Age of information (AoI) and energy efficiency (EE), as two important performance metrics in status update systems, usually cannot be simultaneously optimized. This paper investigates the age and energy tradeoff for multicast networks with retransmissions, where each sensed status update is encoded as a short blocklength packet and is broadcasted to multiple destinations via independent and identically distributed error-prone channels. By considering the stopping threshold, the average AoI and EE expressions for stopping at earliest- l , stopping at preselected- l , and wait-for-all schemes are derived as a function of the packet length. On this basis, the average AoI-EE ratio is introduced and is minimized to trade off age and energy by optimizing the packet length. Numerical results indicate that among the three schemes, earliest- l scheme attains the minimum AoI when the packet length is small, and preselected- l scheme attains the maximum EE when the packet length is large. An optimal packet length can always be found for each scheme to minimize age-energy ratio. Moreover, the selection of stopping threshold l will also impact the age and energy performance.

A novel status update information system is designed by jointly considering wireless energy harvesting diversity, status update transmission diversity, and hybrid automatic repeat request with chase combining (HARQ-CC) diversity, which consists of two sensors and one destination. The two sensors, which have finite-sized batteries, harvest energy from a Bernoulli process, and cooperatively deliver the status update to the destination by sharing a common information source. In addition, the two sensors synchronously operate in half-duplex (HD) mode and are triggered by a common control center. We first propose the sensor energy harvesting model that can be represented by Markov chain (MC) and develop the construction method of the transition matrix of sensor battery energy states as well as the stationary distributions. Secondly, the average age of information (AoI) of the proposed dual-sensor status update system is derived in terms of a closed-form expression by accurately calculating the statistical descriptions of the maximal number of the retransmissions of an update packet and the service time of one packet. Compared with traditional single-sensor system, the proposed dual-sensor system not only harvests more energy, but also has a smaller average AoI.

This paper focuses on the timely delivery of status updates for a multi-relay assisted energy harvesting (EH) Internet of Things system with short packet communications (SPC), where an EH-powered source transmits status updates to a destination with the aid of multiple EH-powered relays. To improve the energy efficiency and information freshness, an earliest-ℓ partial relay selection scheme is proposed, in which the earliest ℓ relays that successfully receive the status update from the source will be selected to forward the status update to the destination, and the selection combining (SC) and maximal-ratio combining (MRC) schemes are used at the destination. Firstly, we investigate the update packet delivery schemes of source-relay (S-R) and relay-destination (R-D) links, and present the packet error probabilities under the SC and MRC schemes based on SPC theory. Secondly, after characterizing the full charge time durations of both the source and relay, we investigate the statistical description of the number of the packet transmission attempts from the source to relay as well as the one from the relay to destination by using order statistics. With the analysis of the evolution of the instantaneous age of information (AoI), the expression for average AoI is derived. Finally, we investigate the average AoI minimization, which is formulated as a coupled triplet problem of the packet lengths at the source and relays and the value of ℓ. To overcome the coupling, we present the convexity approximation of the average AoI as well as the concise proof. Then, an efficient gradient-based two-step optimal search algorithm is proposed to solve the optimization problem, which searches the local optimal packet lengths for S-R and R-D links by iteratively updating the value of ℓ until the global optimal objective parameters are found. Numerical analyses give the effect of the key parameters on the average AoI, and the comparison demonstrates that the proposed gradient-based method converges quickly than the conventional greedy search method.

