A potential use case for the sixth-generation wireless networks is the widespread adoption of eXtended Reality (XR) on mobile devices. These applications require high data rates, which may exhaust the limited available bandwidth ofmid-band(MB) frequencies, comprising frequency range 1 (FR1), i.e., sub-6 GHz, and the lower part of frequency range 3 (FR3), spanning 7-24 GHz, especially in dense urban clusters. In contrast, thehigh-band(HB) frequencies, including the frequency range 2 (FR2), i.e., millimeter-wave frequencies, and the upper part of FR3, offer more bandwidth, but are prone to reliability issues due to obstructions that block line-of-sight links between user equipment (UEs) and base stations (BSs). Therefore, we propose offloading high data rate UEs experiencing link outages in HB to MB. Using a cell-free massive multiple-input multiple-output architecture in MB, we ensure stable throughput for both low data rate UEs and offloaded high data rate UEs, while distributing the traffic load across more BSs. Our results demonstrate significant reduction in the mean outage duration and a hundred-fold reduction in the mean outage probability, with minimal impact on service quality for low data rate UEs, offering a cost-effective, practical solution for reliable HB deployments.

We estimate the channel and analyze the spectral efficiency (SE) of an uplink cell-free (CF) massive multiple-input multiple-output (mMIMO) intelligent reflecting surface (IRS) aided orthogonal time frequency space (OTFS) system. We introduce two novel pilot frames, which significantly reduce the pilot overhead by enabling each access point (AP) to estimate channels of all IRS elements in a single OTFS frame. We show that the delay-Doppler (DD) domain cascaded user-IRS-AP channel can be expressed as the twisted convolution of the user-IRS and IRS-AP DD channels. The cascaded DD channel exhibits twisted convolutional sparsity and common sparsity due to the shared DD profile across IRS elements. We propose a novel convolutional prior to capture these sparsities, and then develop a convolutional Bayesian learning (ConvBL) algorithm, which employs expectation-maximization (EM) procedure to calculate the channel posterior distribution in the E step, and natural gradient descent algorithm to calculate the prior parameters in the M step. We also derive a closed-form SE lower bound for our CF mMIMO IRS-OTFS system. We numerically show that the ConvBL algorithm has a much lower normalized mean squared error than other Bayesian and non-Bayesian algorithms. The algorithm also provides significant SE gains over them.

We investigate a cell-free (CF) massive multi-input-multi-output (mMIMO) system wherein user equipments (UEs) employ generalized superimposed pilot (GSP) in the uplink, and are under a jamming attack. In GSP, pilots are superimposed onto data signals, which are precoded using a matrix orthogonal to that of pilots. This reduces pilot-signal interference in GSP transmission which, consequently, outperforms conventional superimposed pilot, and regular pilot transmissions in the jamming scenario. We also derive a closed-form spectral efficiency (SE) expression for this system, and use that to design a jamming-robust bilinear equalizer (JRBE) by using only the channel statistics. We show that JRBE design reduces the jammer impact on the attacked UE. We develop a percentile-based UE power optimization, which enhances the SE of a predefined percentile of UEs. This optimization, whose objective is a non-smooth function, is solved by developing a minorization maximization framework. We show that in a jammed system, GSP-JRBE combination can provide a high SE to large number of UEs over existing designs. We also show that percentile optimization can enhance the SE of the jammed UE, without sacrificing the SE of unjammed UEs.

We propose a novel channel estimator for an uplink cell-free intelligent reflective surface (IRS)-aided orthogonal time frequency space (OTFS) system by introducing a pilot frame that reduces pilot overhead by enabling each access point (AP) to estimate the channels of all IRS elements in a single OTFS frame. The cascaded user-IRS-AP delay-Doppler (DD) channel is modeled as a twisted convolution of the user-IRS and IRS-AP DD channels, which now exhibits twisted convolutional sparsity, and common sparsity due to the shared DD profile across IRS elements. We develop a convolutional Bayesian learning (ConvBL) algorithm, which uses expectation-maximization for calculating channel posterior distribution, and natural gradient descent for optimizing prior parameters. We show that ConvBL vastly outperforms Bayesian and non-Bayesian algorithms.

We consider the downlink of a massive multiple-input-multiple-output (mMIMO) system, where a base station (BS) serves multiple clusters of single-antenna user equipments (UEs) by using multiple single-antenna relays. The BS employs a novel rate-splitting multiple access (RSMA) private interference cancellation (PIC) protocol wherein, similar to RSMA, a UE first decodes its common message. To decode its private message, a UE then cancels interference not only from the common message but, unlike RSMA, also from the private messages of weaker UEs in its own cluster. The RSMA-PIC protocol integrates the benefits of non-orthogonal multiple access (NOMA) and RSMA protocols, and outperforms them in low and high signal-to-noise regime. The BS employs minimum-mean-squared-error precoder to cancel the inter-relay interference between multiple relays. We also develop a decentralized two layer iterative optimization framework to maximize the weighted sum energy efficiency metric.

We estimate the uplink channel in a multi-user millimeter wave system, which uses a hybrid architecture with low-resolution analog-to-digital converters and low-quality hardware-impaired radio frequency (RF) chains. We propose a hardware-impairment-aware correlated sparse Bayesian learning (HA-CSBL) channel estimation algorithm, which exploits the channel structured sparsity and its correlation by constructing a novel Gaussian prior model. The HA-CSBL algorithm also estimates the statistics of hardware impairments to mitigate their effect. We show that the HA-CSBL algorithm provides i) a lower normalized mean squared error (NMSE) than the existing algorithms in different practical sparsity scenarios. These improvements are due to the better prior design, and the hardware-impairment-awareness of the HA-CSBL algorithm.

We consider the uplink of a hardware-impaired intelligent reflective surfaces (IRS) aided multi-cell massive multiple-input multiple-output (mMIMO) system with mobile user equipments, whose channel age with time. For this system, we design a novel distortion-and-aging-aware MMSE (DAAMMSE) receiver that not only provides a higher spectral efficiency (SE) than conventional maximal ratio and distortionunaware MMSE (DU-MMSE) receivers, but also reduces the pilot overhead. We develop a novel low-complexity IRS phase optimization framework based on minorization-maximization (MM) technique, which requires only channel statistics to calculate the optimal phase. We also show that the SE gain of the DAA-MMSE receiver over DU-MMSE receiver increases with hardware impairments, and channel aging. Along with DAAMMSE receiver, the IRS is also shown to reduce the pilot overhead in a mMIMO system with channel aging.

