# Distributed MIMO Measurements for Integrated Communication and Sensing in an Industrial Environment
## 4 System Calibration  
There are several system errors that need to be handled. Some of these errors are more pronounced than are others and stem from different sources, such as temperature variations, clock drift, clock offsets, and timing offset, to mention a few. Many of these errors can be mitigated with well-synchronized measurement equipment and a stable temperature. Now, we briefly describe five different errors and their possible sources. Let us start with the _time offset_, which simply means that all the USRPs in the system must share the same notion of time so that all saved data from different antennas can be related to each  
Figure 4: Depiction of three of the \(H_{\text{a}}\) antennas distributed in space. In TDMA slot 1, the antenna 1 is transmitting while all the others are listening. In then next TDMA slot, antenna 2 is transmitting. Since antennas are distributed in space, it is clear from the figure that an AGC is needed; antenna \(H_{\text{a}}\) might need all the available gain when antenna 1 is transmitting, while that same gain setting might saturate the ADC when antenna 2 is transmitting. Figure 3: The TDMA-based signal structure. Each antenna is assigned a dedicated TDMA slot. During each transmission, the antenna transmits \(R\) repetitions of the sounding signal, with some being used as guards and the rest for averaging to increase the signal-to-noise ratio. other. If the oscillators on the different transceivers do not provide the exact same carrier frequency, it will result in a _carrier frequency offset_ (_CFO_). If the aforementioned oscillator phase-locked loops (PLLs) locks in different phases, it will result in a _clock phase offset_. If the clock frequency of the ADCs is different or imperfect, another frequency offset will be induced, namely, _sampling clock frequency offset_. Lastly, ADCs might sample the signal at different times due to obtaining the trig signal at different times--e.g., due to different length cables--which is called _sampling time offset_. A summary can be found in Table 2.  
To ensure accurate results, it is essential to perform a back-to-back calibration to remove as much as possible of the described errors. During a back-to-back calibration, the cables from two RF chains are connected together as close as possible to the antenna ports. This gives the transfer function of the complete system between a pair of transceivers. This step must be taken for all combinations of transceiver chains when all radios are operational with the settings intended for use during the measurement campaign. This procedure enables the de-embedding of the radio channel from the measured channel transfer function (CTF), which, in addition to the propagation channel, also includes the influence of cables, connectors, the analog front-end, and digital processing. Furthermore, if possible, it is recommended to characterize the antenna radiation pattern in an anechoic chamber to mitigate the effect of the antenna, thus isolating the wireless CTF. It is important to note that a hardware restart requires a recalibration. This requirement arises due to the reinitialization of the transmit-and-receive chains PLL, which lock onto a random phase after each restart. If the purpose of the sounding is to measure metrics regarding the channel statistics for communication-related evaluation, then this requirement can be relaxed. However, for applications that require the use of coherent signals, such as accurate positioning algorithms, knowing the phase relations between all transceivers is crucial. The next best thing is to perform a back-to-back calibration after a hardware reset using the same hardware (cables, connectors, etc.) as that used during the measurements. With this method, there will be an error in the phase relationship since it is not possible to control at which phase the PLLs of the different radios will lock.