Minimum Signal-to-interference-plus-noise Ratio Research Articles

Robust Max-Min Fairness Transmission Design for IRS-Aided Wireless Network Considering User Location Uncertainty

In this paper, we propose a robust max-min fairness transmission design for intelligent reflecting surface (IRS)-aided wireless network in the presence of user location uncertainty. In particular, the non-isotropic reflection property for the IRS element is considered. We investigate the joint design of the active transmit beamformer at the base station (BS) and the passive phase shift matrix along with the deployment orientation (facing/pointing direction) of the IRS for maximizing the worst-case minimum signal-to-interference-plus-noise ratio (SINR) received by the users. In order to show the potential gains obtained by adjusting the deployment orientation of the IRS, a single-input-single-output (SISO) system is studied where a closed-form signal-to-noise ratio (SNR) of the user is obtained. For the multi-user case, to solve the resulting non-convex problem, an inexact-alternating-optimization algorithm consisting of a double-loop iteration is proposed. Specifically, in the inner loop, an optimization problem with semi-infinite constraints needs to be solved to increase the worst-case min-SINR compared to the given SINR reference value. We first transform the semi-infinite constraints into linear matrix inequality (LMI) constraints with finite form by applying the Taylor expansion approximation method, the general S-procedure, and the general sign-definiteness lemma. Then an efficient alternating optimization (AO) algorithm based on the two-dimensional search method, negative square penalty (NSP) method, and successive convex approximation (SCA) technique is proposed. While in the outer loop, we update the given SINR reference value as the worst-case minimum SINR obtained after each inner loop iteration. The whole algorithm terminates when the updated SINR reference values converge. Simulation results demonstrate the effectiveness of the proposed algorithm, and also show the additional system performance gain brought by the optimization of the IRS deployment orientation compared to its counterpart with fixed IRS deployment orientation, especially for a smaller IRS element number and a more prominent non-isotropic reflection property of the IRS element.

Joint Active and Passive Beamforming Design for IRS-Aided Radar-Communication

In this paper, we study an intelligent reflecting surface (IRS)-aided radar-communication (Radcom) system, where the IRS is leveraged to help Radcom base station (BS) transmit the joint of communication signals and radar signals for serving communication users and tracking targets simultaneously. The objective of this paper is to minimize the total transmit power at the Radcom BS by jointly optimizing the active beamformers, including communication beamformers and radar beamformers, at the Radcom BS and the phase shifts at the IRS, subject to the minimum signal-to-interference-plus-noise ratio (SINR) required by communication users, the minimum SINR required by the radar, and the cross-correlation pattern design. In particular, we consider two cases, namely, case I and case II, based on the presence or absence of the radar cross-correlation design and the interference introduced by the IRS on the Radcom BS. For case I where the cross-correlation design and the interference are not considered, we prove that the dedicated radar signals are not needed, which significantly reduces implementation complexity and simplifies algorithm design. Then, a penalty-based algorithm is proposed to solve the resulting non-convex optimization problem. Whereas for case II considering the cross-correlation design and the interference, we unveil that the dedicated radar signals are needed in general to enhance the system performance. Since the resulting optimization problem is more challenging to solve as compared with the case I, the semidefinite relaxation (SDR) based alternating optimization (AO) algorithm is proposed. Particularly, instead of relying on the Gaussian randomization technique to obtain an approximate solution by reconstructing rank-one solution, the tightness is achieved by our proposed reconstruction strategy. Simulation results demonstrate the effectiveness of proposed algorithms and also show the superiority of the proposed scheme over various benchmark schemes.

User Association for Reconfigurable Intelligent Surfaces Aided Cell-Free Networks

Cell-free (CF) network can efficiently suppress inter-cell interference and enable multiple base stations (BSs) to serve users cooperatively without being affected by cell boundaries. However, to further increase the network capacity, a large number of BSs need to be deployed, resulting in high cost and power consumption. To tackle this problem, reconfigurable intelligent surface (RIS) has emerged as a cost-effective technology to enhance energy and spectral efficiency of wireless communications. In this paper, we consider an RIS-aided CF network by exploiting their complementary advantages where each user assisted by a dedicated RIS can associate with multiple BSs. We first characterize each user's average signal-to-interference-plus-noise ratio (SINR) in the RIS-CF network. Then, we formulate an SINR balancing problem to maximize the minimum SINR among all users by designing the BS-user associations. Despite of the non-convexity and combinatorial feature of this problem, a two-step fractional linearization algorithm is developed to solve it optimally. Specifically, we transform a nested mixed-integer linear fractional program (MILFP) into a solvable mixed-integer linear programming (MILP) problem through the generalized fractional programming and reformulation-linearization method. Finally, we provide numerical results to validate the effectiveness of our proposed algorithm compared to other benchmark schemes.