The evolution of the fifth-generation (5G)/ beyond 5G (B5G) mobile communication networks greatly depends on the seamless integration of terrestrial and sky networks over advanced multi-tier heterogeneous network (HetNet) infrastructure. By using the huge potential of unmanned aerial vehicles (UAVs) and mm-Wave, we develop a novel and practical multi-UAV assisted multi-tier HetNet model which consists of clustered aerial UAV base stations (U-BSs) and Poisson point process (PPP) based ground BSs (G-BSs) for emergency and crowded hotspot area. In a typical cluster, both ground user equipments (GUEs) and UAVs are modeled as Poisson cluster process (PCP) and scattered around the common cluster center. Specially, the analysis is conducted by adding two additional tiers which consist of multiple intra-cluster U-BSs and single G-BS in representative cluster so that the point sets of U-BSs and G-BSs are partitioned into two sub-sets, respectively, and a 4-tier network model is formed. To find the contribution of the inter-cluster associations on the performance of networks, we construct 2-tier and 4-tier association schemes. The 2-tier association allows a GUE associated only with intra-cluster U-BSs and G-BS, while the 4-tier association allows all inter/intra-cluster U-BSs and G-BSs can be associated. Then, according to stochastic geometry methods, statistical description of the downlink interferences experienced at a typical GUE is derived. This derivation yields the downlink coverage probabilities and total network throughput are obtained. It is achieved that association probabilities greatly depend on the distribution of daughter point process. UAVs’ height and the distributions of U-BSs and GUEs impose non-monotonous impact on coverage probabilities. Due to severe inter-cluster interference, the achievable average area throughput is not always increasing with SINR so that there is an optimal SINR threshold. In addition, our analysis finds the proposed 4-tier association scheme outperforms the simple 2-tier one in terms of the average area throughput.

This paper focuses on a secrecy constrained massive multiple-input multiple-output (MIMO) relaying system in terms of the optimal design of system parameters such as the optimal total number of antennas at relay, where a more practical mixed analog-to-digital converters (ADCs) scheme, double-resolution ADCs scheme, is proposed. In the proposed double-resolution ADCs scheme, the total M antennas at relay are divided into two parts, one of which includes M ₀ antennas with medium-resolution ADCs only requiring 5~12 quantization bits and the remainder of which consists of M ₁ antennas with low-resolution ADCs. The transmission from relay to destinations is exposed to a passive eavesdropper. For such massive MIMO relaying systems, we first derive the total achievable ergodic rates of legitimate users as well as the corresponding secrecy outage rates. Then, a reasonable energy consumption model is modeled so that the secrecy energy efficiency (SEE) is derived, where the effect of the source power, the resolutions of ADCs, and the ratio of the antenna numbers with medium- and low-resolution ADCs are exploited perfectly. The presented numerical results show that replacing high-resolution ADCs with medium-resolution ADCs is beneficial for improving the system SEE while the effect on the total achievable rate is very small. Specially, three main insights are achieved: 1) there exists an optimal value of the source power at which the SEE is optimal; 2) with given ratio M ₀ :M ₁ , the optimal value of quantization bits of medium-resolution ADCs is upper-bounded, under which the system has higher SEE, that is to say, we obtain the upper bound of the resolution of the medium-resolution ADCs; and 3) the optimal number of the total antennas is impacted jointly by the number b ₀ of the quantization bits of medium-resolution ADCs and the ratio M ₀ :M ₁ . Specially, while the optimal number of the total antennas is 100 or so for the pure high-resolution ADCs systems, the one for the proposed double-resolution ADCs systems would up to 500~700. Moreover, the optimal antenna number is increasing with the decrease of b ₀ and the ratio M ₀ :M ₁ so that the system performance can be improved further.

In the Internet of Things monitoring systems, the fresh information delivery and efficient energy usage are two significant design concerns. However, they generally cannot be simultaneously achieved. In this paper, we investigate the fundamental tradeoff between the age of information (AoI) and energy consumption (EC) for a generalized $\ell$ th best relay selection policy in two-hop cooperative status update systems with automatic repeat request (ARQ), where the source delivers the sensed status update to the destination through multiple decode-and-forward relays. Among these relays, the $\ell$ th best relay (i.e., the $\ell$ -th earliest one that correctly decodes the update packet) will be selected as a forwarder to relay the data to the sink. When a decoding failure occurs, we can either retransmit the old packet to save sensing EC or sense and transmit a new one to reduce AoI. Accordingly, the classical ARQ and truncated ARQ protocols are employed in the second hop. By considering short packet-based transmissions, the average AoI and average EC expressions are derived, and the weighted combination of them is minimized to attain the tradeoff. Numerical results demonstrate that an optimal packet size that can trade off age and energy always exists. Moreover, the best relay does not always minimize the weighted combination, and the truncated ARQ is superior to the classical one. As a promising candidate, the $\ell$ th best relay selection can be implemented when either the system energy resource is limited or the best relay is unavailable.