tion before the required time slot, it will send to MEC server for joint processing. Specifically, mk is the number of bits that UEs offloads to the MEC securely. The signal received at the AP and Eve becomes: (8.1) (8.2) Figure 8.1 Secure MEC partial User 1 offloading model. User 2 MEC server with AP Offloading STATE User K Result downloading Malicious listening 8.2 System Model here, Sk E C is the information-bearing signal for UE ,NKECN(0,02) are the complex Gaussian noise at the AP and Eve, respectively. The secrecy rate, from information-theoretic perspective, is given as (8.3) where [a]+ = max (a,0) For offloading, the energy consumption consists of two parts: transmission and fixed cir- cuit. In particular, Pr, a constant, is the power of other circuit except for the transmission unit. The rest Lk - Mk bits will be calculated locally, which will be described below. 8.2.2 Local Computing Traditionally, users will process all the computation locally. To model such a process, we first define some parameters. First, we assume user k's CPU needs Ck cycles to finish computation of a single bit of data. Also, let fk be the clock speed of the CPU. For simplicity, we assume the clock speed does not change. Each user is allowed to start the local comput- ing from the beginning to the end of the process; thus, the total number of computation bits becomes Tfk/Ck. Energy consumption for local computing can be modeled as where Ek the CPU energy coefficient [197, 209]. 8.2.3 Receiving Computed Results After receiving the computation task from each user, MEC server will start the calcula- tion. When finished, it will send the result back to each user. Here, like [220, 233], we assume this process takes negligible time because of two reasons: 1) MEC server has pow- erful multi-thread processor, 2) compared with data bits to be computed, result takes way less space; hence, downlink transmission is almost instant. The whole process is illustrated in Figure 8.2. 8.2.4 Computation Efficiency in MEC Systems Like previously ment