Optimal Resource Management for NOMA-Based Visible Light Communication Systems With Shot Noise

In this paper, the problem of power allocation is investigated for downlink visible light communication (VLC) systems with non-orthogonal multiple access. In the system, both input-dependent shot noise and input-independent Gaussian noise are considered due to the properties of practical VLC channels. We consider two scenarios for the transmitter with a single light emitting diode (LED) and multiple LEDs, respectively. For single-LED scenarios, the problem is posed as a joint optimization problem of alternating current and direct current power control, whose goal is to maximize the minimum signal-to-interference-plus-noise-ratio (SINR) of all users. Although the original problem is non-convex, a geometric programming based algorithm is proposed to acquire the global optimal solution. For multi-LED scenarios, the transmit and dimming beamforming vectors are jointly optimized to maximize the minimum SINR of all users. A joint optimization algorithm that alternately optimizes transmit and dimming beamforming vectors is proposed. Particularly, the transmit beamforming problem is converted into a second-order cone programming problem through the successive convex approximation method. The dimming beamforming problem is transformed into a feasibility problem utilizing a low-complexity bisection algorithm. Numerical results reveal the superior performance of the proposed algorithm compared with its orthogonal multiple access counterpart and conventional schemes without shot noise.

Linear Precoding for Space-Time Line Code-Based Multicast Systems

In this article, a linear precoding weight vector is designed to enhance the minimum signal-to-interference plus noise ratio (SINR) of a space-time line code (STLC)-based multicast users. To solve the intractable minimum SINR maximization problem, the optimal weight vector for each STLC user is derived, and then, the individual optimal weight vectors are linearly combined. The designed linear precoding vector improves the minimum and average SINR of the multicast users as verified by numerical results. Numerical results also verify that the STLC-based multicast is a promising scheme, especially, if a transmitter has a large number of transmit antennas and the additive noises are severe at the users.

Optimization of pre-equalized time reversal security transmission systems assisted with artificial noise

Time reversal (TR) transmission technology can focus the power of a signal in both time and space domains and reduce signal energy leakage to unintended receivers, making it suitable for physical layer security systems. By adding a pre-equalizer to the transmitter and optimizing it, the performance of multi-antenna TR transmission system can be improved obviously with an acceptable optimization complexity. In this paper, the pre-equalizer and artificial noise (AN) are jointly optimized to improve the security performance of pre-equalized TR (ETR) systems when eavesdropping channel state information (ECSI) is unknown or known. When ECSI is unknown, null-space AN is adopted, and the pre-equalizer is optimized to minimize the signal power under the constraint of the minimum signal-to-interference-plus-noise ratio (SINR) of the legitimate receiver, so the AN power and the interference with the eavesdropper are maximized. The optimization problem is transformed into the problem of finding the maximum generalized eigenvalue of a matrix pencil. When ECSI is known, under the minimum SINR constraint of the legitimate receiver, the pre-equalizer and AN’s covariance matrix are jointly optimized to minimize the SINR of the eavesdropper. The optimization problem is non-convex and is transformed into a convex problem, which can be solved using the CVX toolbox. The optimization complexity is independent of the number of transmit antennas. Simulation results demonstrate that compared with TR systems, by optimizing the pre-equalizer, the security performance of ETR multi-antenna systems can be significantly improved, and the optimization complexity is acceptable.

Neural Network Based IRSs-UEs Association and IRSs Optimal Placement in Multi IRSs Aided Wireless System.

