Perfect Self-interference Cancellation Research Articles

Exploiting the Direct Link in IRS Assisted NOMA Networks with Hardware Impairments

Hardware impairments (HI) are always present in low-cost wireless devices. This paper investigates the outage behaviors of intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) networks by taking into account the impact of HI. Specifically, we derive the approximate and asymptotic expressions of the outage probability for the IRS-NOMA-HI networks. Based on the asymptotic results, the diversity orders under perfect self-interference cancellation and imperfect self-interference cancellation scenarios are obtained to evaluate the performance of the considered network. In addition, the system throughput of IRS-NOMA-HI is discussed in delay-limited mode. The obtained results are provided to verify the accuracy of the theoretical analyses and reveal that: 1) The outage performance and system throughput for IRS-NOMA-HI outperforms that of the IRS-assisted orthogonal multiple access-HI (IRS-OMA-HI) networks; 2) The number of IRS elements, the pass loss factors, the Rician factors, and the value of HI are pivotal to enhancing the performance of IRS-NOMA-HI networks; and 3) It is recommended that effective methods of reducing HI should be used to ensure system performance, in addition to self-interference cancellation techniques.

Joint Dynamic Passive Beamforming and Resource Allocation for IRS-Aided Full-Duplex WPCN

This paper studies intelligent reflecting surface (IRS)-aided full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid access point (HAP) broadcasts energy signals to multiple devices for their energy harvesting in the downlink (DL) and meanwhile receives information signals in the uplink (UL) with the help of IRS. Particularly, we propose three types of IRS beamforming configurations to strike a balance between the system performance and signaling overhead as well as implementation complexity. We first propose the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fully dynamic IRS beamforming</i> , where the IRS phase-shift vectors vary with each time slot for both DL wireless energy transfer (WET) and UL wireless information transmission (WIT). To further reduce signaling overhead and implementation complexity, we then study two special cases, namely, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">partially dynamic IRS beamforming</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">static IRS beamforming</i> . For the former case, two different phase-shift vectors can be exploited for the DL WET and the UL WIT, respectively, whereas for the latter case, the same phase-shift vector needs to be applied for both DL and UL transmissions. We aim to maximize the system throughput by jointly optimizing the time allocation, HAP transmit power, and IRS phase shifts for the above three cases. Two efficient algorithms based on alternating optimization and penalty-based algorithms are respectively proposed for both perfect self-interference cancellation (SIC) case and imperfect SIC case by applying successive convex approximation and difference-of-convex optimization techniques. Simulation results demonstrate the benefits of IRS for enhancing the performance of FD-WPCN, especially with fully dynamic IRS beamforming, and also show that the IRS-aided FD-WPCN is able to achieve significantly performance gain compared to its counterpart with half-duplex when the self-interference (SI) is properly suppressed.

Throughput Maximization for Asynchronous RIS-Aided Hybrid Powered Communication Networks

Hybrid energy supply composed of batteries and radio frequency (RF) signals has been anticipated to be a prominent solution for balancing the reliability and self-sustainability of future IoT networks. The newly emerging reconfigurable intelligent surface (RIS) is also capable of greatly enhancing spectral and energy efficiencies. In this paper, by considering an asynchronous transmission protocol among all energy receivers (ERs) and assuming the perfect self-interference cancellation (SIC) at the hybrid access point (HAP), we aim to maximize sum throughput in the RIS-aided hybrid powered communication networks (HPCNs) by jointly optimizing the transmit covariance matrices of the HAP and all ERs, the RIS reflection matrix and the downlink/uplink (DL/UL) time allocation. Generally, this optimization problem is intractable to solve due to strongly coupled variables and nonconvex unit-modulus constraints. To draw more insights into this joint design, we firstly carry out feasibility analysis on this problem, and then develop a 2-block alternating optimization algorithm, which consists of the semi-closed-form solution based iterative algorithm for deriving the optimal MIMO transceivers together with the DL/UL time allocation and the alternating direction method of multipliers (ADMM) based algorithm for the RIS design. To avoid the potential high complexity of alternating optimization, we also propose a two-stage scheme, where the RIS design is independent of the others and aims to create favorable DL/UL channels. The extension of our proposed algorithms to the practical imperfect SIC case is then discussed. Numerical results illustrate the superior performance of our proposed algorithms over the baselines in terms of the achievable sum throughput, and their time effectiveness in solving large-scale problems.

