Short-term Power Constraint Research Articles

Short-Term Power Constrained Cell-Free Massive-MIMO Over Spatially Correlated Ricean Fading

This paper considers short-term power constrained cell-free massive multiple-input multiple-output (MIMO) scenarios where a large set of multi-antenna access points (APs) provide service to a group of single-antenna mobile stations (MSs) on a spatially correlated multipath environment. Based on a probabilistic approach, the spatially correlated propagation links are modeled using either Ricean or Rayleigh fading channel models that combine a deterministic line-of-sight (LOS) propagation path with a small-scale fading caused by non-line-of-sight (NLOS) multipath propagation. Assuming the use of minimum mean square error (MMSE) channel estimates, closed-form expressions for the downlink (DL) achievable spectral efficiency of a cellfree massive MIMO network with short-term power constraints (i.e., a vector normalized conjugate beamformer (NCB)) are derived and benchmarked against that provided by the conventional cell-free massive MIMO network with long-term power constraints (i.e., the conventional conjugate beamforming (CB)). These expressions, encompassing the effects of spatial antenna correlation, Ricean/Rayleigh fading and pilot contamination, are then used to derive both pragmatic and optimal max-min peruser power allocation strategies and to gain theoretical insight on the performance advantage provided by the use of short-term power constraints instead of the conventional long-term power constrained approach.

Interleaving Channel Estimation and Limited Feedback for Point-to-Point Systems With a Large Number of Transmit Antennas

We introduce and investigate the opportunities of multi-antenna communication schemes whose training and feedback stages are interleaved and mutually interacting. Specifically, unlike the traditional schemes, where the transmitter first trains all of its antennas at once and then receives a single feedback message, we consider a scenario, where the transmitter instead trains its antennas one by one and receives feedback information immediately after training each one of its antennas. The feedback message may ask the transmitter to train another antenna; or, it may terminate the feedback/training phase and provide the quantized codeword (e.g., a beamforming vector) to be utilized for data transmission. As a specific application, we consider a multiple-input single-output system with $t$ transmit antennas, a short-term power constraint $P$ , and target data rate $\rho $ . We show that for any $t$ , the same outage probability as a system with perfect transmitter and receiver channel state information can be achieved with a feedback rate of $R_{1}$ bits per channel state and via training $R_{2}$ transmit antennas on average, where $R_{1}$ and $R_{2}$ are independent of t , and depend only on $\rho $ and $P$ . In addition, we design variable-rate quantizers for channel coefficients to further minimize the feedback rate of our scheme.

Effective Capacity in MIMO Channels With Arbitrary Inputs

Recently, communication systems that are both spectrum and energy efficient have attracted significant attention. Different from the existing research, we investigate the throughput and energy efficiency of a general class of multiple-input and multiple-output systems with arbitrary inputs when they are subject to statistical quality-of-service (QoS) constraints, which are imposed as limits on the delay violation and buffer overflow probabilities. We employ the effective capacity as the performance metric, which is the maximum constant data arrival rate at a buffer that can be sustained by the channel service process under specified QoS constraints. We obtain the optimal input covariance matrix that maximizes the effective capacity under a short-term average power constraint. Following that, we perform an asymptotic analysis of the effective capacity in the low signal-to-noise ratio and large-scale antenna regimes. In the low signal-to-noise ratio regime analysis, in order to determine the minimum energy-per-bit and also the slope of the effective capacity versus energy-per-bit curve at the minimum energy-per-bit , we utilize the first and second derivatives of the effective capacity when the signal-to-noise ratio approaches zero. We observe that the minimum energy-per-bit is independent of the input distribution, whereas the slope depends on the input distribution. In the large-scale antenna analysis, we show that the effective capacity approaches the average transmission rate in the channel with the increasing number of transmit and/or receive antennas. Particularly, the gap between the effective capacity and the average transmission rate in the channel, which is caused by the QoS constraints, is minimized with the number of antennas. In addition, we put forward the nonasymptotic backlog and delay violation bounds by utilizing the effective capacity. Finally, we substantiate our analytical results through numerical illustrations.