Implementing intelligent reflecting surfaces (IRSs), in high frequency based beyond 5G networks, has become a necessity to overcome the harsh blockage issues that exist in these bands. IRSs can supply user equipment (UEs) with multi alternative virtual line of sight (LOS) links, hence enhancing the spectral efficiency (SE) of the system. As a result of deploying multi IRSs as communication assistants, the step of IRSs-UEs association is required to optimally assign each UE to its best IRS; consideration of the interference between different links is needed, to maximize the system performance. However, this process will be a time and power consuming problem, if conventional schemes, which exhaustively search all possible association patterns to find the optimum one for communication, is adapted. Although iterative search based schemes can reduce this complexity, they still need feedback signaling in real time. Hence, they will be inefficient in terms of power consumption and delay. Moreover, optimal placement of the multi-IRSs in the network, to enlarge the system performance, is still an open issue and needs to be studied. Consequently, in this paper, to handle the IRSs-UEs association problem, we propose a neural network (NN) based scheme using a multi-IRSs aided multi input multi output (MIMO) system. In this system, the estimated angles of arrival (AoAs) of UEs are used as input features for the NN, which is trained to associate each UE to its best IRS based on this information; then, within each IRS, passive beamforming is performed. Adapting this NN in online mode guarantees obtaining better performance while relaxing the complexity of association and increasing response time, giving a performance comparable to the exhaustive and iterative search based schemes. The proposed NN based scheme determines the association pattern without searching or feedback signals. Moreover, the proposed approach maintains the system SE nearly similar to the optimum performance obtained by the conventional scheme. Secondly, a criterion is suggested for optimal deployment of multi IRSs in the network, depending on maximizing the average summation UEs signal-to-interference-plus-noise ratio (SINR). Numerical results prove that this strategy outperforms a reference one, which aims to guarantee certain performance by maximizing minimum UE SINR. In contrast the proposed strategy achieves better system and per UE spectral efficiency.

Multiuser beamforming optimization for IRS‐aided systems with discrete phase shifts

Here, the beamforming design for multiuser multiple-input and multiple-output (MIMO) downlink transmission aided by an intelligent reflecting surface (IRS) with discrete phase shifts is studied. The authors deduce a minimum signal-to-interference-plus-noise-ratio (SINR) maximization fairness problem with the transmit beamformer, the receive beamformer and IRS phase shifts as optimization variables, which is generally NP-hard. Hence, an alternating optimization algorithm based on the gradient extrapolated majorization-minimization (GEMM) approach is employed to solve the above problem. Specifically, when the transmit beamformer and reflective phase shift are fixed, the authors give an optimal closed expression for the receive beamformer. Then, the receive beamformer is fixed, and the minimum SINR maximization problem at the transmitter is transformed into a power minimization problem. Finally, under the zero-forcing (ZF) transmitter beamformer, the GEMM algorithm is used to optimize the reflective phase shift. Simulation results show that by comparing to existing methods, the proposed GEMM algorithm can almost achieve the same performance with lower complexity.

Scalable Deep Reinforcement Learning for Routing and Spectrum Access in Physical Layer

This paper proposes a novel scalable reinforcement learning approach for simultaneous routing and spectrum access in wireless ad-hoc networks. In most previous works on reinforcement learning for network optimization, the network topology is assumed to be fixed, and a different agent is trained for each transmission node—this limits scalability and generalizability. Further, routing and spectrum access are typically treated as separate tasks. Moreover, the optimization objective is usually a cumulative metric along the route, e.g., number of hops or delay. In this paper, we account for the physical-layer signal-to-interference-plus-noise ratio (SINR) in a wireless network and further show that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bottleneck</i> objective such as the minimum SINR along the route can also be optimized effectively using reinforcement learning. Specifically, we propose a scalable approach in which a single agent is associated with each flow and makes routing and spectrum access decisions as it moves along the frontier nodes. The agent is trained according to the physical-layer characteristics of the environment using a novel rewarding scheme based on the Monte Carlo estimation of the future bottleneck SINR. It learns to avoid interference by intelligently making joint routing and spectrum allocation decisions based on the geographical location information of the neighbouring nodes.

Efficient Resource Allocation for Multi-UAV Communication Against Adjacent and Co-Channel Interference

