Implementing a Non-Uniformly Spaced Tapped Delay Line Channel Model

Since you are good on fundamentals I would like to ask you a question that puzzles me. LTE channels models are defined at irregular time intervals as shown in [1].

The EPA, EVA and ETU channel taps can best be described as being sampled at multiples of 10 nsec. However, LTE signal is sampled at multiples of 3.84 MHz (Ts=260.416667 nsec). So how does one perform convolution operation.

Empirical multipath channel is usually characterized as a τ-spaced tapped delay line (TDL), whose power delay profile (PDP) is either uniformly spaced, or more frequently, spaced with arbitrary time delay(s). Converting a τ-spaced empirical model to a more tractable T-spaced (sampling time-spaced) statistical model will greatly facilitate the link-level simulation and performance evaluation of the broadband digital wireless system. The practical approaches to accomplish this task could be either approximation or interpolation,

1. Approximation
a. Ceil or Floor a τ-spaced tap to the neighbouring sampling time.
b. Split the energy of a τ-spaced tap to the adjacent sampling times.
2. Interpolation
An Ideal Bandlimited (sinc) Interpolator can fulfil the goal.

It should be noted that although T-spaced statistical model is simpler for analysis, τ-spaced empirical model represents the channel more accurately.


Author: Yasir Ahmed (aka John)

More than 20 years of experience in various organizations in Pakistan, the USA, and Europe. Worked as a Research Assistant within the Mobile and Portable Radio Group (MPRG) of Virginia Tech and was one of the first researchers to propose Space Time Block Codes for eight transmit antennas. The collaboration with MPRG continued even after graduating with an MSEE degree and has resulted in 12 research publications and a book on Wireless Communications. Worked for Qualcomm USA as an Engineer with the key role of performance and conformance testing of UMTS modems. Qualcomm is the inventor of CDMA technology and owns patents critical to the 4G and 5G standards.

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