Channel measurements in MIMO systems hinge on precise synchronization. While methods for time and frequency synchronization are well established, maintaining real-time phase coherence remains an open requirement for many MIMO systems. Phase coherence in MIMO systems is crucial for beamforming in digital arrays and enables precise parameter estimates such as Angle-of-Arrival/Departure. This work presents and validates a simple local real-time phase calibration method for a digital array. We compare two different approaches, instantaneous and smoothed calibration, to determine the optimal interval between synchronization procedures. To quantitatively assess calibration performance, we use two metrics: the average beamforming power loss and the RMS cycle-to-cycle jitter. Our results indicate that both approaches for phase calibration are effective and yield RMS of jitter in the 2.1 ps to 124 fs range for different SDR models. This level of precision enables coherent transmission on commonly available SDR platforms, allowing investigation on advanced MIMO techniques and transmit beamforming in practical testbeds.
Phase noise in multiple-input multiple-output (MIMO) communication systems significantly degrades data throughput [1] and in the context of joint communication and sensing (JCnS) limits the accuracy of parameter estimates [2]. The compensation of phase noise at the receiver side is well established. For example the 3GPP standard [3] offers the phase tracking reference signal (PT-RS) to compensate for the constant phase error (CPE) induced by phase noise. However to enable transmit beamforming in a digital array, coherence between radio frequency (RF) chains feeding the transmitting antenna array has to be assured.
There are several known calibration approaches in the literature, each with limitations. Reciprocity calibration Overthe-Air (OTA) with distributed sensor nodes such as [4] and [5] lacks a shared phase reference, making it unsuitable for coherent combination of the signals from multiple transmitters. In [6] a reciprocity calibration OTA scheme is employed where both transmit and receive arrays are connected to a common measurement device. This wired connection requires the transmitter and receiver to be co-located, making the approach unsuitable for mobile communication scenarios. The authors in [7] present OTA reciprocity calibration in MIMO systems, where all distributed radio units are connected to a central controller that performs synchronization by pre-coding with phase estimates. A limitation in this work is that the radio units have no method of compensating the local oscillator (LO) phase drifts internally, which imposes a significant overhead on the OTA calibration. Compounding these challenges, the often neglected residual transmit side calibration errors, can substantially degrade achievable MIMO throughput [8].
In this work, we address these limitations by proposing and validating a simple, local method for real-time phase calibration of transmit RF chains. Our approach uses a dedicated reference RF chain at the transmitter to receive calibration signals (PT-RS) from each transmit chain in a time-division multiple access (TDMA) scheme. The transmit-controller estimates the phase of each chain relative to this reference and applies precoding to achieve coherent transmission in passband. The calibration procedure is performed in periodic intervals to continuously track LO drift, to directly address the transmit side phase impairments as highlighted in [8].
The paper is organized as follows. Section II introduces the system model for local transmitter calibration and modeling of phase noise processes for voltage-controlled oscillator (VCO) and phase-locked loop (PLL). Section III presents measurement results and validates the calibration approaches. Section IV explores the effect of different calibration intervals and their impact on the achievable beamforming gain. Finally, the paper is concluded in section V with key results.
Our objective is to calibrate the phase of each element in a transmitting digital antenna array with M elements, as illustrated in Fig. 1. To achieve this objective, the phases of the transmitting chains must be compared to a common reference. Because the transmitting chains and reference RF chain are co- As shown in Fig. 2, each TX chain transmits a synchronization signal x[n] of length N in TDMA before the data or measurement signal. The band-limited baseband signal after D/A conversion and low-pass filtering is denoted x BB (t), defined over t ∈ [0, N T s ]. After up-conversion, the bandpass signal for chain m becomes x BP,m (t) = x BB (t)e j(2πfc,mt+θOS,m(t)) .
(
The synthesized carrier frequency f c,m is variable per chain to model a residual frequency offset. This small residual carrier frequency offset (CFO) models a linear phase shift over time, distinct from oscillator phase noise. The term θ OS,m (t) refers to the time-dependent phase of the oscillator signal for RF chain m. Then the transmitted signal at RF chain m in TDMA is
The term θ RF,m represents a constant phase shift specific to chain m. This shift arises from the cumulative phase response of amplifiers, switches, splitters, filters, and other front-end components. As illustrated in Fig. 2, the synchronization preamble has duration t syn = M N T s and is repeated every t obs seconds to obtain phase observations for each chain periodically. The locally received signal at the reference RF chain is the sum of the transmit signals
Down-converting using the reference chain’s local oscillator at frequency f c yields the baseband received signal
Note that the received signal gain is neglected, assuming it is compensated by an automatic gain control (AGC). Furthermore, the phase shift of the RF components at the reference chain is neglected, as it will induce an identical phase shift for all s TX,m (t) and only the relative phase relation of RF chains are of interest. For simplicity, the phase noise introduced by the oscillator of the reference chain is neglected under the assumption that t sy
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