Unmanned aerial vehicle (UAV) swarm has emerged as a promising novel paradigm to achieve better coverage and higher capacity for future wireless network by exploiting the more favorable line-of-sight (LoS) propagation. To reap the potential gains of UAV swarm, the remote control signal sent by ground control unit (GCU) is essential, whereas the control signal quality are susceptible in practice due to the effect of the adjacent channel interference (ACI) and the external interference (EI) from radiation sources distributed across the region. To tackle these challenges, this paper considers priority-aware resource coordination in a multi-UAV communication system, where multiple UAVs are controlled by a GCU to perform certain tasks with a pre-defined trajectory. Specifically, we maximize the minimum signal-to-interference-plus-noise ratio (SINR) among all the UAVs by jointly optimizing channel assignment and power allocation strategy under stringent resource availability constraints. According to the intensity of ACI, we consider the corresponding problem in two scenarios, i.e., Null-ACI and ACI systems. By virtue of the particular problem structure in Null-ACI case, we first recast the formulation into an equivalent yet more tractable form and obtain the global optimal solution via Hungarian algorithm. For general ACI systems, we develop an efficient iterative algorithm for its solution based on the alternating optimization methods. Extensive simulation results demonstrate that the proposed algorithms can significantly enhance the minimum SINR among all the UAVs and adapt the allocation of communication resources to diverse mission priority.

The Design and Optimization of Random Code Assisted Multi-BD Symbiotic Radio System

Symbiotic radio (SR) is a new paradigm of spectrum sharing that allows passive Internet-of-Things (IoT) device to transmit messages over the ambient RF signal. Considering that the reader needs to collect information from multiple IoT devices in practice, and the traditional multiple access schemes that require coordination among users are unaffordable for the passive devices, we propose a random code assisted multiple access scheme, in which each backscatter device (BD) independently chooses a random code to spread its signal and the incident signal is backscattered. To avoid the need of the instantaneous information, including the specific codes and the instantaneous channel state information of the backscatter links, and to optimize the transmit power and the BD reflection coefficients, we derive the asymptotic BD signal to interference plus noise ratio (SINR) by employing the large-dimension random matrix theory. We formulate the joint optimization problem to maximize the minimum asymptotic SINR among BDs with guaranteeing the primary target rate. By investigating the property of the problem, the original problem is transformed and solved by the proposed iterative-based algorithm. Extensive simulations are executed to verify our theoretical analysis and demonstrate the outperformance of the proposed algorithm.

Max–min fair robust beamforming design for underlay device‐to‐device communications in cellular networks

SummaryThis paper investigates the robust downlink beamforming designs based on max–min fairness and base station (BS) power consumption constraint for device‐to‐device (D2D) communications underlaying cellular network, under the assumption of imperfect channel state information (CSI) at the BS. Our objective is to maximize the minimum signal‐to‐interference‐plus‐noise ratio (SINR) or non‐outage probability of users while guaranteeing that the consumed power at the BS is less than a threshold. In particular, three max–min fairness scenarios are considered. In the first scenario, the worst‐case SINR of cellular users (CUs) is maximized where the D2D SINR is guaranteed to be above a specified predetermined threshold. In the second scenario, we extend the first scenario and maximized D2D SINR while maximizing CUs' SINR. In these two scenarios, it is assumed that the errors are upper bounded in their Frobenius norms. In the third scenario, the minimum non‐outage probability of users is maximized, while a probabilistic model is considered for the uncertainty of channel covariance matrices. Although such optimization problems are not convex, the semidefinite relaxation (SDR) approach is used to obtain the optimal beamforming matrix, which always complies the rank‐one constraint. Simulation results show that significant improvement in terms of minimum SINR of CUs, the minimum non‐outage probability of CUs, and the probability of feasibility and the fairness index can be achieved with our proposed algorithms in comparison with other beamforming schemes.

Asymptotic Max-Min SINR Analysis of Reconfigurable Intelligent Surface Assisted MISO Systems

This work focuses on the downlink of a single-cell multi-user system in which a base station (BS) equipped with $M$ antennas communicates with $K$ single-antenna users through a reconfigurable intelligent surface (RIS) installed in the line-of-sight (LoS) of the BS. RIS is envisioned to offer unprecedented spectral efficiency gains by utilizing $N$ passive reflecting elements that induce phase shifts on the impinging electromagnetic waves to smartly reconfigure the signal propagation environment. We study the minimum signal-to-interference-plus-noise ratio (SINR) achieved by the optimal linear precoder (OLP), that maximizes the minimum SINR subject to a given power constraint for any given RIS phase matrix, for the cases where the LoS channel matrix between the BS and the RIS is of rank-one and of full-rank. In the former scenario, the minimum SINR achieved by the RIS-assisted link is bounded by a quantity that goes to zero with $K$ . For the high-rank scenario, we develop accurate deterministic approximations for the parameters of the asymptotically OLP, which are then utilized to optimize the RIS phase matrix. Simulation results show that RISs can outperform half-duplex relays with a small number of passive reflecting elements while large RISs are needed to outperform full-duplex relays.