We consider an unmanned aerial vehicle (UAV)-relay-assisted massive multi-input multi-output system, where a base station (BS) serves coverage-limited user equipments (UEs) using non-orthogonal multiple access (NOMA). Due to the UAV altitude, the channels contain both line-of-sight (LoS) and non-LoS components. Moreover, the mobility of UAVs and UEs causes channel aging. We analyse the system spectral efficiency (SE) with minimum mean square error precoding, and by considering practical Rician channels with phase-shifts, channel aging, imperfect successive interference cancellation, and pilot contamination. We also develop an iterative stochastic optimization algorithm to optimize the system global energy efficiency. Our algorithm has extremely low complexity, due to its closed-form power updates, and converges faster than the existing state-of-the-art deterministic algorithm, which numerically calculates the SE.

We consider the uplink of a hardware-impaired intelligent-reflective surfaces (IRS)-aided multi-cell massive multiple-input multiple-output (mMIMO) system with mobile user equipments, whose channels age with time. We propose a novel distortion-and-aging-aware minimum-mean-square-error (DAA-MMSE) receiver that not only provides a higher spectral efficiency (SE) than conventional maximal ratio combiner (MRC) and distortion-unaware MMSE (DU-MMSE) receivers, but also reduces the pilot overhead. We also derive an SE lower bound for this system with MRC and DAA-MMSE receivers. We develop a novel low-complexity SE optimization framework using the weighted-MMSE and minorization-maximization (MM) techniques, which provide closed-form expressions for optimal power and phase allocations. The MM technique requires construction of a surrogate function, which we do in this work. We numerically characterize the i) UE velocities for which IRS deployment can tangibly increase their SE; ii) reduced pilot overhead with DAA-MMSE receiver along with IRS.

Orthogonal time-frequency space (OTFS) transmission is a promising multi-carrier modulation scheme for high-mobility communication scenarios. We consider a novel multiple frame-based superimposed pilot (SP)-OTFS system, which exhibits two-dimensional (2-D) delay-Doppler domain channel sparsity. We design a multiple-frame-based coupled prior sparse Bayesian learning (M-CPSBL) algorithm to exploit the 2-D channel sparsity while estimating it. This algorithm, however, inverts a large-dimensional matrix in each iteration with a high complexity. We next design its low-complexity version, which works on a smaller dimensional problem. The two proposed algorithms are used for SP-OTFS systems, which superpose low-powered pilots on to data signals. The combination of M-CPSBL and SP-OTFS frameworks is shown to outperform existing OTFS systems in terms of channel estimation normalized mean squared error, and spectral efficiency (SE). We derive a closed-form expression to optimize pilot and data powers to maximize the signal-to-interference-plus-noise ratio of SP-OTFS systems. We numerically show that optimal power allocation reduces the bit error rate, and increases the SE.

We consider a downlink multi-cell massive multi-input-multi-output system, where the base station (BS) in each cell serves its user equipments (UEs) via a cell-specific intelligent reflecting surface (IRS). The BS, IRS and UEs have dual-polarized antennas. We derive a lower bound on the spectral efficiency (SE) of this system, which operates in practical spatially-correlated Rician-fading channels. We also maximize the system global energy efficiency by optimizing the BS transmit powers and IRS phases. We optimize the transmit powers by designing a low-complexity minorization-maximization algorithm, which provides a closed form solution. We then optimize the IRS phases by using a multi-agent deep deterministic policy gradient method, where each BS learns optimal phases by sharing only the policies with each other, and that too without any supervision. We numerically show i) the BS-UE link attenuation for which an IRS can be replaced with dual-polarized antennas at the BS and UEs; and ii) that dual-polarized antennas enable a multicell IRS system to match its SE with a single-cell system with single-polarized antennas at the BS, IRS and UEs.

For a reflecting intelligent surface (RIS)-aided orthogonal time-frequency space (OTFS) system, we propose a two-dimensional off-grid sparse channel estimation model that exploits the fact that delay-Doppler (DD) locations of non-zero channel gains in a cascaded RIS-OTFS channel are sum of non-zero DD locations in the base station-RIS and RIS-user channels. Using this model, we estimate channel by considering multiple OTFS frames, which results in a block sparse DD domain channel. The multiple frames allow us to model the temporal correlation in a multi-frame OTFS system. We propose a novel correlated coupled prior to capture the DD sparsity of the channel, and estimate it by developing a sparse Bayesian framework. We maximize the achievable rate for our RIS-OTFS system by developing a gradient descent method, which has a high complexity. We also propose a low-complexity dimension-wise sinusoidal maximization (DSM)-based DD domain channel power maximization to obtain sub-optimal phase shifts. We show that the proposed channel estimation and phase optimization algorithms provide substantial gain over their existing counter-parts. We also show the robustness of an RIS-OTFS system over its non-RIS counterpart in a high-mobility scenario.

This work considers a device-to-device (D2D) underlaid multi-cell massive multi-input multi-output (mMIMO) system, wherein multiple cellular users (CUs) and D2D user-pairs support ultra-reliable low-latency communications (URLLC). The CUs are served by the mMIMO base station (BS), while the D2D user-pairs communicate without BS intervention. We design a novel interference-aware maximal ratio (IA-MR) combiner, and show that it has a similar spectral efficiency (SE) as the zero forcing (ZF) combiner, and that too with a much lesser computational complexity. The IA-MR combiner recovers the SE loss due to URLLC and D2D underlaying in multi-cell mMIMO systems. We also derive closed-form SE expression for the IA-MR combiner by assuming spatially-correlated Rician-faded channels, and use them to maximize the global energy efficiency (GEE) metric. The URLLC and D2D operations cause the GEE to become non-convex, as it now contains difference-of-concave and coupled fractional functions of optimization variables. We propose an optimization framework to tackle this non-convexity by using the quadratic and Lagrangian dual transforms. The proposed framework is also clubbed with a stochastic technique to optimize the GEE for ZF and minimum mean squared error equalizers, which do not have closed-form SE expressions.

