The explosive growth of Internet of Things (IoT) and 5G communication technologies have driven the increasing computing demands for wireless devices. In the meantime, an IoT device (e.g., sensor) often carries a capacity-limited battery and an energy-saving low-performance processor under the consideration of the stringent device size constraint and production cost. Recently, wireless powered mobile-edge computing (MEC) has emerged as a promising technique to solve the above problems [1, 2, 3, 4]. In a wireless powered MEC system, WDs are powered by means of wireless power transfer (WPT)  and can offload intensive computations to the edge servers located at the radio access networks [6, 7]. Such an integration of MEC and WPT technologies effectively solves the limitations of both on-chip energy and computing capability of IoT devices.
Existing studies on wireless powered MEC mostly concern the joint offloading and resource allocation to enhance the computing performance of the system. For instance, 
considered a single user following a binary offloading policy that the computation task is non-partitionable and must be offloaded as a whole. It then finds the optimal offloading strategy by optimizing the computation and communication resource to maximize the probability of successful computation. Such design was extended to multiuser MEC systems in, which considered a binary computation offloading policy and jointly optimized the individual computing mode selection and system transmission time allocation to maximize the processed task data in a given time frame. On the other hand,  considered a partial offloading methods where the computation task of each user can be arbitrarily partitioned and executed separately at both the local device and remote edge server. It then jointly optimizes the WPT transfer, spectral and computing resource allocation to minimize the server energy consumption under user computing delay constraint. Several other works have also considered the designs of wireless powered MEC system under random task arrivals 
, using machines learning based structure, and for UAV-enabled scenarios [13, 14].
An inherent problem in wireless powered systems is severe user near-far unfairness caused by drastic attenuation of the RF energy signal over distance. User cooperation is an effective solution to enhance the overall system communication and computing performance. For instance, [15, 16, 17] proposed various user cooperation methods in wireless powered communication networks. Under the wireless powered MEC paradigm,  considered a two-user scenario where one acts as the relay to forward the other’s computation offloading to the AP. It then minimizes the total transmit energy of the AP by jointly optimizing the power and time allocation under computation performance constraint.  investigated a computation cooperation method, in which an active-computing user can offload part of its task to multiple helpers for remote execution. Furthermore,  considered exploiting joint computation and communication cooperation where a helper node acts not only as a communication relay to the AP but also a computing agent that can compute the user’s task locally. Unlike  that considers a dedicated helper, in this paper, we consider the case that the relay helper also has its own task to process, thus needs to carefully allocate its resource, e.g., computing power and energy, to both help the other user and compute its own task. Such situation requires joint optimization of the task offloading of the two users, user computing resource allocation, and the system-level wireless resource allocation to maximize the overall system computing performance.
In this paper, we investigate a novel two-user cooperation method in wireless powered MEC system. As shown in Fig. 1, we consider users powered by an energy node by means of WPT. Using the harvested energy, the two users then compute their own tasks assisted by an edge server (ES), i.e., both users’ tasks can be offloaded for edge execution. In particular, we consider that one user () is blocked from direct communication to the ES, such that the other user () can relay ’s task to the MEC server. Meanwhile, we allow to allocate part of its resource to compute ’s task to reduce the offloading communication delay to the edge server. The main contributions of this paper are summarized as follows:
We present a new user collaboration model in wireless powered MEC, where the helping user acts both as the communication relay and the computing agent for the other user . In particular, we consider a partial offloading scheme, such that the task data of can be partitioned at three parts and computed at itself, , and the ES, respectively. The task of , on the other hand, can be partitioned and computed both locally and offloaded to the ES, respectively.
We formulate an optimization problem to maximize the weighted sum-computation-rates (WSCR) of the two users, which is an direct measure of the data processing capability of the system. This involves a joint optimization of task partitions, user resource allocation (CPU frequency and transmit power), system-level time allocation (on WPT and data transmission). We propose an efficient method to solve the problem optimally.
We compare the performance of the proposed method with two representative benchmark methods, where either computation or communication cooperation is absent. We show that the proposed method significantly outperforms the two benchmarks especially when task offloading is costly for either user, e.g., weak inter-user or user-ES channel. We also show that not only , but also the helper can benefit from the joint communication and computation collaborations.
Ii System Model
Ii-a Protocol Description and Channel Model
As shown in Fig. 1, we consider a wireless powered MEC system consisting of an energy node (EN), two energy-harvesting users and an edge server (ES), where each device is equipped with a single antenna. In particular, we assume that the EN has constant power supply and transfers wireless power to and . The two users have no other embedded energy source and rely on the harvested energy to compute their own tasks. In particular, both users can offload part of their tasks to the ES following a partial offloading policy. Due to the hardware constraint, each user reuses its antenna for both energy harvesting and task data transmission in an time division duplexing (TDD) manner . Specifically, we assume that the direct communication between and ES is blocked, such that may serve as the relay to forward the computation offloading of . Besides, we also assume that the relay user may allocate part of its computation resource to help compute ’s task, for instance, when task offloading to the server is costly under deep channel fading. After the ES finish computing the received task(s), it sends the results back to , and so does to subsequently. For simplicity, all the channels are assumed to be independent and reciprocal and follow quasi-static flat-fading, such that all the channel coefficients remain constant during each block transmission time. As illustrated in Fig. 1, we use , , to denote the corresponding channel gains.
