# Joint Optimization of Data Freshness and Fidelity for Selection Combining-Based Transmissions
## 2 Related Works  
In this Section, we provide a thorough overview of the current academic and state-of-the-art works, to provide a broader perspective and deeper understanding of our work.  
In 2011, a metric termed the age of information (AoI) was widely applied to characterize the freshness of data delivered in a communication system. It is defined as the time elapsed since the generation of the latest received update [7]. Various systems characterized by different queueing models such as M/M/1, D/M/1, M/D/1, M/G/1, and G/G/1/1 adopted AoI to evaluate the freshness of the received data [7; 8; 9]. Authors in [10] considered the multi-source preemptive queuing model and investigated the optimal generation rate of each source achieving the best information freshness. The optimal generation rate of update which induced the minimal violation probability is found in [11]. Apart from the average AoI metric, The metric of peak AoI (PAoI) was introduced to capture information about the maximum value of the AoI [12; 13]. Based on the violation probabilities of AoI and peak AoI, the authors in [14] analyzed the optimal arrival rate of status update in the sight of asymptotical optimality. Authors in [15] proposed a new metric termed age upon decisions (AuD) to evaluate the freshness of received updates at some decision epochs.  
In WSN, the mean square error metric is widely applied to characterize the fidelity of the system. In [16], techniques for designing robust pre-coders and combiners to the linear decentralized estimation of unknown vector parameters in a coherent multiple-input multiple-output (MIMO) network with multiple sensors under imperfect channel state information (CSI) were presented. Their proposed techniques were based on the criteria that minimize the MSE of the estimated signal at the FC limited by total network power constraint. The authors in [17] proposed a framework of joint collaboration-compression for sequential estimation of a random vector parameter in WSN. By alternatively minimizing the sequential MMSE, they designed near-optimal and linear compression strategies under power constraints. Following from [16], the authors continued to develop optimal precoders minimizing the sum-MSE for the scenario of transmitting quantized observations in [18].  
There have been typical works focusing on freshness and fidelity metrics in WSN [19; 20; 21; 22]. An adaptive monitoring framework was introduced in [19] to achieve a balance between efficiency and accuracy on Internet-enabled physical devices. The authors in [20] determined the age-optimal policies for the update request and processing times subject to a maximum allowed distortion constraint on the updates. In [21], it was proved that there is an optimal number of quantization bits that optimizes the tradeoff of AoI and the MMSE. In [22], the AoI and MSE metrics were explicitly characterized by deriving the closed-form expressions for the block lengths and accuracy levels, after which they optimized the coding schemes by demonstrating a reachable region of AoI and MSE.  
The above-mentioned works focused on the impact of request time, quantization bits, and the block length, respectively, on system freshness and fidelity. While our work is distinguished from them in that we try to optimize system performance through adjusting the number of sensor nodes, which is of paramount significance at the very beginning deploying phase.