Joint opportunistic user scheduling and power allocation: throughput optimisation and fair resource sharing

Despite extensive studies on optimal power allocation, how to design an efficient joint user scheduling and power allocation scheme for uplink multiuser networks remains largely unexplored. This study investigates joint opportunistic user scheduling and power allocation in uplink multiuser networks to maximise user throughput subject to the power and resource sharing constraints . By exploiting the cumulative distribution function-based scheduling method, the authors first characterise the optimal power allocation subject to both long-term and short-term power constraints. Instead of calculating the transmit power in an iterative and central manner, users can independently decide their instantaneous transmit power in the proposed scheme, which facilitates the algorithm implementation for each user in uplink networks. The closed-form throughput of the proposed scheme is also derived, which can provide an efficient way to estimate and evaluate user performance. Numerical results reveal that compared with several benchmark schemes, the proposed scheme improves throughput performance significantly.

On the Performance of Multigroup Multicast Cell-Free Massive MIMO

We investigate the performance of a multigroup multicast cell-free massive multiple-input multiple-output system where many access points (APs) multicast signals to many groups of users. A distributed conjugate beamforming with short-term power constraint (STPC) policy is proposed to use at the APs. In addition, we propose a new transmission scheme in which the APs beamform pilots so that each user can estimate the effective channel gains for signal detection. The analytical expressions for the per-user net throughputs are derived. The results show that when the number of groups is small, STPC outperforms long-term power constraint used in the literature. Furthermore, at a small number of user groups, the transmission with downlink pilots improves the system performance noticeably.

Improper Signaling Versus Time-Sharing in the SISO Z-Interference Channel

It has recently been shown that improper signaling enlarges the rate region of the Gaussian single-antenna one-sided interference channel (Z-interference channel, ZIFC) under the assumptions that all input signals are Gaussian and that interference is treated as noise. It was pointed out that this result also holds if time-sharing between different operation points is allowed. However, the existing literature has considered the problem only for time-sharing under short-term average power constraints, i.e., if the average transmit powers are limited individually in each time slot. We consider the same problem under long-term average power constraints, where the transmit powers are limited only after averaging over all time slots. Interestingly, this modification changes the outcome of the study significantly: we can show that improper signaling can no longer bring any gains in this case.

Dynamic Transmit Covariance Design in MIMO Fading Systems With Unknown Channel Distributions and Inaccurate Channel State Information

This paper considers dynamic transmit covariance design in point-to-point multiple-input multiple-output fading systems with unknown channel state distributions and inaccurate channel state information subject to both long-term and short-term power constraints. First, the case of instantaneous but possibly inaccurate channel state information at the transmitter (CSIT) is treated. By extending the drift-plus-penalty technique, a dynamic transmit covariance policy is developed and is shown to approach optimality with an $O(\delta)$ gap, where $\delta $ is the inaccuracy measure of CSIT, regardless of the channel state distribution and without requiring knowledge of this distribution. Next, the case of delayed and inaccurate channel state information is considered. The optimal transmit covariance solution that maximizes the ergodic capacity is fundamentally different in this case, and a different online algorithm based on convex projections is developed. The proposed algorithm for this delayed-CSIT case also has an $O(\delta)$ optimality gap, where $\delta $ is again the inaccuracy measure of CSIT.

Optimal Power Control for Real-time Applications in Cognitive Satellite Terrestrial Networks

Cognitive satellite terrestrial networks have received considerable attention as a promising candidate to address the spectrum scarcity problem in future wireless communications. When satellite networks act as cognitive users in the networks, power control is a significant research challenge in the uplink case, especially for real-time applications. We propose two optimal power control schemes for maximizing the delay-limited capacity and outage capacity, respectively, which are useful performance indicators for real-time applications. From the long-term and short-term aspects, average and peak power constraints are adopted, respectively, at the satellite user to limit the harmful interference caused to the terrestrial base station. Extensive numerical results demonstrate the impact of interference constraints and channel condition parameters on the performance limits of satellite users.