We consider the downlink of a massive multi-input-multi-output (mMIMO) system where a base station (BS) serves ultra-reliable and low-latency communication (URLLC) user equipments (UEs) by employing rate-splitting multiple access (RSMA) technology. The UEs are assumed to be mobile, and their channels consequently age. The channels are spatially-correlated and Rician faded, with a phase-shifted line-of-sight (LoS) component, and the BS employs maximum ratio (MR) and minimum mean squared error (MMSE) precoders. A closed-form spectral efficiency (SE) expression is derived for the MR precoder, which is then used to develop a novel low-complexity optimal power allocation algorithm for the BS to maximize the global energy efficiency (GEE) metric. For the MMSE precoder, whose closed-form SE expression is difficult to derive, an iterative stochastic optimization algorithm is proposed. This algorithm, which is designed to have closed-form power update expressions, converges faster to the optimal solution than a conventional technique, which numerically calculates the SE. These low-complexity practically-implementable algorithms are developed by applying the epigraph, Lagrangian dual and quadratic transformations. We numerically show that RSMA outperforms spatial division multiple access when channels age faster, have a low Rician factor, and have a low correlation.

We consider the uplink of a cell-free (CF) massive multi-input multi-output (MIMO) system with superimposed pilot (SP) transmission, wherein user equipments (UEs) superimpose low-powered pilots onto data signals. This is unlike regular pilot (RP) transmission, where data and pilots use orthogonal spectral resources. Our CF mMIMO system has hardware impairments which occur due to i) low-quality radio frequency (RF) chains at the access points (APs) and UEs; and ii) dynamic analog-to-digital converter (ADC) architecture at the APs, which enables each RF chain to be connected to different resolution ADC. We derive a closed-form spectral efficiency (SE) expression for this CF system, wherein UEs observepracticalspatially-correlated Rician-faded channels. The derived lower-bound is generic, and reduces to the ones in the existing CF mMIMO SP works,which have only considered ideal hardware. Using this lower-bound, we optimally balance pilot and data transmit powers to maximize the SE. We analytically show that the optimal power balance is insensitive to AP impairments, but sensitive to that of UEs. We numerically show that SP can provide a higher SE than RP for low-to-severe hardware impairment levels, when supported by dynamic ADC architecture at the APs. With low resolution ADCs, RP always outperforms SP. The RP is also shown to be suitable for low UE speeds.

We consider two-way full-duplex (FD) massive multiple-input multiple-output decode-and-forward (DF) relaying with ultra-reliable low-latency communication (URLLC) users. The FD relay employs hybrid architecture with a fewer radio frequency (RF) chains than the antennas. Further, the users observe spatially-correlated Rician channels. For this system, we propose a novel optimal bilinear equalizer (OBE) that not only provides a much higher spectral efficiency (SE) than the conventional maximal ratio (MR) combiner, but also has better multi-user-interference (MUI) cancellation capability, which translates to low latency, as the system can schedule a large number of URLLC users. The OBE achieves this gain by exploiting spatial correlation in the system, an aspect we analytically demonstrate. We also derive a SE lower bound for this system, which is used to maximize the global energy efficiency (GEE) metric. The objective of GEE is a fractional function of the optimization variables, and is non-convex. We extend the fractional programming tools – Lagrangian dual and Quadratic transforms – to optimize the GEE. We show that a hybrid DF relay has a higher GEE, and a similar SE as that of a digital amplify-and-forward relay. We also show the higher GEE provided by a combination of OBE design and hybrid architecture, when compared with conventional combiners and digital architecture.

We consider the problem of estimating channel in reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) systems. We propose two variational expectation maximization (VEM) based channel estimation algorithms, which exploit the angular domain sparsity of RIS-assisted mmWave channel. To fully capture this sparsity, both within and across UEs, we construct a novel column-wise coupled Gaussian prior. The first proposed structured-mean-field-based VEM (SMF-VEM) algorithm uses the proposed prior, and calculates the posterior distribution of the unknown channel by assuming that it belongs to a set of multivariate distributions. This algorithm inverts a high-dimensional matrix in its posterior update, and consequently does not scale well for a large number of RIS elements and base station antennas, which are commonly used in practical systems. The second proposed fast mean field-based VEM (FMF-VEM) algorithm reduces complexity by assuming a fully-factorized posterior. It also bounds the variational objective to remove the residue coupling between the channel and phase matrices. Using extensive numerical investigations for a practical RIS mmWave system, and by using multiple metrics, we show that the proposed i) SMF- and FMF-VEM algorithms outperform several of their state-of-the-art counterparts; and ii) FMF-VEM has a much lower time complexity than SMF-VEM.

We consider the downlink of a cache-aided cell-free (CF) massive multi-input multi-output (mMIMO) system, wherein user equipments (UEs) exploit cached data to cancel multi-user interference (MUI) in the downlink. This work shows the importance of downlink pilots transmitted by the APs, which are used by the UEs to first estimate the instantaneous downlink channel state information (CSI), and then perform cache-aided MUI cancellation. We derive a closed-form SE expression for this system by considering practical spatially-correlated Rician fading channels with phase shifts, pilot contamination, and hardware impairments, both at the APs and UEs. We also propose a joint cache placement and power control optimization to maximize the global energy efficiency (GEE) metric. The cache placement problem is solved via clustering, while the power is optimized by designing a novel low-complexity parallel block minorization-maximization optimization. We numerically validate the benefits of downlink CSI for cache-aided CF mMIMO systems, and also show that degradation in CSI quality dramatically negates the UEs cache-aided MUI cancellation capability. We also show that the proposed optimization yields the same GEE as existing state-of-the-art optimizations, but with a much lower complexity.

We consider a multi-way massive multi-input multi-output (mMIMO) relaying system wherein a relay aids multi-way data exchange between multiple users by employing non-orthogonal multiple access (NOMA). The relay achieves this by superposing different user signals in the power domain. Each user then sequentially decodes the data of all other users by performing successive interference cancellation (SIC). To perform SIC, a user utilizes the downlink channel information, which it estimates using the precoded pilots transmitted by the relay. We derive a closed-form spectral efficiency (SE) expression for this downlink-pilot-aided NOMA multi-way relaying system by considering spatially-correlated channels, and imperfect SIC at the user. We next design two algorithms to maximize this SE by optimally allocating the user transmit powers and the NOMA variables. Both these algorithms provide a similar SE, but the latter one, due to its closed-form power updates, has a much lesser complexity. The efficacy of downlink pilots in multi-way NOMA relaying, with practical correlated Rayleigh-faded channels, is shown by demonstrating that they vastly outperform the case when users perform SIC using channel statistics.

