Comments on “Generalized Co-Prime MIMO Radar for DOA Estimation With Enhanced Degrees of Freedom”

It is known that in direction-of-arrival (DOA) estimation with a coprime multiple-input-multiple-output (MIMO) radar, the lags of the generalized sum and difference coarray (GSDC) can be utilized. Shi et al. carried out a commendable work in proposing a novel coprime MIMO radar configuration for DOA estimation, where the intersensor spacing of the transmitter array of the configuration is expanded by a specific expansion factor. The authors analyzed the structure using three different cases based on different expansion factors of the transmitter. The mathematical formulas of the uniform and unique lags of the GSDC are provided for each of the cases. However, there is a mistake in the expression of the unique lags of the GSDC for the case where it provides the maximum unique lags by using the largest expansion factor. In fact, we will prove that for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}\neq {2}$ </tex-math></inline-formula> (where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> is the parameter of the coprime array), there will always be an error whenever we calculate the unique lags of the GSDC of the coprime MIMO configuration by the expression provided in <xref ref-type="table" rid="table1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Table I</xref> of that article. Here, we provide the correct expression of the unique lags of the GSDC for this case and also carry out the corresponding proof of that expression. We also comment in detail why this correction is not required for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}={2}$ </tex-math></inline-formula>.