Statistical Inference – methods by which generalizations are made about a population Two Major Areas of Statistical Inference 1. Estimation – a parameter is established based on the sampling distribution of a proportion, establishing a certain degree of accuracy from the estimate 2. Test of Hypothesis – a decision is arrived at about a prestated hypothesis, thereby accepting or rejecting the hypothesis.

http://ieeexplore.ieee.org/iel5/9/24158/01101399.pdf

Estimation theory

Hardware impairments (HI) always exist in wireless devices, especially the low-cost ones. However, due to the complicated mathematical analysis, previous studies on wireless networks usually neglected the HI, particularly for full-duplex relaying (FDR) systems. In this paper, we consider the impact of the HI on the outage probabilities (OPs) and ergodic capacities (ECs) of both one-way (OW) and two-way (TW) amplify-and-forward (AF) FDR systems. We also take into account the residual self-interference (RSI) due to the imperfect self-interference cancellation (SIC), which appears at the FDR node of the considered HI-OW-AF-FDR system and all nodes of the considered HI-TW-AF-FDR system. Particularly, we derive the exact expressions of the outage probabilities and ergodic capacities for the HI-OW-AF-FDR and HI-TW-AF-FDR systems using mathematical analysis. Numerical results show that the OPs and ECs of the two systems are significantly affected by both HI and RSI, however the impact of the HI is more serious. It is recommended that besides SIC techniques, effective methods to reduce the HI should also be used to guarantee the system performance.

Impact of Hardware Impairments on the Outage Probability and Ergodic Capacity of One-Way and Two-Way Full-Duplex Relaying Systems

Because of the large number of antennas at the base station, the power consumption and cost of the low-noise amplifiers (LNAs) can be substantial. Therefore, we investigate the feasibility of inexpensive, power efficient LNAs, which inherently are less linear. To characterize the nonlinear distortion, the LNAs are described using a polynomial model, which allows for the derivation of the second-order statistics of the distortion. We show that some terms of the distortion from the LNAs combine coherently, and that the SINR of the symbol estimates therefore is limited by the linearity of the LNAs. Furthermore, the impact of a strong transmitter in the adjacent frequency band is investigated. The second-order statistics show how the power from that transmission leaks into the main band and interferes with the symbol estimates. The term that scales with the cube of the power received from the blocker can be filtered out by spatial processing. Only the coherent term that scales with the square of the power remains. Nonlinear distortion from the LNAs can be reduced by spatial processing in massive MIMO. However, it does not vanish as the number of antennas is increased.

Impact of Spatial Filtering on Distortion from Low-Noise Amplifiers in Massive MIMO Base Stations

Imperfect channel state information (I-CSI) and imperfect transceiver hardware often happen in wireless communication systems due to the time-varying and random characteristics of both wireless channels and hardware components. The impacts of I-CSI and hardware impairments (HI) reduce not only the system performance but also the self-interference cancellation (SIC) capability of full-duplex (FD) devices. To investigate the system performance in realistic scenarios, in this paper, we consider the performance of an FD multiple-input multiple-output (MIMO) relay system under the effects of I-CSI, imperfect SIC (I-SIC), and imperfect transceiver hardware. We mathematically derive the exact closed-form expressions of the outage probability (OP) and ergodic capacity of the considered HI-FD-MIMO relay system over Rayleigh fading channels with the existence of I-CSI, I-SIC, and HI. Numerical results indicate that the performance in terms of OP and capacity reaches saturation faster, especially when the channel estimation error, the residual self-interference (RSI), and HI levels are remarkable. Therefore, various solutions for effectively reducing the channel estimation error, RSI, and HI levels in the HI-FD-MIMO relay system should be carried out to improve the system performance. All derived mathematical expressions are verified through Monte-Carlo simulations.

Impacts of Imperfect Channel State Information, Transceiver Hardware, and Self-Interference Cancellation on the Performance of Full-Duplex MIMO Relay System

Hardware impairments (HI) due to imperfect manufactured electronic parts degrade the performance of wireless systems. In this paper, we consider a bidirectional full-duplex (FD) spatial modulation (SM) multiple-input multiple-output (MIMO) system with non-ideal hardware and residual self-interference (RSI). We propose to use the transmission antenna selection (TAS) as a solution to mitigate this degradation. The performance of the considered system is analyzed using mathematical analysis. Specifically, we first derive the exact closed-form expressions of the outage probability (OP), symbol error probability (SEP), and achievable data rate (ADR) for two cases: with and without TAS. Given these expressions, we conduct a detailed evaluation of the system performance under various scenarios to gain insight into its behavior. Essential conclusions are then made on HI and RSI’s impacts, especially for the case with TAS and high transmission rates.