Performance analysis and SINR‐based power allocation strategies for downlink NOMA networks

This study analyses the performance of downlink non-orthogonal multiple-access (NOMA) networks over independent but not necessarily identically distributed Rayleigh fading channels by deriving closed-form expressions for the average signal-to-interference-plus-noise ratio (SINR), average achievable rate, and outage probability of all network users. Moreover, SINR-based power allocation strategies are studied. Specifically, the optimisation problems of max–min SINR, multi-objective SINR, sum-SINR and proportional-fairness-SINR maximisation under minimum SINR constraints are formulated and shown to be non-convex. Additionally, the problems of total power and sum-SINR minimisation are also formulated. Particularly, the formulated problems take the form of linear-fractional programming problems. By applying intelligent reformulation techniques, these problems have been reformulated into convex optimisation problems, and thus efficiently solved. Numerical evaluations are presented to validate the derived closed-form expressions for the different performance metrics, which are found to be in agreement with the network simulation results. More importantly, it has been demonstrated that the user with the best channel conditions achieves full diversity order, whereas all the other users achieve diversity orders equivalent to their ordered channel conditions. Finally, the reformulated power allocation strategies are evaluated, and shown to coincide with the original problem formulations.

Reconfigurable Intelligent Surface Assisted Two–Way Communications: Performance Analysis and Optimization

In this paper, we investigate the two-way communication between two users assisted by a reconfigurable intelligent surface (RIS). The scheme that two users communicate simultaneously over Rayleigh fading channels is considered. The channels between the two users and RIS can either be reciprocal or non-reciprocal. For reciprocal channels, we determine the optimal phases at the RIS to maximize the signal-to-interference-plus-noise ratio (SINR). We then derive exact closed-form expressions for the outage probability and spectral efficiency for single-element RIS. By capitalizing the insights obtained from the single-element analysis, we introduce a gamma approximation to model the product of Rayleigh random variables which is useful for the evaluation of the performance metrics in multiple-element RIS. Asymptotic analysis shows that the outage decreases at (log(ρ)/ρ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sup> rate where L is the number of elements, whereas the spectral efficiency increases at log(ρ) rate at large average SINR p. For non-reciprocal channels, the minimum user SINR is targeted to be maximized. For single-element RIS, closed-form solution is derived whereas for multiple-element RIS the problem turns out to be non-convex. The latter one is solved through semidefinite programming relaxation and a proposed greedy-iterative method, which can achieve higher performance and lower computational complexity, respectively.

Min-SINR Maximization for mmWave Massive MISO-NOMA System With Randomly Directional Beamforming

Based on the high-direction characteristic of millimeter wave (mmWave) transmission, randomly directional beamforming (RDB) can be used for the mmWave massive multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) system to reduce the number of radio frequency (RF) chains. However, the impact of RDB on the signal-to-interference-plus-noise ratio (SINR) of each user is related to the corresponding beamforming gain and interference from other users. Thus, in this paper, we investigate the max-min SINR among all users to evaluate user fairness. In particular, we focus on the single-cell downlink mmWave MISO-NOMA system with RDB, where single-antenna users are divided into multiple NOMA clusters according to their azimuth angles. We formulate the minimum achievable SINR maximization problem associated with power allocation and propose the sum of power allocation coefficients based iterative algorithm (SPACIA) to find the max-min SINR. We also prove that the max-min SINR monotonically decreases as the number of paired users in an NOMA cluster increases as well as the number of beams in the cell with large-scale base station (BS) antenna array increases. Moreover, we derive the upper bound of the max-min SINR. Simulation results verify our theoretical analyses and demonstrate that the proposed algorithm guarantees user fairness, thus outperforming existing schemes.