We estimate the uplink channel of an extra large-scale multiple-input-multiple-output (XL-MIMO) system, with the base station (BS) consisting of multiple antenna sub-arrays. The BS has a decentralized processing architecture, wherein each sub-array is connected to a local processing unit (LPU), which performs its signal processing tasks. The non-stationarity in XL-MIMO channel causes it to become sparse. We design a decentralized channel estimation algorithm to exploit this sparsity. In this algorithm, each LPU decentrally estimates the channel of a sub-array by exchanging information with other LPUs. This exchange is required to exploit the XL-MIMO sparsity. This decentralized algorithm is designed in two steps. The first step designs a centralized sub-array-based variational Bayesian learning (cS-VBL) algorithm. The second step extends this centralized design to a decentralized S-VBL (dS-VBL) implementation, which converts the centralized hyperparameter updates in cS-VBL algorithm to equivalent decentralized optimization problems. Each LPU decentrally solves this problem using asynchronous alternating direction method of multipliers. We show that the proposed i) cS-VBL and dS-VBL algorithms exploit the XL-MIMO channel sparsity, and outperform their existing centralized and decentralized counterparts; and ii) dS-VBL algorithm is robust to LPU failures, and has a lower complexity than cS-VBL algorithm.

We consider the downlink of a cell-free (CF) massive multi-input multi-output (mMIMO) system, wherein multiple access points serve clustered users by employing non-orthogonal multiple access (NOMA) technology. This work shows the importance of transmitting downlink pilots for a NOMA CF mMIMO system, and derives a closed-form spectral efficiency (SE) expression with spatially-correlated Rician channels by addressing the complexity due to i) dynamic-resolution analog to digital converters; and ii) channel estimation errors. We also design a low-complexity parallel block minorization-maximization (MM) algorithm to optimize the non-convex global energy efficiency (GEE) metric. The MM algorithm requires a surrogate function for the GEE metric, which we construct in this work. We show that the NOMA CF mMIMO system, wherein channels estimated using downlink pilots are used for performing successive interference cancellation (SIC), significantly outperforms its counterpart which uses channel statistics to perform SIC. We also show that our parallel block MM optimization yields the same GEE as an existing optimization, but with a much lower complexity.

We propose a novel coupled prior-based sparse Bayesian framework for superimposed pilot (SP)-aided OTFS systems. The SP-OTFS system, wherein low-powered pilot signals are superimposed on to data signals, reduces the large pilot overhead, which is common in the existing OTFS systems. In the proposed coupled prior, sparsity of each channel gain is controlled not only by its own sparsity, but by also that of all other channel gains. OTFS channel has an inherent two-dimensional sparsity which can be exploited to increase its estimation accuracy. Using the proposed prior, we design a multiple received frame-based coupled prior sparse Bayesian learning (M-CPSBL) OTFS channel estimation algorithm, which is shown to outperform its state-of-the-art counterparts.

We study the impact of channel aging on the uplink of a cell-free massive multiple-input multiple-output system with hardware impairments. We consider a dynamic analog-to-digital converter architecture at the access points (APs), and low-resolution digital-to-analog converters at the user equipments (UEs). We derive a closed-form spectral efficiency expression by considering i) practical spatially-correlated Rician channels; ii) hardware impairments at the APs and the UEs; iii) channel aging; and iv) large-scale fading decoding (LSFD). We show that LSFD can effectively mitigate the detrimental effects of i) channel aging for both low and high UE velocities; and ii) inter-user interference for low-velocity UEs but not for high-velocity UEs.

We consider a hardware-impaired multi-cell Rician-faded massive multi-input multi-output (mMIMO) system with two-layer pilot decontamination precoding, also known as large-scale fading precoding (LSFP). We derive a closed-form spectral efficiency (SE) expression by assuming a flexible dynamic analog-to-digital converter (ADC)/digital-to-analog converter (DAC) architecture, and hardware-impaired radio frequency chains at the base stations (BSs) and user equipments. The dynamic ADC/DAC architecture enables us to vary the resolution of ADC/DAC connected to each BS antenna, and suitably choose them to maximize SE. We design a distortion-aware minimum mean squared error (DA-MMSE) precoder, and investigate its usage by combining it with the two-layer LSFP, and conventional single-layer precoding (SLP). We show that the DA-MMSE precoder with SLP outperforms its distortion-unaware counterpart, which is used with LSFP. We analytically show that for pure LoS channels, the LSFP reduces to SLP, and its implementation can thus be avoided. It is shown that the LSFP can tolerate high hardware impairments at the BS, but is extremely sensitive to the ADC resolution of the user. We also optimize the global energy efficiency by using a minorization-maximization based algorithm, and show its improved performance over the conventional SE optimization techniques.

We consider a full duplex (FD) multi-cell massive multi-input-multi-output (mMIMO) network, wherein FD mMIMO base-stations (BSs) serve multiple FD user equipments (UEs) on the same time-frequency resource. We derive closed-form uplink and downlink spectral efficiency (SE) expressions by considering i) radio-frequency impairments at the BSs and the UEs; ii) dynamic-resolution analog-to-digital converter/digital-to-analog converter (ADC/DAC) architecture at the BSs and low-resolution ADC/DAC at the UEs; and iii) spatially-correlated Rician channels. We optimize the non-convex global energy efficiency metric for this FD system by using the minorization-maximization (MM) framework, which transforms the optimization into a sequence of surrogate concave problems. We construct a novel surrogate function to exploit the MM framework. We numerically characterize the effect of FD interference on Rayleigh- and Rician-faded mMIMO networks, and show the higher immunity of the latter to the FD interference. We also show the SE gain provided by the dynamic ADC/DAC architecture which allows us to judiciously choose ADC/DAC resolution, while reducing the power consumption.