On the Outage Performance of Non-Orthogonal Multiple Access With 1-bit Feedback

In this paper, the outage performance of downlink non-orthogonal multiple access (NOMA) is investigated for the case where each user feeds back only one bit of its channel state information (CSI) to the base station. Conventionally, opportunistic one-bit feedback has been used in fading broadcast channels to select only one user for transmission. In contrast, the considered NOMA scheme adopts superposition coding to serve all users simultaneously in order to improve user fairness. A closed-form expression for the common outage probability (COP) is derived, along with the optimal diversity gains under two types of power constraints. Particularly, it is demonstrated that the diversity gain under a long-term power constraint is twice as large as that under a short-term power constraint. Furthermore, we study dynamic power allocation optimization for minimizing the COP, based on one-bit CSI feedback. This problem is challenging, since the objective function is non-convex; however, under the short-term power constraint, we demonstrate that the original problem can be transformed into a set of convex problems. Under the long-term power constraint, an asymptotically optimal solution is obtained for high signal-to-noise ratio.

Delay-Limited Capacity in the Low Power Regime

Outage performance of the $M$ -block fading with additive white Gaussian noise (BF-AWGN) is investigated in the low-power regime. We consider delay-constrained constant-rate communications with perfect channel state information (CSI) at both the transmitter and the receiver (CSI-TR), under a short-term power constraint (STPC) and a long-term power constraint (LTPC). Subject to STPC, we show that selection diversity that allocates all the power to the strongest block is asymptotically optimal. Then, we provide a simple characterization of the outage probability in the regime of interest. We quantify the reward due to CSI-TR over the constant-rate constant-power scheme and show that this reward increases with the delay constraint. For instance, for Rayleigh fading, we find that a power gain up to 4.3 dB is achievable. Subject to LTPC, we show that the above guidelines still holds and that the outage performance improves due to the flexibility of the LTPC over the STPC. More interestingly, we prove that LTPC allows zero-outage communication even at low SNR and characterize the delay-limited capacity at low SNR in a simple form. More precisely, we establish that the delay-limited capacity scales linearly with the power constraint, for a given $M . Our framework highlights the benefit of fading at low SNR as the delay-limited capacity may outperform the AWGN capacity. For instance, for Rayleigh fading and with $M=3$ , the delay-limited capacity is 16% higher than the capacity of an AWGN channel.

Optimum Power Control at Finite Blocklength

This paper investigates the maximal channel coding rate achievable at a given blocklength $n$ and error probability $\epsilon$, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-$n$ expansion of the maximal channel coding rate is characterized both for additive white Gaussian noise (AWGN) channels and for quasi-static fading channels with perfect channel state information available at both the transmitter and the receiver. It is shown that in both cases the second-order term is proportional to $\sqrt{n^{-1}\ln n}$. For the quasi-static fading case, this second-order term is achieved by truncated channel inversion, namely, by concatenating a dispersion-optimal code for an AWGN channel subject to a short-term power constraint, with a power controller that inverts the channel whenever the fading gain is above a certain threshold. Easy-to-evaluate approximations of the maximal channel coding rate are developed for both the AWGN and the quasi-static fading case.

The Generalized Diversity-Multiplexing Tradeoff of the MIMO Z Interference Channel

The generalized diversity-multiplexing tradeoff (GDMT) of the two-user, quasi-static fading, multi-input, multi-output (MIMO) Z interference channel (Z-IC) is established for the general case with an arbitrary number of antennas at each node under the assumptions of full channel state information at the transmitters (CSIT) and a short-term average power constraint. In the GDMT framework, which captures the rate versus reliability tradeoff in the high signal-to-noise ratio (SNR) regime, the direct link SNR and cross-link interference-to-noise ratio (INR) are allowed to be disparate, so that their ratios relative to a nominal SNR in the decibel scale, i.e., the SNR and INR exponents, are arbitrary and fixed. It is shown that a simple Han-Kobayashi message-splitting/partial interference decoding scheme that uses only partial CSIT-in which the second transmitter's signal depends only on its cross-link channel matrix and the first user's transmit signal does not need any CSIT-can achieve the full-CSIT GDMT of the MIMO Z-IC. The GDMT of the MIMO Z-IC under the No-CSIT assumption is also obtained for some range of multiplexing gains. The size of this range depends on the numbers of antennas at the four nodes and the SNR and INR exponents of the direct and cross links, respectively. For certain classes of channels including those in which the interfered receiver has more antennas than do the other nodes, or when the INR exponent is greater than a certain threshold, the GDMT of the MIMO Z-IC under the No-CSIT assumption is also completely characterized.