Fundamental Limits of Full-Duplex Spectrum Sharing Under Peak Interference Power Constraint

Cognitive radio (CR) and full-duplex (FD) have received extensive attention and research due to their high spectrum efficiency, which can effectively solve the problem of low spectrum efficiency in current communication systems. Based on CR and FD techniques, in this paper, a FD spectrum sharing CR networks is considered, in which both secondary users (SU1 and SU2) are each equipped with dual antennas, one antenna is used to transmit signals, and the other antenna is used to receive signals at the same time and frequency. Under peak interference power and peak transmit power constraints, we analysis the ergodic sum capacity and the outage probability based on the FD spectrum sharing CR networks and the conventional spectrum sharing CR networks. Furthermore, under no peak transmit power constrain and perfect self-interference cancellation (SIC), based on the FD spectrum sharing CR networks and the conventional spectrum sharing CR networks, the closed-form expressions of the theoretical performance upper bound of the ergodic sum capacity and the outage probability are derived by two lemmas and four propositions. Accurate mathematical analysis display, under the same bandwidth, the upper bound of ergodic sum capacity for the full-duplex spectrum sharing CR networks is twice as much as the traditional spectrum sharing CR networks, and the FD spectrum sharing CR networks based on SU1, also has better performance upper bound on the outage probability than the traditional spectrum sharing CR networks. Simulations results also validate that, the FD spectrum sharing CR networks obtains better communication performance than the conventional spectrum sharing CR networks, especially when the mean of self-interference channel power gain is small. Finally, we also can see that the simulation performance upper bound is completely consistent with the theoretical analysis performance upper bound, whether in the FD spectrum sharing CR networks or the conventional spectrum sharing CR networks. So also verifies the correctness of the theoretical performance upper bound derivation.

Self-Interference-Resistant IEEE 802.11ad-Based Joint Communication and Automotive Radar Design

The IEEE 802.11ad based joint communication and radar sensing (JCRS) has attracted great attention for vehicles in recent years. Existing studies mostly assume full-duplex radio for radar receiver based on perfect self-interference cancellation. However, the self-interference may not be fully cancelled in practice. In this paper, imperfect self-interference cancellation is considered. To combat the strong self-interference, a novel JCRS is developed based on IEEE 802.11ad orthogonal frequency division multiplex physical-layer (OFDM PHY) for multi-target sensing. More specifically, the received radar signal is designed to be synchronized with self-interference, and two radar sensing functions are developed for short-range sensing and long-range sensing separately. The synchronization with self-interference resolves the difficulty in self-interference calibration in short-range sensing and prevents the inter-subcarrier-interference (ICI) from self-interference in long-range sensing. The Golay sequences in the preamble are leveraged to combat self-interference for short-range sensing, thanks to the relatively strong reflection signal. For long-range sensing, the pilot signal and a few self-interference-free OFDM symbols at the end of the data frame are leveraged to combat self-interference. Particularly, a novel pilot signal design is first developed to achieve subcarrier-wise pulse radar for accurate velocity and coarse range estimation, and then the self-interference-free OFDM symbols are utilized to achieve accurate range estimation. A strategy of frame transmissions is finally developed to integrate these two functions while balancing the performance between communications and sensing. Simulation results show that cm/s level velocity estimation and cm level range estimation can be achieved for up to 200-meter radar sensing.

Impacts of Imperfect CSI and Transceiver Hardware Noise on the Performance of Full-Duplex DF Relay System With Multi-Antenna Terminals Over Nakagami-m Fading Channels