We consider the problem of detecting active devices and estimating their channels in the uplink of a massive machine type communication (mMTC) network. The base station (BS) in this mMTC system is equipped with massive multiple input multiple output (mMIMO) technology, and the channels across its antennas are correlated, an aspect ignored by most of the existing mMTC works. We propose three Bayesian learning algorithms which exploit channel spatial correlation, and comprehensively outperform several existing state-of-the-art algorithms, which do not exploit it. The proposed algorithms perform better in terms of the normalized mean squared error, activity error rate, and spectral efficiency (SE). The first correlated vector approximate message passing (AMP) algorithm has the best performance, but fails when the BS does not have knowledge of channel large scale fading and device activity probability. The second block sparse Bayesian learning (B-SBL) algorithm overcomes these limitations, but has a high complexity. The third combined AMP-BSBL algorithm retains the advantages of B-SBL, but with a much reduced complexity. We show that all three channel estimators can be represented as plug-in linear minimum mean squared estimators. This crucially helps us in deriving a common lower bound on the SE of mMIMO mMTC systems.

We study the impact of channel aging on the uplink of a cell-free (CF) massive multiple-input multiple-output (mMIMO) system by considering i) spatially-correlated Rician-faded channels; ii) hardware impairments at the access points and user equipments (UEs); and iii) two-layer large-scale fading decoding (LSFD). We first derive a closed-form spectral efficiency (SE) expression for this system, and later propose two novel optimization techniques to optimize the non-convex SE metric by exploiting the minorization-maximization (MM) method. The first one requires a numerical optimization solver, and has a high computation complexity. The second one with closed-form transmit power updates, has a trivial computation complexity. We numerically show that i) the two-layer LSFD scheme effectively mitigates the interference due to channel aging for both low- and high-velocity UEs; and ii) increasing the number of AP antennas does not mitigate the SE deterioration due to channel aging. We numerically characterize the optimal pilot length required to maximize the SE for various UE speeds. We also numerically show that the proposed closed-form MM optimization yields the same SE as that of the first technique, which requires numerical solver, and that too with a much reduced time-complexity.

This work considers a multi-way massive multi-input multi-output (mMIMO) relaying system wherein several wireless information and power transfer capable users, first harvest energy, and then exchange information via a relay. The mMIMO relaying system is practically modelled by considering spatially-correlated relay-user channels, and by using a non-linear energy harvesting (EH) model. A closed-form spectral efficiency expression is derived for this system, which is then used to jointly allocate the relay and users transmit powers, and the charging time to optimize the weighted sum energy efficiency (WSEE) metric. The spatially-correlated channel and the non-linear EH model not only couple the optimization variables, but also introduce nested scalar fractional optimization functions. This makes the WSEE metric non-convex. The proposed solution first uses the existing quadratic transformation (QT) to decouple the scalar fractional forms. It then applies novel results, which are developed by extending the QT framework, to decouple the optimization variables. The proposed WSEE optimization algorithm is shown to provide close-to-optimal WSEE. It is also shown that channel spatial correlation increases the amount of energy harvested by the users, but reduces their WSEE.

We consider a practical hardware-impaired multi-cell massive multi-input multi-output (mMIMO) system with spatially-correlated Rician fading channels, whose line-of-sight component experiences a random phase-shift. The multi -cell mMIMO system employs two-layer large-scale fading decoding (LSFD) to mitigate the interference due to pilot contamination. We consider a dynamic analog-to-digital converter (ADC) architecture at the base stations (BSs), which enables us to independently vary the resolution of ADC connected to each of its antenna, and thus properly choose them to achieve a high spectral efficiency (SE). Both BS and user equipments (UEs) are also equipped with low-cost radio frequency chains, which introduce additional hardware impairments. We first derive a closed-form SE expression for this system, and then optimize the LSFD vectors to maximize the sum SE metric using generalized Rayleigh quotient. We investigate the ADC resolution and hardware impairments values for which LSFD is highly effective, and the values for which its effectiveness reduces.

We consider the downlink of massive multi-input-multi-output (mMIMO) rate-splitting multiple-access (RSMA) system with spatially-correlated Rician channels that experience phase shifts in their line-of-sight (LoS) component. We also assume that channel ages due to highly mobile users. We estimate the channels at the beginning of the coherence block, and use it to design the precoders using maximum ratio (MR) technique in the data transmission phase. We derive a closed-form spectral efficiency (SE) expressions for the above system, and numerically validate its correctness by comparing with the ergodic SE. We investigate the SE gain provided by RSMA over its conventional spatial-division multiple access (SDMA) counterpart. We crucially show only at lower Rician factor, which indicates the strength of LoS component over its non-LoS (NLoS) counterpart, RSMA has a higher SE than SDMA. For higherRician factor, SDMA has a higher SE than RSMA. We also show that the SE gain of RSMA over SDMA increases with increase in channel aging.

We consider a hardware-impaired multi-cell Rician- faded massive multi-input multi-output (mMIMO) system with two-layer pilot decontamination precoding, also known as large-scale fading precoding (LSFP). Each BS is equipped with a flexible dynamic analog-to-digital converter (ADC)/digital-to-analog converter (DAC) architecture and the user equipments (UEs) have low-resolution ADCs. Further, both BS and UEs have hardware-impaired radio frequency chains. The dynamic ADC/DAC architecture allows us to vary the resolution of ADC/DAC connected to each BS antenna, and suitably choose them to maximize the SE. We propose a distortion-aware minimum mean squared error (DA-MMSE) precoder and investigate its usage with two-layer LSFP and conventional single-layer precoding (SLP) for hardware-impaired mMIMO systems. We discuss the use cases of LSFP and SLP with DA-MMSE and distortion-unaware MMSE (DU-MMSE) precoders, which will provide critical insights to the system designer regarding their usage in practical systems.

We consider two-way massive multiple-input multiple-output (mMIMO) relaying with ultra-reliable low-latency communication (URLLC) users. The full-duplex (FD) relay employs hybrid architecture, with a lesser number of radio frequency chains than the antennas. For this system, we first propose a novel digital optimal bilinear equalizer which not only provides a much higher spectral efficiency (SE) than the conventional maximal ratio combiner, but also yields a lower latency when a large number of URLLC users are scheduled. We also derive a SE lower bound for this system by considering spatially-correlated Rician fading channels. We also show that the hybrid decode-and-forward relay provides much higher SE to its URLLC users than a full-RF chain amplify-and-forward relay, which only serves non-URLLC users.

We consider a relay-aided massive multi-input multi-output (mMIMO) system where a base station (BS) serves various users via multiple relays by employing non-orthogonal multiple access (NOMA). We practically model this system by considering spatially-correlated Rician-faded channels, and channel estimation errors both at the BS and at the users, which consequently perform imperfect successive interference cancellation (SIC). We consider these two artifacts, and derive a lower bound on the spectral efficiency (SE) of this multi-relay NOMA system, which is valid for arbitrary number of BS antennas. We crucially show that i) Rician-faded channels are immune to the errors caused by imperfect SIC at users; ii) high spatial correlation improves the spatial diversity among relays located close to BS and achieves better sum SE than its uncorrelated counterpart.

