Traditional methods for channel impulse response (CIR) 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: sending a pseudo-noise (PN) signal from the transmitter and correlating with a slightly slowed version of the PN signal at the receiver.
- Frequency Domain Channel Sounding: performing a frequency sweep,
*e.g.*, with a network analyzer.

Our method for channel measurement uses any standard 802.11b transmitter, including those ambient sources in the environment. These transmitters send a known (Barker code) PN signal. However, our work is different from traditional CIR estimation in four main ways. First, we cannot change the PN sequence -- it is fixed by the IEEE 802.11 standard. Second, traditional spread spectrum-based channel sounders use unmodulated data, while the data input to our channel sounder is modulated. Third, partially as a result of the second point, we may not use a sliding correlator, that is, a slower rate PN signal at the receiver, so we must correlate with the known PN signal in real time. Finally, our sounder can be widely used; *i.e.*, any router or device that produces 802.11b packets may serve as a transmitter for use with our channel sounder.

This project is related our project to build a real time PHY-based location distinction. We believe that CIR estimation is very useful for many purposes, including location estimation, security against identity attacks, a means to provide privacy in broadcast wireless networks. Future wireless devices will, in order to take advantage of these benefits, include real-time CIR estimation as one of the outputs which are provided to higher layers of the networking stack.

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

In general, we want to estimate $h(t)$ from known $r(t)$ and $s(t)$. This is a "deconvolution" 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 frequencies $f$ inside the band of operation. 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 the frequency domain this is equivalent to:

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

where $S(f)$ and $H(f)$ are the Fourier transforms of $r(t)$ and $h(t)$ respectively. To develop an estimate of $h(t)$, which we call $q(t)$, we convolve the received signal $r(t)$ with $c(-t)$:

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

Convolving with $c(-t)$ is called "de-spreading". The output of the de-spreading block is thus the convolution of the channel impulse response and a modulated autocorrelation function of the pulse shape. When higher resolution is desired, we can estimate a discretized CIR using a second deconvolution algorithm. We exploit the deconvolution method proposed in [2] to estimate the number of paths and, for each of them, the associated attenuation and delay.

More details about the algorithm, and the testing and validation of the system, is reported in our paper [3]. As part of the paper, we conduct a drive test in Salt Lake City, collecting millions of CIR measurements, and summarize the channel delay statistics as a function of environment.

- [1] T. S. Rappaport.
*Wireless Communications: Principles and Practice*. Prentice Hall, 2nd ed., 2002. - [2] J. Fuchs, "Multipath time-delay detection and estimation",
*IEEE Transactions on Signal Processing*, vol. 47, no. 1, pp. 237-243, Jan 1999. - [3] D. Maas, M. H. Firooz, J. Zhang, N. Patwari, and S. K. Kasera, "Channel Sounding for the Masses: Low Complexity GNU 802.11b Channel Impulse Response Estimation",
*IEEE Transactions on Wireless Communications*, (to appear).