Correctly Modeling TX and RX Chain in (Distributed) Massive MIMO—New Fundamental Insights on Coherency

Abstract

This letter shows that the TX and RX models commonly used in literature for downlink (distributed) massive MIMO are inaccurate, leading also to inaccurate conclusions. In particular, the Local Oscillator (LO) effect should be modeled as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+\varphi $ </tex-math></inline-formula> in the transmitter chain and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-\varphi $ </tex-math></inline-formula> in the receiver chain, i.e., different signs. A common misconception in literature is to use the same sign for both chains. By correctly modeling TX and RX chain, one realizes that the LO phases are included in the reciprocity calibration and whenever the LO phases drift apart, a new reciprocity calibration becomes necessary (the same applies to time drifts). Thus, free-running LOs and the commonly made assumption of perfect reciprocity calibration (to enable blind DL channel estimation) are both not that useful, as they would require too much calibration overhead. Instead, the LOs at the base stations should be locked and relative reciprocity calibration in combination with downlink demodulation reference symbols should be employed.