# Emerging Topics in Joint Radio-Based Positioning, Sensing, and Communications
## 1 Introduction and Definitions
Some of the most relevant performance metrics in the joint processing of communication, sensing, and positioning are:  
* Accuracy in terms of positioning and sensing, measured, for example, as Root Mean Square Error (RMSE) or Mean Absolute Error (MAE) between the estimate (e.g., position, velocity, orientation, etc.) and ground truth;
* Achievable data rates or channel capacity for a certain ISAC/JPSAC system;
* Ambiguity Function (AF)--this provides a two-dimensional representation of how a signal behaves in terms of time delays and Doppler frequency shifts; in a sensing context, it assesses the ability of a waveform to distinguish between targets at different ranges and velocities; in a positioning context, it provides the resolution and accuracy of the positioning system; and in a communication context, it helps in understanding the impact of time and frequency shifts on the signal;
* Cramer-Rao Lower Bound (CRLB)--this is a lower bound on the variance of any unbiased estimators, indicating the best possible accuracy that can be achieved for estimating a parameter given a certain amount of data; the parameter can be a sensing, a positioning, or a communication parameter;
* Detection probabilities in the context of positioning or sensing, measuring, for example, LOS/NLOS path detection, obstacle detection, etc. * Data Information Rate (DIR)--this is the rate at which data can be transmitted while simultaneously performing sensing tasks; the higher the better;* Mutual Information (MI)--this measures the amount of information that one random variable (e.g., a sensing-related parameter) contains about another random variable (e.g., a communication-related parameter);
* Signal to Interference plus Noise Ratio (SINR)--this measures the ratio of the signal power to the combined power of interference and noise, and is relevant in all three areas of positioning, sensing, and communications; the higher, the better;
* Squared Position Error Bound (SPEB)--this is a lower bound on the mean squared error of position estimates, indicating the best possible accuracy that can be achieved for the positioning part of the JPSAC systems. * The sum rate--this represents the total data rate achieved by the system across all communication links and is a key performance indicator used to evaluate the efficiency and capacity of the communication aspect of the JPSAC systems. The main methodological tools when dealing with joint performance metrics in two or three areas among communication, sensing, and positioning are listed in the fourth column of Table 2. This table summarizes the main surveys from the current literature on joint or integrated algorithms for receivers, simultaneously addressing at least two of the three above-mentioned targets (i.e., communication, positioning, and sensing) and relying on RF wireless signals. The fifth column in Table 2 also mentions the technologies addressed as examples in the listed surveys, with the note that most of the methods, algorithms, and performance metrics in these surveys are in fact applicable for a wide area of technologies and they are not limited only to the technologies mentioned in the table.