/pdf/on-the-performance-of-full-duplex-spatial-modulation-mimo-5gtub34j80.pdf

On the Performance of Full-Duplex Spatial Modulation MIMO System With and Without Transmit Antenna Selection Under Imperfect Hardware Conditions

We consider two-way multi-pair full-duplex (FD) massive multi-input-multi-output (mMIMO) relaying, where multiple FD user-pairs exchange information via a shared FD relay. We derive a closed-form spectral efficiency (SE) lower bound by considering i) dynamic analog-to-digital converter (ADC) and digital-to-analog converter (DAC) architecture at the relay, where each antenna is connected to a different resolution ADC/DAC; and ii) low cost radio frequency (RF) chains at the relay and users. The dynamic ADC/DAC architecture allows us to judiciously choose ADC/DAC resolution to achieve high SE with low power consumption. We unlike, the most existing mMIMO relaying works, consider a correlated Rician fading channel, which captures realistic line-of-sight (LoS) signal propagation and spatial correlation between closely-packed relay antennas. We maximize the derived SE lower bound by first proposing its valid surrogate function, and then by using minorization-maximization approach. We investigate the impact of ADC/DAC and RF impairments, and show that the proposed optimization allows reduction in ADC/DAC resolution without compromising the SE.

Hardware-Impaired Rician-Faded Massive MIMO FD Relay: Analysis and Optimization

We consider a multipair two-way full-duplex massive multiple-input multiple-output (mMIMO) hardware-impaired relay, and derive a novel closed-form spectral efficiency (SE) expression for the zero-forcing (ZF) relay processing. We scale the hardware impairments for an $N$ -antenna relay as $N^{z}$ with $z\ge 0$ , and analyze the asymptotic SE limits for three relay power scaling schemes. This current letter provides valuable insights in deciding favorable $z$ values for the ZF relay processing, using which the hardware impairments can be scaled for the three relay power scaling schemes considered herein while maintaining a high SE.

Scaling Analysis of Hardware-Impaired Two-Way Full-Duplex Massive MIMO Relay

Most of the existing spectral efficiency (SE) investigations for massive multi-input multi-output (MIMO) relaying assume that each antenna has a dedicated radio-frequency (RF) chain with high-quality user and relay hardware. We consider a hybrid massive MIMO multi-pair two-way half-duplex relay, wherein each RF chain steers multiple antennas and assume that both users and relay have hardware impairments. We derive i) a novel closed-form SE expression using large-scale approximation; and ii) asymptotic SE expressions for two different power scaling schemes. We numerically demonstrate that i) a hardware-impaired hybrid relay has measurably degraded SE than a hardware-impaired conventional full-RF chain relay; and ii) the impact of hardware impairments do not vanish asymptotically as $N\rightarrow \infty$ , mainly due to users hardware impairments.

Hybrid Massive MIMO Two-Way Relaying With Users and Relay Hardware Impairments

Most of the existing works on massive multi-input multi-output (MIMO) relaying consider the hardware distortion to be uncorrelated across antennas. We consider multi-pair two-way half-duplex massive MIMO relaying with correlated hardware distortion. We study the effect of distortion correlation on the spectral efficiency (SE) in two scenarios when i) relay is equipped with low-quality hardware; and ii) both relay and users are equipped with low-quality hardware. We numerically show that the distortion correlation considerably affects the SE in the former case, especially for small number of users and/or large number of relay antennas. We also numerically show that when the user has low-quality hardware, the hardware distortion correlation can be neglected for moderate number of users and/or number of relay antennas.

Spectral Efficiency of Multi-pair Two-Way Massive MIMO Relay With Correlated Hardware Distortion

We consider a two-way full-duplex (FD) system where a massive multi-input-multi-output FD base station (BS) communicates with multiple FD users via an intelligent reflecting surface (IRS). We derive a closed-form network spectral efficiency lower bound by considering spatial correlation at the BS and IRS. We demonstrate the importance of modelling spatial correlation by simplifying this lower bound for uncorrelated channels to show that the IRS capability to modify the wireless medium now is significantly impeded. This lower bound, which is a function of only the long-term channel statistics, is also used to maximize the non-concave global energy efficiency metric by optimally allocating the transmit powers, and by designing the IRS phases. We derive closed-form updates for optimizing the transmit powers using Lagrangian dual, Quadratic, and Dinkelbach’s transforms. We then optimize the IRS phases by using the projected gradient ascent algorithm. We numerically show that increasing the number of IRS elements can help a FD mMIMO BS outperform its half-duplex counterpart, which otherwise under-performs due to its limited ability to cancel various FD interferences.

Sauradeep Dey

Papers

Hardware-Impaired Rician-Faded Massive MIMO FD Relay: Analysis and Optimization

Scaling Analysis of Hardware-Impaired Two-Way Full-Duplex Massive MIMO Relay

Hybrid Massive MIMO Two-Way Relaying With Users and Relay Hardware Impairments

Spectral Efficiency of Multi-pair Two-Way Massive MIMO Relay With Correlated Hardware Distortion

Spatially-Correlated IRS-Aided Multiuser FD mMIMO Systems: Analysis and Optimization