Notice that in the above cooperative communication and computation model, ’s task can be executed at , and ES, while ’s task can be executed at and ES.
Ii-B System Time Allocation
For a tagged time frame of duration , we show the detailed transmission time allocation in Fig. 2. At the beginning of a time frame, the EN transfers wireless power to and for a duration of with a fixed transmit power . After the WPT period, offloads part of its computation task to in the subsequent period . In the next time slot of duration , first relays the received ’s task with power for amount of time to the ES and then offloads its own task to the server with power for amount of time. We denote as the total task offloading time of . After receiving the tasks from , the server computes and returns the results to . Here, we assume the ES has much stronger transmit power and computing capability than the energy-harvesting users, thus neglect the time consumed on computing at the edge server and data transmission back to (similar to the assumptions in [10, 9]). Notice that can also compute part of ’s task locally. Here we assume that can only compute one task at a time, such that it computes ’s task immediately after receiving it. The total computation time of spent on computing ’s task is denoted as . We use to denote the duration from starts to receive the task offloading from until it starts to send the results back to . Evidently, equals the longer duration between and , i.e.,
After receiving the computation result of from the server, it first combines the server’s feedback with the locally computed result for , and then sends back to . We denote the corresponding transmission time and transmit power as and , respectively. Overall, we have a total system time allocation constraint
In the following section, we derive the computation performance of both users and formulate the problem to maximize the system’s data processing capability.
Iii Computation Performance Analysis and Problem Formulation
Iii-a Wireless Energy Transmission
In the first part of a tagged time frame, the EN broadcasts wireless energy to each user for a duration of . We let denote the fixed transmit power of the EN such that the amount of energy harvested by can be expressed as
where denotes the energy harvesting efficiency assumed equal for both users.111Although a single energy harvesting circuit exhibits non-linear energy harvesting property due to the saturation effect of circuit, it is shown that the non-linear effect can be effectively rectified by using multiple energy harvesting circuits concatenated in parallel, resulting in a sufficiently large linear conversion region in practice .
With the harvested energy, the two users compute their tasks locally or/and offload the computations to other devices for remote execution. We let denote the amount of the -th user’s task data processed at the -th device within a tagged time block (in bits), where the ES is indexed as 0. Accordingly, the total number of processed bits of the two users are denoted as and , respectively. The major performance metric is computation rates of the two users (in bits/second), which are expressed as and , respectively. Without loss of generality, we assume in the following analysis, such that we use and interchangeably. In the following, we derive the expressions of and .
Iii-B Individual Local Computation
Recall that the -th user computes amount of its own task locally, where Let denotes the number of CPU cycles required for computing one input bit, which is assumed equal for both users without loss of generality. Besides, we denote as the -th user’s CPU computing speed (cycles per second), where is the maximum CPU frequency. Notice that each user can compute throughout the time block without being interrupted by information or energy transmissions. We denote as the corresponding local computation time of the -th user. Then, the local computation rate of is
Meanwhile, the corresponding energy consumption is 
where is the effective capacitance coefficient that depends on the chip architecture at user .
Iii-C Computation Offloading to Edge Server
Besides local computation, each user can also offload part of their computing task to the edge for remote execution. The computation rate due to edge computation of the two users are denoted as and . In particular, the amount of task data that is offloaded from to is constrained by
where denotes the system bandwidth, represents the power of receiver noise, and is a constant term accounting for the gap from the channel capacity due to a practical modulation and coding scheme. Meanwhile, the energy consumption on transmitting the information of is
After receiving from , acts as a relay to help offload task data to the ES with the time duration and transmit power . Therefore, is constrained by
Then offloads its own task data to the ES with the time duration and power , such that we have
The energy consumption of on offloading the tasks to the edge server is
Iii-D Collaborative Computing at
Besides forwarding the received computation task from to the edge server, also executes part of ’s task, whose amount is denoted as . We denote and as the corresponding computation time and CPU frequency for processing , which are related as
Besides, the corresponding consumed energy by is
Notice that the total local computation time of is constrained by
In time slot , first combines the computation outcomes of received from the edge server and produced locally, and then transmits the result back to . Here, we assume the amount of computation outcome is proportional to the task input, such that needs to send bits back to , where is a fixed parameter. We denote the transmit power used for feeding back the result to as . Evidently, the transmission rate cannot exceed the channel capacity, i.e.,
Besides, the consumed energy is denoted as . From the above discussion, the consumed energy of the two users are constrained by the total individual harvested energy
Iii-E Problem Formulation
In this paper, we are interested in maximizing the weighted sum-computation-rates (WSCR) of the two users by jointly optimizing the number of task bits processed at each device (), user resource allocation (CPU frequency and transmit power ), and system-level time allocation (on WPT and data transmission . Thus, the problem can be mathematically expressed as
Here denotes the weight associated with and . Note that problem is a non-convex optimization problem in the above form, e.g., due to the multiplicative terms in (4) and (14), and the non-concave functions in (8) and (9). In the following, we provide the optimal solution to .
