The analysis is based on estimating the individual multipath components, and it focuses on their spatial area of visibility. A measurement in this work is a collection of responses measured with a stationary transmitter and a receiver located at positions that were uniformly spread over a one-meter rail in steps of 2 to 10 mm. The receiver was held stationary during the measurement of each impulse response.
We analyze the measured channel responses using a raised cosine window with 3 dB points at 2 GHz and 17.2 GHz and 
for the full-band results (Section 4.1) and 3 dB bands of 1 GHz in Section 4.2. After filtering, the measured responses were converted to the time (delay) domain with a 28 psec time step, to generate a two-dimensional real representation of the channel as shown in the example in Figure 1. The channel measurement matrix 
has rows that span a single channel impulse response the columns span receiver positions. The delay range was set at 150 nsec around the maximal (absolute) response at one end of the rail; this seemed sufficient to include all the significant parts of the response.
The temporal resolution of 28 psec was maintained in all our analyses that is, responses with bandwidths of 1 GHz are heavily oversampled. Due to the oversampling, apparent multipath components with similar delays are correlated.
All the measurements included in this analysis were of sufficient SNR, that is, at least dB, and most cases above 20 dB (42 out of 50 ). To calculate the SNR we used the maximum (absolute) amplitude among the multipath components, and normalized its square by the noise variance, calculated from a late 5 nsec section of the response over all the available receiver positions.
A significant feature of our measurements is the finite, and usually short, spatial extent of the multipath components. Figure 1 is typical in this sense, this feature can be seen also in channel responses presented in [27]. The diagonals extend 10–60 cm over receiver positions in Figure 1. Line of sight (LoS) measurements have more stable direct components that extend beyond the one meter measured length.
Our analysis is based on a software tool designed to extract the multipath components from the measurements. This tool received measured impulse responses of the type shown in Figure 1 and returned a list of diagonals, each defined by its endpoints its width and a constant real (possibly negative) amplitude. A brief overview of multipath extraction tools follows and then a description of our multipath extraction tool.
3.1. Wideband Multipath Extraction
The CLEAN algorithm was introduced from radio astronomy into the analysis of UWB measured channels by Cramer [28] and coauthors [29, 30]. CLEAN is essentially an iterative search for the strongest multipath component in channel responses from a single transmitter measured at an array of receivers. The algorithm receives (temporal) impulse responses as input it searches over delay and angles of arrival and iteratively removes the strongest MPC from the measurement data until the remaining data is weak enough.0020Liu et al. [31] suggest a modification that accounts for distortion, based on the usage of multiple templates of the received pulse shape.
The SAGE (Space-Alternating Generalized Expectation-maximization) algorithm was introduced for radio channel analysis by Fleury et al. [32, 33] for the extraction of delay and angle of arrival from narrowband and wideband signals. The extension to UWB and the addition of successive cancellation into SAGE were suggested by Chong et al. (FD-SAGE) [34] and Haneda & Takada (UWB-SAGE) [35]. The FD-SAGE algorithm was further enhanced in [36] from SIMO to MIMO settings.
RIMAX [37] is an algorithm similar to SAGE in the fact it iterates over the MPC parameters RIMAX is based on an improved gradient-based parameter estimation that operates simultaneously over the entire set of parameters. It iterates between the specular and the diffuse components of the channel.
An extension RIMAX that is based on an extended Kalman Filter was suggested in [38]. The Kalman Filter utilizes a state-space approach on top of RIMAX and tracks parameters over successive measurement locations. The introduction of the state-space approach made it possible to derive parameters faster than conventional high-resolution algorithms (including RIMAX) since the parameter estimates at one terminal location were used as the initial values for estimates at adjacent terminal locations. This approach extracts long MPCs sustained over a sufficiently large area of terminal locations and attributes other parts of the channel response to the diffuse component.
A high-resolution algorithm of this family for ultrawideband signals was presented in [39], and a path tracking mechanism was introduced in [40], that says that "significant paths constantly exist in many (terminal) positions" and attempts to estimate only such MPCs.
The method used in the current work is based on a non-parametric search for energetic sections in the two-dimensional (spatial-temporal) channel response matrix. No assumptions are made on the channel model, and only two threshold parameters are used.