In this paper, we investigate the performance of a full-duplex (FD) relay system where multi-antennas are exploited at source and destination. Unlike previous works, the impacts of imperfect channel state information (I-CSI), transceiver hardware noise (THN), and residual self-interference (RSI) are taken into account. We mathematically derive the exact closed-form expressions of the outage probability (OP), symbol error rate (SER), and ergodic capacity (EC) of the FD relay system with I-CSI, THN, and RSI over Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading channels. From the derived expressions, the performance of the considered system under the effects of three negative factors (I-CSI, THN, and RSI) is compared with that system in the case of all ideal factors (perfect channel state information (P-CSI), perfect transceiver hardware (P-TH) and perfect self-interference cancellation (P-SIC)), two ideal factors (P-CSI and P-TH, P-CSI and P-SIC, P-TH and P-SIC), or one ideal factor (P-CSI or P-TH or P-SIC). Numerical results show a strong impact of three negative factors on the OP, SER, and EC of the considered FD relay system, especially when the data transmission rate of the system and signal-to-noise ratio (SNR) are high. In particular, OP, SER, and EC go to the floors in the high SNR regime due to the three negative factors. Therefore, when I-CSI, THNs, and RSI exist in the FD relay system, we should use suitable source and relay transmission power to obtain excellent performance while saving energy consumption. Moreover, when two of the three negative factors are large enough, the remaining factor’s impact becomes weaker and may be neglected in certain circumstances.

Power Splitting-Based SWIPT Systems With Full-Duplex Jamming

The simultaneous wireless information and power transfer (SWIPT) has recently attracted much attention since both information and energy are integrated within radio frequency signals, which is considered to be one of the most important technologies for future networks. However, security becomes one of the most critical issues in SWIPT networks due to its broadcasting features over wireless media and the transferring requirements for strong signal strength. To improve the security of SWIPT networks, in this paper, a SWIPT system enabled by full-duplex (FD) jamming is proposed, where an FD energy-limited receiver with the power splitting (PS) structure, powered by a transmitter, generates jamming signals. Both linear and nonlinear energy harvesting (EH) models are considered. To evaluate the secrecy throughput (ST) of the system, we derive the closed-form connection outage probability and secrecy outage probability for the proposed PS-based scheme in the delay-constrained transmission (DCT) mode. The ST is maximized by optimizing the PS ratio based on the asymptotic cases of the high signal-to-noise ratio as well as the perfect self-interference cancellation (SIC). Besides, the exact integral forms of the ergodic secrecy capacity and their closed-form lower bounds are presented for both the PS-based and the time switching (TS)-based schemes in the delay-tolerant transmission (DTT) mode. Simulation results suggest that the PS-based scheme outperforms the TS-based scheme for the DTT mode. For the DCT mode, the PS-based scheme can achieve better performance than the TS-based scheme only in low target communication rate, small PS/TS ratio, high transmit power, and weak path loss. Meanwhile, given a tolerable amount of SIC, the ST obtained in the linear EH model is higher than that achieved in the nonlinear EH model.

Half-duplex multiple-relay multiple-antenna diamond networks with perfect full-duplex performance

Diversity-multiplexing tradeoff (DMT) of a full-duplex diamond network where the inter-relay interference (IRI) is suppressed, global channel state information (CSI) is available in all nodes, and perfect self-interference cancellation (SIC) technique is used, which we call it the perfect full-duplex diamond network, is an upper bound for the DMT of the equivalent half-duplex diamond network, i.e., the perfect full-duplex diamond network outperforms the half-duplex case. Nevertheless, the implementation of the perfect full-duplex diamond network is a high-cost operation and requires significant hardware changes in current systems. The main question addressed in this paper is: under which condition (or perhaps conditions) does a prevalent half-duplex diamond network provide the same performance as the perfect full-duplex one? In this regard, first, we calculate the DMT of a perfect full-duplex multiple-relay and multiple-antenna (MRMA) symmetric diamond network. Then, we demonstrate that for the same network but with half-duplex relays, when the number of antennas in relays satisfies a specific condition, there exists a fixed listen-transmit schedule combined with quantize-map-and-forward (QMF) relaying to achieve the optimal DMT. Also, we attain a lower bound for the total number of antennas of the MRMA symmetric diamond network to achieve the optimal DMT.