We consider the problems of active user detection (AUD) and channel estimation (CE) in the uplink of massive machine type communication (mMTC) network. We propose a coupled prior sparse Bayesian learning algorithm that exploits the sporadic user activity and variable-sized block channel sparsity. We first design a novel coupled hierarchical Gaussian prior model which captures the variable size block-sparsity. We then derive its sub-optimal precision hyperparameter updates using majorization-minimization technique. We extensively investigate the proposed algorithm performance and show that it, due to its generic prior, outperforms the existing ones.

Orthogonal time frequency space (OTFS) modulation establishes reliable communication over highly time-varying wireless channels. This work designs a low-complexity linear minimum mean square error (LMMSE) receiver for practical pulse-shaped multiple-input multiple-output (MIMO)-OTFS systems. The proposed design reduces complexity by exploiting inherent channel sparsity and channel-agnostic structure of matrices involved in the LMMSE receiver. The proposed design, with log-linear complexity order, does not make any approximation, and provides exactly the same solution, and consequently the same bit error rate, as that of the conventional LMMSE receiver, which has a cubic complexity order.

We consider the downlink of a relay-aided multi-cell massive multi-input multi-output (mMIMO) system, where in each cell the base station (BS) serves its users via multiple relays by employing non-orthogonal multiple access (NOMA). We model this system by considering spatially-correlated Rician-faded channels and their estimation errors. The users, consequently, perform imperfect successive interference cancellation (SIC). We derive a lower bound on the spectral efficiency (SE) of this system. We then optimize the non-convex global energy efficiency (GEE) metric, which is a fractional function of the optimization variables. We solve this problem by considering a low-complexity alternating minimization maximization approach, which splits a complex joint problem into multiple simpler convex surrogate sub-problems. We propose a novel surrogate function to exploit this framework, and analytically show that it satisfies the desirable properties of a valid surrogate function. We numerically show that 1) reusing the pilots in each cell, when the channel has sufficiently hardened, provides higher SE than using orthogonal pilots in all cells and 2) the proposed GEE algorithm provides similar GEE as that of an existing joint optimization framework, but with much less complexity.

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.

We consider a full duplex (FD) massive multiple-input multiple-output (mMIMO) cell-free (CF) system, where a large number of multi-antenna FD access points (APs) jointly serve multiple FD user equipments (UEs). The APs transmit precoded downlink pilots for the UEs to estimate the effective downlink channel. For this system, we derive closed-form uplink and downlink spectral efficiency (SE) expressions by considering i) radio-frequency (RF) impairments at the APs and UEs; ii) dynamic resolution analog-to-digital converter/digital-to-analog converter (ADC/DAC) architecture at the APs and low-resolution ADC/DACs at the UEs; and iii) spatially-correlated Rician channels. We then maximize the non-convex global energy efficiency metric by using the block minorization-maximization technique, which decomposes the main optimization into multiple convex surrogate sub-problems. We analytically show that the SE gain obtained with downlink training is limited for practical CF systems with RF and ADC/DAC impairments, Rician channel and pilot contamination. We also extensively investigate the impact of FD interferences on the downlink training gain.

We consider the problem of estimating channel and detecting active users in the uplink of a massive machine type communication (mMTC) network. We propose a centralized coupled prior based sparse Bayesian learning (cCP-SBL) algorithm that exploits the sporadic user activity and variable-sized block mMTC channel sparsity in the virtual angular domain. To achieve this objective, we first design a generalized coupled hierarchical Gaussian prior which captures this variable-sized block sparsity. We then derive its sub-optimal precision hyperparameter updates using majorization minimization framework. We next design a decentralized CP-SBL (dCP-SBL) algorithm for the emerging base station architectures with multiple processing units. The dCP-SBL algorithm converts the centralized hyperparameter cCP-SBL updates to an equivalent optimization problem, and solves it decentrally using asynchronous alternating direction method of multipliers. We also theoretically analyze the convergence of the dCP-SBL algorithm. We show using extensive numerical investigations that the i) proposed cCP- and dCP-SBL algorithms outperform several existing state-of-the-art designs; and ii) dCP-SBL algorithm is robust to processing unit failures and has a lower time complexity than the cCP-SBL algorithm.

Orthogonal time frequency space modulation (OTFS) scheme establishes reliable communication in a rapidly time-varying wireless channel with a high Doppler spread. We design a low-complexity linear minimum mean squared error (LMMSE) receiver for practical-pulse-shaped multiple-input multiple-output (MIMO)-OTFS systems. The proposed receiver exploits the inherent channel sparsity and the channel-agnostic structure of matrices involved in the LMMSE receiver, and has only a log-linear complexity. It provides exactly the same solution, and hence the same bit error rate (BER), as that of the conventional LMMSE receiver with a cubic order of complexity. We also derive, by using the Taylor series expansion and the results from random matrix theory, a tight closed-form approximation for the post-processing signal-to-noise-plus-interference ratio (SINR) expression of the proposed receiver. This expression is derived by assuming imperfect receive channel state information. We show using extensive numerical investigations that the derived SINR expression, when averaged over multiple channel realizations, accurately characterizes the BER of a MIMO-OTFS system.

We derive closed form bit error rate (BER) expression for orthogonal time frequency space (OTFS) zero-forcing (ZF) receiver with perfect and imperfect receive channel information. Depending on the delay-Doppler locations of the propagation paths of the OTFS channel H, the expression$\mathrm {H}^{H}\mathrm {H}$is shown to have either distinct or repetitive eigenvalues. When$\mathrm {H}^{H}\mathrm {H}$has two or less distinct eigenvalues and the remaining ones are repetitive, we derive the probability distribution function (pdf) of the signal-to-noise-plus-interference-ratio (SINR) of the ZF receiver. A closed form BER expression is then derived by averaging the conditional BER over the SINR pdf. When$\mathrm {H}^{H}\mathrm {H}$has$n$distinct eigenvalues, we use numerical integration to derive a generalized expression for the SINR pdf. We show that this pdf can be tightly approximated by the Gamma pdf, and then use it to derive the BER expression. The derived OTFS ZF BER expression therefore, unlike the existing ones in the literature, does not require averaging over multiple channel realizations. We show, for different modulation schemes and OTFS system parameters, that the BER calculated using the derived expressions closely matches the one calculated numerically.

