular location where the transition took place. The swing of signal strength during motion is due to fading.
Figure 40.19 Fading study with six antennas in a stop‐move‐stop sequence.
The performance ranking among the six DTV antennas is 4 > 3 > 2 > 5 > 6 > 7. That is, the horizontally placed antenna on the side above the right rear wheel outperformed the rest. It happens that the DTV station at 653 MHz uses a horizontally polarized antenna and the signal comes from the right, which is in direct sight of Ant4 with matched polarization.
Mobile Test 2: Clock Errors and Calibration. Six radio channels are assigned to six DTV stations for simultaneous data collection: Ch1 @ 551 MHz (data not shown) and Ch2 @ 635 MHz on San Bruno Mountain, Ch3 @ 563 MHz and Ch4 @ 617 MHz on Sutro Tower, Ch5 @ 605 MHz on Monument Peak, and Ch6 @ 683 MHz on Mt. Allison. A passive UHF whip antenna, magnetically mounted on the roof of a minivan, is split to drive the six radio channels for data acquisition. During the test, the van was stationary for about 40 s and was driven up to about 20 miles per hour for the remaining 50 s.
As shown in Figures 14.20(a)–(e), prior to field number 2000, the minivan was stationary. The reference ranges stayed constant. Except for some small variations (oscillatory), the calibrated ranges were rather close to the reference values, indicating that the calibration algorithms were able to find the offset between the clocks of the receiver and DTV stations.
The transmitters in San Bruno and Sutro Tower are in the north (San Francisco), whereas those in Monument Peak and Allison are in the south (Freemont). Since the minivan was traveling from north to south, it was expected that the pseudoranges to the northern stations would increase (see Figures 14.20(a) and (b)), while those to the southern stations would decrease (see Figure 40.20(c)). However, this is not obvious for the two stations in Figures 14.20(d) and (e) that exhibit large variations.
In Figure 40.20(d), the linearly calibrated pseudorange shows a parabolic shape, meaning that the range rate is not constant but under a
