l-to-noise-ratio (SNR) at the BS can be expressed as (14.11) where hm,n is the small scale fading for the m-th sensor at time index n, gm is the path loss, Nm.n is the number of allocated bandwidths, Pm is the allocated transmission power spectral density for the m-th sensor, B is the separation among subcarriers, and No is the single-sided noise spectral density. Then, the allocated bandwidth for the m-th sensor is Bm.n = BoNm.n. Based on the received SNR, the Shannon capacity can be expressed as (14.12) In URLLC, with the constraints on ultra-reliability and low-latency, the blocklength is short and small packet sizes are adopted [8]. In addition, the size of payload data transmitted by sensors in control systems is usually small (e.g. about 100 bits [17]), which is suitable to be used in URLLC scenario. In such a scenario, the impact of the decoding error cannot be ignored. We assume that channel dispersion Vm.n is adopted to represent the capacity loss caused by transmission error, which can be expressed as [23] (14.13) When SNR is higher than dB, we have Vm,n 22 (loge)², which is very accurate [8]. When Vm,n (loge)², we can obtain a lower bound of the achievable rate with channel dispersion by substituting Vm.n = (loge)2. = Thus, in the rest of this chapter, we adopt Vm.n = (loge)2. = (14.14) 14.3 Communication-Control Co-Design For the m-th plant, the available uplink rate with finite block length is the uplink capacity eliminating the error bits that are introduced by channel dispersion, which can be expressed as (14.15) where log(Nm.nTm.,BB) is the approximation of the remainder of order terms log(Nm.nTm.,Bo)/ 2Nm,nTm,nBo (Nm.nTm.nBo), and f1. is the inverse of the Q-function. Then, the packet error probability can be expressed as (14.16) where fo() is the Q-function. The above channel model consists of path loss and small scale fading. According to [31], the path loss gm can be expressed as (14.17) where I'm is the distance between the m-th plant and the BS with unit km and is larger than 0.035 km [31]. 