A new speed enhancement technique for pulsed laser rangefinders based on Lagrange's theorem in group theory using an undersampling method has been developed. In the undersampling method, frequency conversion for high-resolution ranging and digitizing are conducted by sampling a reference frequency signal at the timings of the reception of pulsed light from the target. In the present work, the rangefinder generates different sampling intervals of the reference frequency signal: different numbers of sampling points within the period of a reference signal, over a wide range. This is accomplished by slightly changing the period of the pulsed light emitted, without changing the synthesizer frequency which generates the period. This technique requires a minimum of additional hardware. In this paper, we describe the detail of the selection of the number of sampling points based on Lagrange's theorem. And we demonstrate a possibility of expanding the sampling interval to the point where an aliasing of the harmonic components of the reference signal occurs by simulations that focus on the calculation of the phase of the fundamental frequency of the reference signal. And we report on the results of rangefinder experiments for a reduction in the number of the sampling points. We have achieved a 10-fold enhancement of speed by selecting 10 sampling points over the results from the previous studies that had 100 sampling points within a period of a reference signal. And we have confirmed that the reduction in sampling points has a very little influence on the linearity, which is an acceptable trade-off for achieving the speed enhancement. This technique, based on Lagrange's theorem in group theory, allows us to control the minimum number of samplings required to calculate distances, so that high-speed data acquisition for coarse measurements and normal-speed data acquisition for fine measurements become selectable. Such a system with high flexibility in measurement modes has been developed.

We investigate the relationship between microwave path-loss characteristics and line-of-sight (LOS) blocking in an urban environment with a low base-station antenna using LOS-blocking measurement equipment that we have developed. Changes in path loss, traffic conditions, and LOS-blocking caused by vehicles were measured simultaneously. It was found that path loss exhibits a Rayleigh distribution even in a LOS environment if the amount of traffic is such that LOS- blocking occurs for 80% of the time or more, but the other case path loss exhibits a Nakagami-Rice distribution. It was also found that ratio of coherent wave level to envelope level (c/r) depends heavily on rate of road traffic flow.

The authors have performed a simple computer simulation for a topography that models change in propagation characteristics due to change in traffic volume. The results of this simulation revealed that path loss for a traffic volume of about 2000 vehicles every 30 minutes in a typical urban environment exhibits a Rayleigh distribution. This result agrees well with that of actual measurements demonstrating that even a simple simulation can be a useful tool in system design.