Dynamic Decode‐and‐Forward Relaying with Partial CSIT and Optimal Time Allocation

A Dynamic decode-and-forward (DDF) relaying protocol with partial Channel state information at the transmitter (CSIT) for a three-node half-duplex single-antenna network, which consists of a single source destination pair and a relay, is proposed. A Diversity multiplexing trade off (DMT) analysis is presented, in which the DMT of the proposed protocol is derived in a closed form and an adaptive time allocation strategy is also developed to achieve the optimal performance. It is shown that time allocation with partial CSIT significantly improves the achievable DMT for DDF relaying. Moreover, unlike the existing DDF protocol with CSIT, which is performed with the assumption of long-term power constraint, the proposed protocol can be generalized to the practical scenarios where a strict short-term power constraint is often imposed on, due to the environmental safety and interference prevention.

Ergodic Secret Message Capacity of the Wiretap Channel with Finite-Rate Feedback

We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers, under both a short term power constraint (STPC) and a long term power constraint (LTPC). We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free public channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that the lower and the upper bounds coincide asymptotically as q → ∞. When applied to Rayleigh fading channels, we show that, a 4-bit feedback achieves about 90% of the secrecy capacity when perfect main CSI is available at the transmitter. Finally, asymptotic analysis at high and low Signal-to-Noise Ratio (SNR) is presented. It is found that the capacity is bounded at high-SNR, whereas at asymptotically low-SNR, the lower bounds and the upper bound scale linearly with SNR under STPC. Furthermore, subject to LTPC, the capacity at low-SNR is equal to the capacity of the main channel without secrecy constraint and with perfect CSI at both the transmitter and the receiver, under a mild condition on the fading statistics. We also show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q=1.

Optimal power policies and throughput scaling analyses in fading cognitive broadcast channels with primary outage probability constraint

Abstract This paper focuses on a spectrum-sharing-based fading cognitive radio broadcast channel (BC) with a single-antenna secondary base station (SBS) and M single-antenna secondary receivers (SRs) utilizing the same spectrum band with a delay-sensitive primary user (PU). The service-quality requirement for the primary user is set by an outage probability constraint (POC). We address the optimal power allocation problem for the SBS ergodic sum capacity (ESC) maximization in the secondary BC network subject to POC and a transmit power constraint at SBS specified by either a long-term or a short-term power constraint. The optimality conditions reveal that in each joint channel state, the SBS allocates transmission power to the only one selected SR with the highest value of a certain metric consisting of the ratio of the SR’s direct channel power gain and the sum of interference power and noise power at the SR. Then, the secondary network throughput scaling analysis as the number of SRs becomes large, is also investigated, showing that if PU applies a truncated channel inversion (TCI) power policy, the SBS ESC scales like ε p log(logM) where ε p is the PU outage probability threshold. To reduce the amount of channel side information (CSI) transferred between the two networks, we propose a suboptimal transmission scheme which requires only 1-bit feedback from the delay-sensitive PR (partial CSI). We show that the new power control policy is asymptotically optimal, i.e. the SBS ESC under this reduced feedback scheme still scales like ε p log(logM).

Maximum Expected Rates of Block-Fading Channels with Entropy-Constrained Channel State Feedback

We obtain the maximum average data rates achievable over block-fading channels when the receiver has perfect channel state information (CSI), and only an entropy-constrained quantized approximation of this CSI is available at the transmitter. We assume channel gains in consecutive blocks are independent and identically distributed and consider a short term power constraint. Our analysis is valid for a wide variety of channel fading statistics, including Rician and Nakagami-m fading. For this situation, the problem translates into designing an optimal entropy-constrained quantizer to convey approximated CSI to the transmitter and to define a rate-adaptation policy for the latter so as to maximize average downlink data rate. A numerical procedure is presented which yields the thresholds and reconstruction points of the optimal quantizer, together with the associated maximum average downlink rates, by finding the roots of a small set of scalar functions of two scalar arguments. Utilizing this procedure, it is found that achieving the maximum downlink average capacity C requires, in some cases, time sharing between two regimes. In addition, it is found that, for an uplink entropy constraint H <; log2 (L), a quantizer with more than L cells provides only a small capacity increase, especially at high SNRs.

