# 6G Goal-Oriented Communications: How to Coexist with Legacy Systems?
## 2 Definition of a Goal
### Identifying Goal-Achieving Communication KPIs  
In edge AI/ML scenarios and use cases, multiple agents (at least two), equipped with more or less powerful computing units and complex (ML) models, communicate to achieve a (possibly common) goal. The issue is then how to allocate connect-compute resources in order to guarantee a target goal effectiveness subject to short and long-term constraints, paying the lowest possible goal cost. First, when exchanging data, availability of communication resources affects the level of distortion on the received data with respect to the original information. In classical communication systems, communication KPIs are defined a priori, depending on the different service requirements. This paradigm has started a long race towards adding \"9s\" to the communication reliability [38] in terms of, e.g., packet success rate. Here, based on the definitions provided in the previous section, we argue that this is not the most efficient way of designing the system and orchestrating operations and resources. Indeed, we do not formulate a problem in which communication KPIs are explicitly taken into account, but they are rather controlled by learning and adaptation to communication policies that achieve target levels of goal effectiveness. In this context, let us denote by \(\pi_{\text{comm}}\) a _communication policy_ entailing, in the most general case: _(i)_ source encoding (e.g., data compression schemes) [25; 26]; _(ii)_ modulation and channel coding [39]; _(iii)_ wireless channel scheduling, including node participation selection [40] and association [41] ; _(iv)_ multiple antenna transmission scheme, devising power allocation and precoding [42]. Moreover, let us denote by \(\pi_{\text{comp}}\) a _computation policy_ entailing, in the most general case: _(i)_ local computing resource scheduling at each device/agent; _(ii)_ computation resource scheduling at shared computing units (e.g., in MEHs) [43; 44; 45]; _(iii)_ selection of a single one or multiple collaborative AI agents containing relevant ML models for ensemble-based inferencing [24; 46] or federated learning [40]. Finally, we denote by \(\pi_{\text{contr}}\) a _control policy_ entailing AI agents' mobility and trajectories. A general GO communication problem can be then formulated as follows:  
\[\min_{\{\pi_{\text{comm}},\pi_{\text{comp}},\pi_{\text{contr}}\}} \mathcal{C}:=\lim_{T\to\infty}\frac{1}{T}\sum_{t=0}^{T-1}\mathbb{E}\{C_{t}\}\] (5) subject to \[(a)\ \pi_{\text{comm}}\in\mathcal{P}_{\text{comm}}\] \[(b)\ \pi_{\text{comp}}\in\mathcal{P}_{\text{comp}}\] \[(c)\ \pi_{\text{contr}}\in\mathcal{P}_{\text{contr}}\] \[(d)\ \mathcal{E}_{g}\geq\mathcal{E}_{g,\text{th}}\] \[(e)\ \mathcal{G}_{s}\leq\mathcal{G}_{g,\text{th}},\ \ s=1,\ldots,S,\]  
where \(\mathcal{P}_{\text{comm}}\), \(\mathcal{P}_{\text{comp}}\), \(\mathcal{P}_{\text{contr}}\) denote the feasible sets of communication, computation and control actions, respectively. The constraints in (5) have the following meaning: \((a)\) the communication policy belongs to the feasible set \(\mathcal{P}_{\text{comm}}\) (e.g., the transmit power is non-negative and lower than a threshold); \((b)\) the computation policy belongs to the feasible set \(\mathcal{P}_{\text{comp}}\) (e.g., the sum of all CPU resources of an MEH assigned to a set of users does not exceed the maximum CPU computing power); \((c)\) the control policy belongs to the feasible set \(\mathcal{P}_{\text{contr}}\) (e.g., a robot can move towards a predefined set of possible directions); \((d)\) the goal effectiveness is above a predefined threshold (e.g., the inference accuracy of an edge inference system is above a threshold); \((e)\) other long-term constraints are satisfied (e.g., the average energy of an agent does not exceed a predefined threshold). The problem formulation in (5) is quite general, and it can be easily customized to specific use cases. In the next section, we present a specific scenario in which a GO and a DO communication system coexist.