Wireless Surveillance With Interference Exploitation in Unauthorized Underlaid D2D Networks

Interference exploitation has been considered an effective method to improve secrecy in underlaid device-to-device (D2D) communication networks. This paper studied interference exploitation in unauthorized underlaid D2D communication networks, where a cellular user (CU) transmits uplink information to a base station (BS) and a pair of suspicious D2D users (DUs) transmit the suspicious information at the same time. We used the beamforming of the full-duplex (FD) CU to simultaneously achieve the legitimate uplink transmission of the CU and wireless surveillance on the suspicious DUs. Considering the different priority levels of the tasks, we divided the real-time quality of service (QoS) requirements of the CU into three cases and formulated the problem in each case. We derived beamforming expressions for each problem in the perfect self-interference cancellation (PSIC) and then proposed targeted algorithms in the imperfect self-interference cancellation (ISIC). Finally, simulation results are provided to validate the effectiveness and the advantages of our proposed schemes in situations with different QoS requirements.

An Adaptive Self-Interference Cancelation/Utilization and ICA-Assisted Semi-Blind Full-Duplex Relay System for LLHR IoT

In this article, we propose a semi-blind full-duplex (FD) amplify-and-forward (AF) relay system with adaptive self-interference (SI) processing assisted by independent component analysis (ICA) for low-latency and high-reliability (LLHR) Internet of Things (IoT). The SI at FD relay is not necessarily canceled as much as possible like the conventional approaches, but is canceled or utilized based on a signal-to-residual-SI ratio (SRSIR) threshold at relay. According to the selected SI processing mode at relay, an ICA-based adaptive semi-blind scheme is proposed for signal separation and detection at destination. The proposed FD relay system not only features reduced signal processing cost of SI cancelation but also achieves a much higher degree of freedom in signal detection. The resulting bit error rate (BER) performance is robust against a wide range of SRSIR, much better than that of conventional FD systems, and close to the ideal case with perfect channel state information (CSI) and perfect SI cancelation. The proposed system also requires negligible spectral overhead as only a nonredundant precoding is needed for ambiguity elimination in ICA. In addition, the proposed system enables full resource utilization with consecutive data transmission at all time and same frequency, leading to much higher throughput and energy efficiency than the time-splitting and power-splitting-based self-energy recycling approaches that utilize only partial resources. Furthermore, an intensive analysis is provided, where the SRSIR thresholds for the adaptive SI processing mode selection and the BER expressions with ICA incurred ambiguities are derived.

Perfect Self-Interference Cancellation Based on Mode-Switching for Differential Channel-Unaware Two-Way Relay Networks

We consider channel-unaware two-way relay networks in which two single-antenna nodes exchange information through multiple single-antenna half-duplex amplify-and-forward relays. For these networks, we develop a novel self-interference (SI) cancellation scheme that does not invoke channel information neither at the relays nor at the nodes. Unlike its previous counterparts, the scheme proposed herein enables perfect SI cancellation even when the relays have a single antenna each. This was not possible previously without employing an even number of antennas at each relay. In the first phase of the proposed scheme, the network is operated in a one-way relaying mode, whereas in the second phase it is operated in a two-way relaying mode. In the latter mode, the vectors received by the nodes at the end of the first phase are used to completely eliminate SI, without estimating the channel as in existing methodologies. To analyze the effectiveness of the proposed scheme, we derive upper bounds on the pairwise error probability for the Alamouti and $SP(2)$ codes. Using these bounds, we investigate the dependence of the system performance on the data rate. In addition, we show that for all data rates, the proposed scheme outperforms previously proposed ones. Theoretical results are confirmed by simulations.

Secret-Key Generation: Full-Duplex Versus Half-Duplex Probing

A secret-key agreement for in-band full-duplex (FD) technology can be regarded as a valuable method for establishing security at the physical layer level. In this paper, we study an FD system model in conjunction with a secret-key agreement. The legitimate users interact through two-way channel probing and one-way reconciliation. We first introduce two complementary key generation models for FD and half-duplex (HD) settings, and compare their performances by introducing the key-reconciliation function. Furthermore, we study the impact of probing-reconciliation tradeoff and the role of a strong eavesdropper, and analyze the system performance in the high-signal-to-noise ratio regime. We show that under certain conditions, the FD mode negatively affects the capabilities of the eavesdropper and offers several advantages in terms of secret-key rate over the conventional HD setups. Our analysis reveals that the perfect self-interference cancellation is not necessary to obtain performance gains over the HD mode.

