Doppler Shift Time Expansion Resolution and Spectral Performance in Wideband Real-Time RF Channel Emulators

Round  1

Reviewer 1 Report

It is quite unclear why the authors expect to see quantization error (formulas 6 and 7) for the resulting signal after application of Doppler effect. The simplest way to apply Doppler is via interpolation of original time samples onto a new time axis, which results in ability to arbitrarily smoothly subdivide time between actual samples, all while keeping sampling rate very manageable. While clearly no interpolator is perfect, one can limit impact of interpolation errors by using appropriate windowing (subject to original signals bandwidth relative to the original sampling rate). In fact, even linear interpolator produces nearly perfect spectrum for most practical cases.

For specific application of CSI emulation one would need to buffer the signal for at least 1 sample to apply interpolation, but for most channels one would expect a propagation delay of at least 1 chip. All of the processing can be done in baseband, and thus for very narrowband signals this may be a limiting factor.

Either way the approach to Doppler emulation proposed in the paper is extermely wasteful in terms of errors produced, resulting in the need for all the error analysis presented. As there are better ways to perform required operation, it remains unclear why authors are not using them. Suggest authors analyze proposed approach with interpolation and, if errors still present, analyze those.

Author Response

I agree with the reviewer regarding the way to perform the delay of a signal in a discrete time domain. The goal here is not to delay a signal for a fraction of the sample time once, in fact there exists several efficient ways to do so. The paper doesn’t focus the attention to a particular implementation: one of the suitable ways here is probably to adopt a Farrow structure that allows also a continuous adaptation of the coefficients while assuring a constant latency and enough bandwidth in order to realize the delay with a negligible error. Even if we are dealing with instantaneous bandwidth of several hundred of MHz, this is still possible and it will be more in the future with the increase of the performance of digital devices. Despite this, the process remains a discrete-time realization i.e. I can delay nearly perfectly a signal for a fraction of the available sample period thus resorting to interpolation, but the realized delay is always discrete, and in this sense quantized, so I have to apply this (variable) delay continuously according to the receiver’s dynamic. This is true for each discrete path I need to consider during the emulation. The formulas 6 and 7 addresses in a general way just this phenomenon, remembering that a nearly perfect realization could be possible with an ideal continuous time-variant analog delay line. So, starting from the assumption that it is possible to use efficient time-variant fractional delay filters able to guarantee the necessary bandwidth, the aim of the paper is to try to find out which is the required resolution of such filters in order to control the unavoidable spectral degradation introduced.

Reviewer 2 Report

The contribution and novelty are very limited. Without citing any literature, author has presented some results when a time expansion is adopted in order to emulate the transceiver dynamic and the consequent Doppler spread with the aim to control the spectral purity of the emulated propagation channel. Author must clearly describe the novelty and motivation in the Introduction Section by citing some literature and also compare the performance of the proposed model with existing one.

Author Response

I wish to thank the reviewer as the comments has helped me to improve the paper expanding the text, citations and literature. The paper focuses on one aspect of a particular class of wideband real-time RF channel emulator that, to the knowledge of the author, is not so widespread. The spirit that underline the paper is not to outline the performance of the method, nor to focus the attention to a particular implementation, but to investigate better the drawbacks of it.

The premise is that the time expansion could be a viable method when there is no direct access to the baseband of the signal (by assumptions with instantaneous bandwidth of several hundred of MHz) or you don’t know its characteristics, maybe even for reasons of confidentiality. The time expansion approach assumes the availability of efficient tools that can faithfully delay the signal. One of the suitable ways is probably to adopt a Farrow structure that allows a continuous adaptation of the coefficients while assuring a constant latency and enough bandwidth in order to realize the (fractional) delay with a negligible error. So, starting from the assumption that it is possible to use efficient time-variant fractional delay filters able to guarantee the necessary bandwidth, the aim of the paper is to try to find out which is the required resolution of such filters in order to control the unavoidable spectral degradation introduced. The results of the paper are general and could be useful in system implementations.

Round  2

Reviewer 2 Report

No more comments.