Iv Optimal Solution to
In this section, we study the optimal solution to
, which is transformed into a convex problem and accordingly solved optimally with off-the-shelf convex algorithms, e.g., interior point method. To begin with, we introduce an auxiliary vector,, where and . Then, we have that
Notice that the above constraint (19)-(22) are jointly convex in . From , each of the two energy-constrained users should compute throughout the time block to maximize the local computation rate. This indicates that and holds. Accordingly, constraints (15) and (16) can be respectively transformed into
where , , and are constant parameters. Similarly, constraint (4) reduces to
From the above discussion, problem is equivalently transformed into
Notice that the above problem is still non-convex because of the multiplicative terms in (24) and (25). However, it becomes a convex problem once we fix , thus can be efficiently solved given . For simplicity, we denote the optimal value of given as , where . Therefore, reduces to a one-dimensional search to find the optimal that maximizes , where we devise a golden-section search over the scalar variable in Algorithm. 1. After solving optimally, we can retrieve the optimal transmit power to from (18).
V Simulation Results
In this section, we use simulations to evaluate the performance of the proposed cooperation method. In all simulations, we set , , , . For simplicity of illustration, the wireless channel gain between two devices, denoted by , follows a path-loss model , where denotes the distance of the two devices considered, denotes carrier frequency, denotes the path loss factor, and denotes the antenna power gain. Unless otherwise stated, we set , , , the EN- and EN- distances as and , the -ES distance as , and the - distance as . Besides, we set equal computing efficiency parameter , , and for both devices. For data offloading, we set the bandwidth and . For performance comparison, we consider the following representative benchmark methods:
Communication cooperation only (Benchmark 1): only acts as a relay to help offload parts of its task to ES , i.e., .
Computation cooperation only (Benchmark 2): only acts as a computing agent to help process parts of its task, i.e., .
We first show the impact of -to-ES channel to the optimal WSCR performance in Fig. 3. Here, we let (the distance between and ES) vary from to , while the channel degrades with . As expected, the WSCR of all the three schemes degrade with the increase of due to the larger time and energy consumption required to offload the tasks to the ES. We see that the proposed method evidently outperforms the two benchmark methods, where on average it achieves and higher WSCR than benchmark 1 and 2, respectively. In particular, benchmark 2 has the worst performance as cannot utilize the powerful edge computation. Benchmark 1 has comparable performance with the proposed method but the performance gain becomes larger as the -ES channel weakens, due to the high cost on task offloading becomes the performance bottleneck of the system.
In Fig. 4, we further investigate the impact of inter-user channel to the system performance. Here, we set , , and let increase from to . As expected, with the increase of , the performances of the proposed method and benchmark 1 decline due to the larger cost on data offloading. Benchmark 2 has relatively steady performance with the change of inter-user channel, because most of the tasks are computed locally for at optimum. On average, the proposed cooperation achieves and higher WSCR than the two benchmark methods.
Fig. 5 shows the impact of EN- channel to the system performance. Here, we vary from to while the others are default values. Still, the performance of all the methods degrades due to the smaller available energy received by under a larger . Nonetheless, on average the proposed scheme still outperforms the two benchmarks by and , respectively.
Finally, in Fig. 6, we plot computation rate regions (by varying from to ) achieved by the proposed method and the better performing benchmark method, i.e., benchmark 1, under different path-loss factor . Evidently, with a larger , both schemes achieve a smaller rate region due to the smaller energy harvested and larger cost on data offloading. For both values of , the proposed scheme has an evident advantage over benchmark 1, where the regions of the benchmark are inside those of the proposed scheme. This indicates that both users can benefit from the considered cooperation.
The above results verify that the proposed cooperation method has strong flexibility in adapting the resource allocation to the change of network parameters for supporting high-performance computation service. In particular, not only the weak user , but also the helper can benefit from the proposed joint communication and computation cooperation. The performance advantage is especially evident when the offloading channel, either due to - or -ES, is weak.
In this paper, we investigated a joint communication and computation cooperation method in a two-user wireless powered MEC system. We formulated an optimization problem to maximize the two users’ weighted sum computation rates and proposed an efficient method to solve it optimally. Simulation results show that the proposed cooperation method can effectively enhance the computation performance of the system under different network setups compared to other representative benchmark methods, especially when task offloading is costly for either user. Besides, both users can benefit from the proposed cooperation.
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