Santos, Karedal et al. [41, 42] recently presented a frequency-based algorithm that searches over reflector positions and uses successive cancellation it is different from CLEAN and SAGE in two significant points: (1) each MPC may be received at delays that can vary nonlinearly over a linearly spaced receiver array and (2) each MPC may be received over part of the receiver array.
Our method is similar to that of Santos et al. in that it allows MPCs that impinge over parts of the receiver array. The significant new feature is the millimetric resolution that enables a detailed study of the spatial structure of individual MPCs. The work offered by Santos et al. investigated outdoor responses measured with a spatial resolution of 4.8 cm and concentrated on clustered MPCs from distinct reflectors.
3.2. A Simple Multipath Extraction Algorithm
Input
The algorithm receives a matrix 
of measured impulse responses, where each row includes a single impulse response. It also receives two vectors: a vector of receiver positions 
with uniformly spaces positions and a vector of delays 
with uniformly spaced delays. In our data the spatial resolution 
varies between 2 mm and 10 mm for different measurements, and the temporal resolution 
equals 28 psec.
In the following description we refer to the 
position in matrices as the 
position, in order to maintain the physical significance of the indices.
Two control parameters are given: a minimal spatial extent of 
set to 4 cm and an amplitude threshold Thr set at 0.1 (−20 dB).
Initialization
Set to zero all points in 
with an absolute value below a threshold set at 
. Set to zero a matrix 
with dimensions 
that will be used to indicate which pixels were processed.
MPC Extraction
For each location 
for each delay 
and if 
, that is, the 
pixel in the matrix 
was already checked, continue to the next pixel (next step of the loop). If 
, continue to the next pixel.
Set 
to indicate that the current pixel was checked. Collect an environment of pixels around 
where 
is nonzero and has the same sign as 
. Pixels are collected iteratively by searching over adjacent neighbors (in position or delay) for pixels already collected. For every pixel checked, set to zero the corresponding cell in the matrix 
.
After having collected a set of pixels around 
, approximate it by a parallelogram (over delay and receiver positions) and calculate its effective amplitude. If the resulting parallelogram extends at least 
over receiver locations, save it as an estimated MPC. Otherwise reject it.
Output
A list of parallelograms over receiver position and delay, each with a signed amplitude.
for the full-band results (Section 4.1) and 3 dB bands of 1 GHz in Section 4.2. After filtering, the measured responses were converted to the time (delay) domain with a 28 psec time step, to generate a two-dimensional real representation of the channel as shown in the example in Figure 
has rows that span a single channel impulse response the columns span receiver positions. The delay range was set at 150 nsec around the maximal (absolute) response at one end of the rail; this seemed sufficient to include all the significant parts of the response.
of measured impulse responses, where each row includes a single impulse response. It also receives two vectors: a vector of receiver positions 
with uniformly spaces positions and a vector of delays 
with uniformly spaced delays. In our data the spatial resolution 
varies between 2 mm and 10 mm for different measurements, and the temporal resolution 
equals 28 psec.
position in matrices as the 
position, in order to maintain the physical significance of the indices.
set to 4 cm and an amplitude threshold Thr set at 0.1 (−20 dB).
with an absolute value below a threshold set at 
. Set to zero a matrix 
with dimensions 
that will be used to indicate which pixels were processed.
for each delay 
and if 
, that is, the 
pixel in the matrix 
was already checked, continue to the next pixel (next step of the loop). If 
, continue to the next pixel.
to indicate that the current pixel was checked. Collect an environment of pixels around 
where 
is nonzero and has the same sign as 
. Pixels are collected iteratively by searching over adjacent neighbors (in position or delay) for pixels already collected. For every pixel checked, set to zero the corresponding cell in the matrix 
.
, approximate it by a parallelogram (over delay and receiver positions) and calculate its effective amplitude. If the resulting parallelogram extends at least 
over receiver locations, save it as an estimated MPC. Otherwise reject it.
, where 
is the amplitude returned by the extraction tool (see Section 3.2), 
is the spatial extent of the diagonal, and 
is the length of the entire receiver range, usually one meter. This choice of amplitude is best in the sense that the square error between the two types of reconstruction is minimal.
. The responses measured per each receiver location along the rail were then converted to the time (delay) domain, to generate a two-dimensional representation of the channel as shown in the example in Figure 