Fixed-Rate Transmission Over Fading Interference Channels Using Point-to-Point Gaussian Codes

This paper investigates transmission schemes for fixed-rate communications over a Rayleigh block-fading interference channel. There are two source-destination pairs where each source, in the presence of a short-term power constraint, intends to communicate with its dedicated destination at a fixed data rate. It encodes its messages using a point-to-point Gaussian codebook. The two users' transmissions can be conducted orthogonally or non-orthogonally. In the latter case, each destination performs either direct decoding by treating the interference as noise, or successive interference cancellation (SIC) to recover its desired message. For each scheme, we seek solutions of a power control problem to efficiently assign power to the sources such that the codewords can be successfully decoded at destinations. However, because of the random nature of fading, the power control problem for some channel realizations may not have any feasible solution and the transmission will be in outage. Thus, for each transmission scheme, we first compute a lower bound and an upper bound on the outage probability. Next, we use these results to find an outer bound and an inner bound on the $\epsilon$ -outage achievable rate region, i.e., the rate region in which the outage probability is below a certain value $\epsilon$ .

Power Allocation in Multi-Antenna Wireless Systems Subject to Simultaneous Power Constraints

We address the problem of power allocation to maximize ergodic capacity subject to multiple power constraints assuming that perfect causal channel state information (CSI) is available at both the transmitter and the receiver. We characterize the optimal power allocation subject to both long-term and short-term power constraints, which depends upon the ratio of the two power levels. Additionally, we find a suboptimal power allocation if the input power is subject to long-term and per-antenna power constraints. We characterize the conditions for which one power constraint dominates and the other can be ignored. Numerical results suggest that, for the Rayleigh fading case, a short-term power constraint that is larger than a long-term power constraint does not significantly impact the ergodic capacity of the channel. The effect of per-antenna power constraints is also explored for the case of Rayleigh fading through our numerical results.

Multi-User Downlink System Design with Bright Transmitters and Blind Receivers

This paper considers a scenario for multi-user multi-input multi-output (MIMO) communication systems when perfect channel state information at the transmitter (CSIT) is given while the equivalent channel state information at the receiver (CSIR) is not available. Such an assumption is valid for the downlink multi-user MIMO systems with linear precoders that depend on channels to all receivers. We propose a concept called dual systems with zero-forcing design based on the duality principle, originally proposed to relate the Gaussian multi-access channel (MAC) and the Gaussian broadcast channel (BC). For the K-user N×2 MIMO BC with N antennas at the transmitter and two antennas at each of the K receivers, we design a downlink interference cancellation (IC) transmission scheme by obtaining the dual of uplink MAC systems employing IC methods. The transmitter simultaneously sends K precoded Alamouti codes, one for each user. Each receiver zero-forces the unintended user's Alamouti codes and decouples its own data streams using two simple linear operations independent of CSIR. Analysis shows that the proposed scheme achieves a diversity gain of 2(N - K + 1) for equal energy constellations with short-term power and rate constraints. Power allocation among K users can also be performed to improve the array gain but not the diversity gain. Numerical results demonstrate that the bit error rate of the downlink IC scheme has a diversity gain improvement compared to the block diagonalization (BD) method, which requires global channel information at each node.

On Hybrid ARQ and Quantized CSI Feedback Schemes in Quasi-Static Fading Channels

Recently, substantial attention has been paid to increase the achievable rates of wireless networks using different kinds of limited channel quality information feedback. Hybrid automatic repeat request (ARQ) and quantized channel state information (CSI) feedback are two well-known approaches applied by experts to provide the limited channel quality information at the transmitter. Considering quasi-static fading channels, this paper aims to provide some comparisons between the performance of these methods from different points of view. The paper first investigates the power- and outage-limited performance of hybrid ARQ and quantized CSI schemes under short- and long-term power constraints. Then, 1) the feedback signaling load, 2) robustness and 3) the complexity of these schemes are compared under short-term transmission power constraint. Both INcremental Redundancy (INR) and Repetition Time Diversity (RTD) approaches are considered for hybrid ARQ feedback. Finally, approximate low-complexity solutions are presented for power allocation in the INR ARQ-based scheme under long-term transmission power constraint. Analytical and numerical results demonstrate the equivalency or the superiority of these approaches in different circumstances.