Robust Transceiver Design for AF Asymmetric Two-Way MIMO Relaying

We consider a multiple-input multiple-output (MIMO) asymmetric two-way relay (A-TWR) system, wherein the base station (BS) serves a transmit-only user (TU) and receive-only user (RU). The TU transmits data to the BS and the RU receives data from the BS. Because of the asymmetric nature of A-TWR, the RU experiences interference and necessitates a joint transceiver design at the TU, RU, and relay. The existing literature has designed such transceivers by assuming perfect channel state information (CSI) at all the nodes. Obtaining perfect CSI at all the nodes is, however, not viable in practice due to the distributed nature of the system. This work constructs a transceiver design with perfect CSI at the relay and perturbed CSI at the TU, RU and BS. The perturbed signal-to-interference-plus-noise ratio (SINR) is analyzed by exploiting the properties of the singular value decomposition and the results from theory of matrix normal distributions. The resulting closed-form SINR expressions are then used to perform robust power allocation at all the nodes. Two different settings, namely maximization of the minimum SINR across all streams and minimization of the total network transmit power are considered. The performance gains from the proposed robust designs are validated numerically.

Weighted Sum-SINR and Fairness Optimization for SWIPT-Multigroup Multicasting Systems With Heterogeneous Users

The development of next generation wireless communication systems focuses on the expansion of existing technologies, while ensuring an accord between various devices within a system. In this article, we target the aspect of precoder design for simultaneous wireless information and power transmission (SWIPT) in a multi-group (MG) multicasting (MC) framework capable of handling heterogeneous types of users, viz., information decoding (ID) specific, energy harvesting (EH) explicit, and/or both ID and EH operations concurrently. Precoding is a technique well-known for handling the inter-user interference in multi-user systems, however, the joint design with SWIPT is not yet fully exploited. Herein, we investigate the potential benefits of having a dedicated precoder for the set of users with EH demands, in addition to the MC precoding. We study the system performance of the aforementioned system from the perspectives of weighted sum of signal-to-interference-plus-noise-ratio (SINR) and fairness. In this regard, we formulate the precoder design problems for (i) maximizing the weighted sum of SINRs at the intended users and (ii) maximizing the minimum of SINRs at the intended users; both subject to the constraints on minimum (non-linear) harvested energy, an upper limit on the total transmit power and a minimum SINR required to close the link. We solve the above-mentioned problems using distinct iterative algorithms with the help of semi-definite relaxation (SDR) and slack-variable replacement (SVR) techniques, following suitable transformations pertaining the problem convexification. The main novelty of the proposed approach lies in the ability to jointly design the MC and EH precoders for serving the heterogeneously classified ID and EH users present in distinct groups, respectively. We illustrate the comparison between the proposed weighted sum-SINR and fairness models via simulation results, carried out under various parameter values and operating conditions.

Space–Time Line Codes With Power Allocation for Regenerative Two-Way Relay Systems

In this paper, a general two-way relay (TWR) transmission method is proposed under per-antenna power constraints by combining space-time line codes (STLCs) with transmit power allocation for two source nodes. We introduce a general STLC-based encoding scheme for a decode-and-forward TWR and derive the detection signal-to-interference-plus-noise ratio (SINR) values at two source nodes. An optimal encoder structure with power allocation is proposed in terms of maximizing the minimum SINRs, and it is verified that the optimal encoder is identical to the superposition of two conventional STLCs. An iterative method is proposed to find the optimal power allocation for detection at two source nodes. Moreover, a low-complexity suboptimal encoder is proposed for practical implementation. Numerical simulations present that the proposed STLC-based transmission method outperforms a conventional eigen-beamforming scheme with nulling and an STLC-based scheme with equal power allocation, in terms of the average bit error rate of source nodes, regardless of the distribution of source nodes, the number of TWR antennas, and the transmit power.

A Unified Asymptotic Analysis of Area Spectral Efficiency in Ultradense Cellular Networks

This paper studies the asymptotic properties of average area spectral efficiency (ASE) of a downlink cellular network in the limit of very dense base station (BS) and user densities. This asymptotic analysis relies on three assumptions: 1) interference is treated as noise; 2) the BS locations are drawn from a Poisson point process; and 3) the path loss function is bounded above satisfying mild regularity conditions. We consider three possible definitions of the average ASE, all of which give units of bits per second per unit bandwidth per unit area. When there is no constraint on the minimum operational signal-to-interference-plus-noise ratio (SINR) and instantaneous full channel state information (CSI) is available at the transmitter, the average ASE is proven to saturate to a constant, which we derive in a closed form. For the other two ASE definitions, wherein either a minimum SINR is enforced or CSI is not available, the average ASE is instead shown to collapse to zero at high BS density. We provide several familiar case studies for the class of considered path loss models, and demonstrate that our results cover most previous models and results on ultradense networks as special cases.