We consider a cell-free (CF) massive multi-input multi-output (mMIMO) system, where multi-antenna access points (APs) serve single-antenna unmanned aerial vehicles (UAVs) and ground users (GUEs). We assume, unlike the existing CF mMIMO literature, hardware-impaired UAVs and GUEs, which observe a mixture of spatially-correlated Rician- and Rayleigh-faded channels while communicating with hardware-impaired APs. We derive a closed-form downlink spectral efficiency (SE) expression by using practical models for the channel mixture, and by considering channel estimation errors. We propose a novel block quadratic transformation (block-QT) technique to optimize non-convex network-centric global energy efficiency (GEE) by appropriately modeling circuit, UAV propulsion and fronthaul powers. The novel block-QT approach combines block optimization and quadratic transformation technique to decompose GEE optimization into simpler convex sub-problems. We numerically show that i) it is better to operate a UAV at a larger height when it has severe hardware impairments; and ii) when UAVs operate at a lower height, they do not significantly affect the SE of GUEs.

We propose a superimposed pilot (SP)-based channel estimation and data detection framework for orthogonal time-frequency space (OTFS) systems, which superimposes low-powered pilots on to data symbols in the delay-Doppler domain. We propose two channel estimation and data detection designs for SP-OTFS systems which, unlike the existing OTFS designs, do not designate any slots for pilots, and consequently have higher spectral efficiency (SE). The first SP design estimates channel by treating data as interference, which degrades its performance at high signal to noise ratio. The second SP design alleviates this problem by iterating between channel estimation and data detection. Both these designs detect data using message passing algorithm which exploits OTFS channel sparsity, and consequently has low computational complexity. We also derive a lower bound on the signal-to-interference-plus-noise ratio of the proposed designs and maximize it by optimally allocating power between data and pilot symbols. We numerically validate the derived analytical results, and show that the proposed designs have superior SE than the existing OTFS channel estimation and data detection designs.

We consider a multi-user system where a massive multi-input-multi-output (mMIMO) full-duplex (FD) base-station (BS) communicates with multiple FD users via an intelligent reflecting surface (IRS). We derive novel uplink and downlink spectral efficiency (SE) lower bound expressions when the BS estimates composite BS-IRS-user channels. The lower bounds are derived considering spatially-correlated IRS and user channels, and require only statistical channel state information (CSI). We propose a projected gradient ascent based IRS phase optimization algorithm, which also uses only statistical CSI, and enables the system to achieve a higher SE in the presence of the loop and inter-user interferences. We analytically investigate the dependence of SE on the IRS phase for spatially correlated channels considered herein. We show that the proposed analysis can help in increasing the SE by appropriate IRS placement.

We consider a full-duplex cell-free massive multiple-input-multiple-output system with limited capacity fronthaul links. We derive its downlink/uplink closed-form spectral efficiency (SE) lower bounds with maximum-ratio transmission/maximum-ratio combining and optimal uniform quantization. To reduce carbon footprint, this paper maximizes the non-convex weighted sum energy efficiency (WSEE) via downlink and uplink power control, and successive convex approximation framework. We show that with low fronthaul capacity, the system requires a higher number of fronthaul quantization bits to achieve high SE and WSEE. For high fronthaul capacity, higher number of bits, however, achieves high SE but a reduced WSEE.

We consider a multi-way massive multi-input multi-output (mMIMO) relay via which several energy-constrained MIMO users exchange information by switching between wireless power generation and information transfer. The mMIMO relay and MIMO users experience spatially-correlated channels, which the current multi-way relaying literature ignores. We derive closed-form spectral efficiency (SE) expression for this system that is valid for a practical number of relay antennas. We design a max-min power control algorithm which ensures user fairness by jointly optimizing the charging time and transmit powers of the relay and users.

We consider an unmanned aerial vehicle (UAV) enabled cell-free (CF) massive multi-input multi-output (mMIMO) system, where multi-antenna access points (APs) assist various single-antenna UAVs and ground users (GUEs). Unlike, existing CF mMIMO works, we assume non-ideal transceiver hardware at the UAVs, GUEs and APs, and derive a closed-form downlink spectral efficiency (SE) expression by considering spatially-correlated Rician channels and channel estimation errors. We also propose a novel block quadratic transformation technique to optimize the system global energy-efficiency (GEE) by incorporating practical backhaul power, circuit and UAV propulsion power. We numerically show that severely hardware-impaired UAVs will have a higher SE when they operate at a larger height.

Most of the existing massive multi-input-multi-output (mMIMO) relaying works assume ideal transceiver hardware and spatially uncorrelated channels. A practical mMIMO relay, however, due to limited antenna spacing and the use of cost-effective equipment, usually experiences spatially-correlated channels and hardware impairments, respectively. We consider a hardware-impaired two-way full-duplex (FD) spatially-correlated mMIMO relaying with multiple MIMO FD user-pairs, and derive a closed-form spectral efficiency (SE) expression which is valid for a practical number of finite relay antennas. We use this expression to develop a quadratic transformation approach to optimize the non-convex global energy efficiency (GEE) and weighted sum energy efficiency (WSEE) metrics, which are fractional functions of optimization variables. The proposed approach first converts the fractional problem into its equivalent fraction-free counterpart, and then uses novel transformations to make the problem concave, and solve it using an iterative algorithm. We use this optimization to i) investigate the impact of spatial correlation and hardware impairments on GEE; ii) decide hardware impairment values for a tolerable reduction in GEE; and iii) investigate the impact of weights in WSEE on the users energy efficiency.

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.

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 → ∞, mainly due to users hardware impairments.

The massive multiple-input multiple-output (MIMO) full-duplex two-way relaying (FD-TWR) literature has extensively investigated power scaling for rate guarantees by considering a fixed number of users. We investigate the pairwise error probability (PEP) and the per-user rate of a FD-TWR with N, relay antennas that employs maximal ratio combining/transmission to enable two-way communication between K FD users. We propose novel relay and user powers scalings, with both N, and K tending to infinity, and show that the PEP of each user converges almost surely to its AWGN counterpart. These power scalings are different from the existing ones, which are derived by fixing K and by assuming that only N, tends to large values. We show that the analysis developed herein applies to both Gaussian and non-Gaussian complex channels with finite number of moments. We numerically show that when both K and N, increase concurrently to large values, the proposed power scaling schemes not only have better per-user PEP and rate than the existing schemes, but they are also robust to the FD self loop-interference power.

