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# Channel Sounder for 802.11b

## Overview

Traditional methods for channel impulse response estimation can be categorized as follows[1]:

• Direct RF Pulse System: sending a short duration pulse as an approximate impulse and simply measuring the received signal.
• Spread Spectrum Sliding Correlator Channel Sounding: sending a PN signal and correlating the known PN signal at the receiver. In the literature, this kind of channel sounders are also referred as match filter channel sounders.
• Frequency Domain Channel Sounding: performing a frequency sweep, e.g with a network analyzer.

Our method for channel measurement is sort of similar to the second one as 802.11b uses barker code as a PN sequence. However, our work is different in three points of view. First of all, we cannot change the PN sequence it is fixed for all of transmitted signal. Second, traditional spread spectrum correlation channel sounders use unmodulated data while the data input to our channel sounder is modulated. Finally, our sounder can be widely used;i.e anywhere that has a base station of 802.11b our channel sounder works. This project is related our project to build a real time PHY-based location distinction.

### Channel Recovery Using Match Filter

The received signal, r(t), is the convolution of the channel filter and the transmitted signal s(t), r(t)=s(t)*h(t)

In general, estimating h(t) from known r(t) and s(t) in is a de-convolution problem. In some cases, it is reasonable to assume that digital signals have power spectral densities (PSD) which are aproximately flat within the band (the frequency range of the channel). Digital modulations tend to acheive such PSDs in order to maximize spectral efficiency. Specifically, |S(f)|^2 is approximately equal to a known constant, here denoted P_s, for all f inside the band. Motivated by this fact, we can estimate h(t) in using only convolution and scaling as follows:

\hat{h}(t)={1 \over P_s} r(t)*s(-t)={1 \over P_s}(s(t)*h(t))*s(-t)

in frequency domain we have:

\hat{H}(f)={1 \over P_s}S(f)H(f)S^*(f)={1 \over P_s}H(f)|S(f)|^2 \approx H(f)

where S(f), H(f) are fourier transform of r(t) and h(t) respectively.

Here we convolved received signal with c(-t) which results in:

q(t) = r(t)*c(-t) = s(t)*h(t)*c(-t) = h(t)*[\sum_j b(j)c(t-jT_s)]*c(-t) = h(t)*[\sum_j b(j)R_c(t-jT_s)]

Therefore the output of de-spreading block (which has been explained in Receiver Part) is the convolution of channel impulse response and modulated raised cosine. To estimate the CIR we need a deconvolution algorithm. We exploit the de-convolution method proposed in [2] to estimate the number of paths and, for each of them, the associated attenuation and delay. More explanation on that can be found in our paper.

### Testing and Valodation

We have performed a experimental validation on our implementation using drect connection between transmitter and channel sounder. For that reason, the wireless router is directly connected to the USRP via a coaxial cable. To simulate multi-path channels an splitter and a combiner are used which are connected to each other using wires with different length. A schematic of our validation system follows:

In the following figure channel impulse response, estimated by our channel sounder whit direct cable connection is depicted.

Figure 1. single path validation for channel sounder

In the next experiment, the router is connected to the receiver via 2 cables, a short one with the length less than one foot and a long one which has a length around 100 feet. So the delay difference between them is greater than 90ns. In below figure output of channel sounder is presented. This picture presents that the second path corresponding to the pulse located n 90ns has a delay between 90ns and 120ns which is completely consistent with what has been expected.

Figure 2. 2 paths validation for channel sounder

Using a LadyBug power sensor (LB479A), the power of each path is measured before the combiner to see the power difference between two paths. For our D-link router it turns out to be around 9.5dBm; i.e the amplitude of second path (the long one) is 10^{-9.5 \over 20} times less than the short one and this is confirmed by result of our channel sounder in above figure.

Considering Figure 1 and 2 determines the noise floor for this channel sounder to be 20dB below the signal power. This threshold has been depicted as a dash line in these figures.