# Unstable Phase of Channel Impulse Response

I'm using DW1000 UWB radio transceiver and extract its channel impulse response (CIR). The CIR output by the transceiver is the complex baseband CIR. In a static environment, the CIR is a LTI filter expressed as

$$h_b(\tau) = \sum\limits_{i} a_i^b \cdot \delta(\tau-\tau_i)$$

where

$$a_i^b = a_ie^{-j2 {\pi} f_c \tau_i}$$

$$\ i \$$ is the index of (multi-) paths. $$\ a_i \$$ is the (complex) scaling factor including distance, antenna gains, etc. $$\ f_c\$$ is the carrier frequency. $$\ \tau_i \$$ is the time delay due of path $$\ i \$$.

What I'd like to have is the phase of the direct path. Let direct path have index $$\ i=0 \$$, the phase is then $$\ a_i e^{-j2 {\pi} f_c \tau_0} \$$. Since the direct path is the shortest, i.e. $$\ \tau_0 < \tau_j, \forall j \ne 0\$$, if I take the phase of the first peak in the CIR, I would get the phase of direct path.

So I have two DW1000 transceivers, one Tx and one Rx (whose local oscillators are not synchronized), keep everything static, and take multiple CIR measurements from the Rx. However, the first peak CIR phase varies quite a bit from one measurement to another (it even seems changing randomly). I understand carrier frequency offset (CFO) might be causing this, and tried a technique to eliminate it but with no luck. So I'd like to ask if there's any other potential reason for the unstable phase?

Since I'm still learning about RF systems, an explanation from up/down-conversion and channel estimation point of view is greatly appreciated!

In the figure below, x-axis is the first peak phase of n-th CIR and y-axis is phase.

Thank you!

I have two such transceivers ...

With two independent transcievers, there's no reason they should drift together in phase.

You would have to supply both from the same 10 MHz reference signal if you wanted them to stay coherent. Even then, reprogramming one to a different frequency and back again would randomise the phase.

Generally the absolute phase of a channel is unimportant, which is why there's little effort made to control it.

• Hi @Neil_UK, thank you for replying. Just to be clear, the CIR is measured only on one device. Would you mind being more specific where does the random phase drift come from? Since I'm still learning about RF systems, I really appreciate it if you can explain the phase drift from an up-conversion/down-conversion perspective. Thank you! – jleng Apr 14 at 20:07