Cooperative Full Duplex Device to Device Communication Underlaying Cellular Networks

Recently, device-to-device (D2D) communication and full duplex communication are both considered key technologies for 5G networks. In this paper, two novel cooperative modes are developed for full duplex D2D communication underlaying cellular networks: the network MU-MIMO based mode (N-mode) and the sequential forwarding mode (S-mode). In the N-mode, two D2D users work as network MIMO to forward the data to cellular users and thus leverage the channel diversity. In the S-mode, the spatial distribution of D2D users and cellular users is explored to improve the transmission rate. Based on these modes, two D2D users share the downlink resources with two nearby cellular users simultaneously to achieve both proximity gain and reuse gain. Moreover, these modes are well suited for edge cellular users. To optimize the performance of the two modes, optimal power allocation is conducted by considering the influence of residual self-interference at full duplex radios and the requirements of the minimum transmission rate for both cellular users and D2D users. Simulation results show that, compared with the dedicated mode, the sum rate of cooperative modes in the perfect self-interference cancellation case can achieve 32% overall improvement and about 70% improvement in the scenario with non-edge D2D users and edge cellular users. With residual self-interference at a full duplex radio, the overall performance improvement is reduced to 15%. However, the cooperative modes can still achieve 40% improvement in the scenario with non-edge D2D users and edge cellular users.

Physical Layer Security in Wireless Ad Hoc Networks Under A Hybrid Full-/Half-Duplex Receiver Deployment Strategy

This paper studies physical layer security in a wireless ad hoc network with numerous legitimate transmitter–receiver pairs and eavesdroppers. A hybrid full-duplex (FD)/half-duplex receiver deployment strategy is proposed to secure legitimate transmissions, by letting a fraction of legitimate receivers work in the FD mode sending jamming signals to confuse eavesdroppers upon their information receptions, and letting the other receivers work in the half-duplex mode just receiving their desired signals. The objective of this paper is to choose properly the fraction of FD receivers for achieving the optimal network security performance. Both accurate expressions and tractable approximations for the connection outage probability and the secrecy outage probability of an arbitrary legitimate link are derived, based on which the area secure link number, network-wide secrecy throughput, and network-wide secrecy energy efficiency are optimized, respectively. Various insights into the optimal fraction are further developed, and its closed-form expressions are also derived under perfect self-interference cancellation or in a dense network. It is concluded that the fraction of FD receivers triggers a non-trivial tradeoff between reliability and secrecy, and the proposed strategy can significantly enhance the network security performance.

Outage Analysis of the Full-Duplex Decode-and-Forward Two-Way Relay System

Contrary to the traditional theoretical analysis with perfect self-interference cancellation, this paper studies the outage performance of a full-duplex (FD) decode-and-forward two-way relay system with the consideration of the residual self-interference incurred by the FD mode. The exact closed-form outage probability expressions are derived in this paper. In addition, the asymptotic outage performance is investigated when the transmit powers increase to infinity, and the result demonstrates that the outage probabilities monotonically increase and finally converge to 1 as the transmit power exceeds a certain threshold. Furthermore, optimal power allocation schemes and optimal relay node placement strategies are then proposed to improve the outage performance. Finally, simulation results are conducted to verify the accuracy of the theoretical analysis.

Outage Performance of the Full-Duplex Two-Way DF Relay System Under Imperfect CSI

Contrary to the most existing works about the full-duplex (FD) relaying with perfect channel state information (CSI), this paper studies the outage performance of the two-way FD decode-and-forward relay network under the joint effects of the residual self-interference and imperfect CSI. We first derive the exact closed-form expressions of the system outage probability, based on which we obtain the outage probability under the perfect self-interference cancellation to investigate the impacts of the imperfect CSI on the system performance. In addition, to gain more insights about the imperfect CSI, we analyze the optimal power allocation scheme and an optimal relay node placement strategy, which minimize the system outage probability. The results reveal that the imperfect CSI will only affect the optimal power allocation, and the optimal relay node placement is related to the power ratio between the user nodes. Finally, analytical evaluations are performed to verify the theoretical results, and Monte Carlo simulations guarantee the correctness of the analytical evaluations.

Transmit Power Allocation for Physical Layer Security in Cooperative Multi-Hop Full-Duplex Relay Networks.

In this paper, we consider a transmit power allocation problem for secure transmission in multi-hop decode-and-forward (DF) full-duplex relay (FDR) networks, where multiple FDRs are located at each hop and perform cooperative beamforming to null out the signal at multiple eavesdroppers. For a perfect self-interference cancellation (PSIC) case, where the self-interference signal at each FDR is completely canceled, we derive an optimal power allocation (OPA) strategy using the Karush-Kuhn-Tucker (KKT) conditions to maximize the achievable secrecy rate under an overall transmit power constraint. In the case where residual self-interferences exist owing to imperfect self-interference cancellation (ISIC), we also propose a transmit power allocation scheme using the geometric programming (GP) method. Numerical results are presented to verify the secrecy rate performance of the proposed power allocation schemes.

Joint Subcarrier and Power Allocation Methods in Full Duplex Wireless Powered Communication Networks for OFDM Systems

In this paper, we investigate wireless powered communication network for OFDM systems, where a hybrid access point (H-AP) broadcasts energy signals to users in the downlink, and the users transmit information signals to the H-AP in the uplink based on orthogonal frequency division multiple access. We consider a full-duplex H-AP which simultaneously transmits energy signals and receives information signals. In this scenario, we address a joint subcarrier scheduling and power allocation problem to maximize the sum-rate under two cases: perfect self-interference cancelation (SIC) where the H-AP fully eliminates its self-interference (SI) and imperfect SIC where residual SI exists. In general, the problems for both cases are nonconvex due to the subcarrier scheduling, and thus it requires an exhaustive search method, which is prohibitively complicated to obtain an optimal solution. In order to reduce the complexity, for the perfect SIC scenario, we jointly optimize subcarrier scheduling and power allocation by applying the Lagrange duality method. Next, for the imperfect SIC case, the problem becomes more complicated due to the SI at the H-AP. To solve this problem, we propose an iterative algorithm based on the projected gradient method. Simulation results show that the proposed algorithm for the case of perfect SIC exhibits almost the same sum-rate performance compared to the optimal algorithm, and the proposed iterative algorithm for the imperfect SIC case offers a significant performance gain over conventional schemes.

Relay-Assisted Multiple Access With Full-Duplex Multi-Packet Reception

The effect of full-duplex cooperative relaying in a random access multiuser network is investigated here. First, we model the self-interference incurred due to full-duplex operation, assuming multi-packet reception capabilities for both the relay and the destination node. Traffic at the source nodes is considered saturated and the cooperative relay, which does not have packets of its own, stores a source packet that it receives successfully in its queue when the transmission to the destination has failed. We obtain analytical expressions for key performance metrics at the relay, such as arrival and service rates, stability conditions, and average queue length, as functions of the transmission probabilities, the self interference coefficient, and the links' outage probabilities. Furthermore, we study the impact of the relay node and the self-interference coefficient on the per-user and aggregate throughput, and the average delay per packet. We show that perfect self-interference cancelation plays a crucial role when the SINR threshold is small, since it may result to worse performance in throughput and delay comparing with the half-duplex case. This is because perfect self-interference cancelation can cause an unstable queue at the relay under some conditions.

Impact of Channel Estimation Error on the Performance of Amplify-and-Forward Two-Way Relaying

In this paper, the impact of channel-state information (CSI) estimation error on the performance of an amplify-and-forward two-way multiple relay network has been investigated. In contrast to the existing literature, which assumes perfect self-interference cancellation, we consider imperfect self-interference cancellation at both sources that exchange information through multiple relays, and maximal-ratio combining is then applied to improve the decision statistics under imperfect signal detection. We derive the effective signal-to-noise ratio (SNR) subject to noisy channel estimation, and based on this SNR, the system outage probability is given. In addition, we derive the closed-form expression of the average system bit error rate (BER) and the asymptotic expressions for both outage probability and BER. Furthermore, instead of employing all relays, we examine the impact of imperfect CSI on a single relay selection (RS) scheme. To mitigate the negative impact of imperfect CSI, we show that power allocation (PA), by minimizing either the outage probability or the BER, can suitably be cast as the geometric-programming problem. Numerical results validate the correctness of the derived expressions and show that the adaptive-PA scheme outperforms the equal-PA scheme under the aggregated effect of imperfect CSI.