Spatial modulation (SM) uses antenna indices to transmit information, along with modulation symbols. The conventional SM scheme fixes the number of active antennas, and consequently the number of transmit symbols, in a transmit vector to avoid detection ambiguity. This work proposes a generalized block-based spatial modulation (GBSM) scheme which varies the number of active antennas in each transmit vector, but fixes their number over a transmission block. The proposed GBSM scheme, which transmits information using the spatial dimensions created over a block of transmit vector, resolves detection ambiguity as the number of transmit symbols over a block remains fixed. It crucially also has a large constellation cardinality, which we exploit by proposing novel low bit error rate (BER) constellation design algorithms. We also propose a novel low-complexity semi-definite relaxation detector, which has similar BER as that of the optimal maximum likelihood detector but with ≈ 85% lower complexity.

We consider a massive multi-input multi-output (mMIMO) system where in a base station (BS) serves its users via multiple relays by employing non-orthogonal multiple access (NOMA). We practically model this system by considering channel estimation errors both at the BS and at the users, which consequently perform imperfect successive interference cancellation. We consider these two artifacts, and derive a lower bound on the spectral efficiency (SE) of this multi-relay NOMA system, which is valid for arbitrary number of BS antennas. We then jointly allocate the BS and relay powers to optimize non-convex global energy efficiency (GEE) and the weighted sum energy efficiency (WSEE) metrics, which are fractional functions of sum-of-products/ratios of optimization variables. These two optimizations require extension of an existing fractional programming framework, which we do by proposing two novel transformations. We analytically prove the monotonic convergence of the transformed problems to a stationary point of their respective original counterparts. We numerically show that i) a multi-relay mMIMO NOMA system outperforms its orthogonal counterpart only with accurate channel information; and ii) the proposed GEE and WSEE algorithms significantly improve the energy efficiency by avoiding additional power use, after attaining optimal value.

We optimize the weighted sum energy efficiency (WSEE) of two-way amplify and forward relaying, where multiple full-duplex (FD) user-pairs exchange information via a shared FD massive multiple-input multiple-output (MIMO) relay. Optimization of user-centric WSEE metric, which prioritizes links of users with high energy efficiency (EE) requirements by suitably choosing their weights, is a non-convex problem due to its sum-of-ratio form. We optimize it by first approximating WSEE as a concave-convex fractional function, and then by using the quadratic transform. We then use Karush-Kuhn-Tucker (KKT) conditions to derive a closed-form solution to optimize WSEE. We numerically show that the i) proposed solutions achieve significant WSEE gains; and ii) suitable choice of weights can help prioritize EE requirements of different users.

Design of energy-efficient wireless systems has recently attracted attention to reduce their carbon footprint. This paper optimizes non-convex weighted sum energy efficiency (WSEE) of a multi-pair two-way amplify-and-forward half-duplex massive multiple-input multiple output relay system. We optimize it by developing a two-layer decentralized successive convex approximation optimization framework. The first layer approximates the non-convex WSEE either as a generic convex program (GCP) or as a second order cone program (SOCP). The second layer decentrally solves the approximated problem using alternating direction method of multipliers. We show that the proposed iterative algorithm yields a Karush-Kuhn-Tucker point of the original WSEE problem. We numerically analyze the effect of weights on the energy efficiency (EE) of individual users, and show that the proposed framework enable us to meet the heterogeneous EE requirements. We also analytically and numerically show that the decentralized algorithm has lesser complexity than its centralized counterpart, but yields the same WSEE.

We consider multipair two-way full-duplex massive multiple-input multiple-output (mMIMO) hardware- impaired relay which facilitates single-antenna full-duplex users to exchange information. The key to cost-efficient implementation of mMIMO relays is to use low cost relay hardware which are prone to impairments. These impairments however, degrade the system performance. The existing literature models the relay hardware impairments as additive noise, by ignoring the multiplicative phase noise. In this paper, we study the impact of multiplicative phase noise along with the residual hardware impairments and receiver noise at the relay. We derive a closed form spectral efficiency (SE) lower bound with maximum ratio combining/maximum ratio transmission at the relay, which is applicable for arbitrary number of relay antennas. We also numerically validate the tightness of the derived closed-form SE expression with the ergodic SE expression and analyze the impact of phase noise along with additive hardware impairments on SE.

We consider a multi-pair two-way full-duplex (FD) amplify-and-forward relaying, where multiple FD multi-input multi-output (MIMO) users exchange information via a shared FD massive MIMO relay. We derive a closed-form spectral efficiency (SE) lower-bound for maximal-ratio combining/maximal-ratio transmission relay processing considering spatially correlated relay and user antennas, which most of the existing works have ignored. The derived SE lower-bound is applicable for arbitrary number of relay antennas, and simplifies to the following results available in the literature i) the asymptotic SE for number of relay antennas tending to infinity; and ii) the SE lower-bound with independent relay antennas and single-antenna users. We use this SE lower-bound to maximize the non-convex SE, which is of matrix fractional form. We optimize SE by approximating it as concave-convex function, and then by applying matrix quadratic transformation. We numerically validate the SE lower-bound for various system configurations and also characterize their performance for different spatial correlation and interference values. We investigate the gains achieved by the optimal SE over equal power allocation.

The maturing massive multiple-input multiple-output (MIMO) literature has provided asymptotic limits for the rate and energy efficiency (EE) of maximal ratio combining/ maximal ratio transmission (MRC-MRT) relaying on two-way relays (TWRs) using the amplify-and-forward (AF) principle. Most of these studies consider time-division duplexing and a fixed number of users. To fill the gap in the literature, we analyze the MRC-MRT precoder performance of an N-antenna AF massive MIMO TWR, which operates in a frequency-division duplex mode to enable two-way communication between 2M = [Nα] single-antenna users, with α ∈ [0, 1), divided equally into two groups of M users. We assume that the relay has realistic imperfect uplink channel state information (CSI), and that quantized downlink CSI is fed back by the users relying on B ≥ 1 bits per-user per relay antenna. We prove that for such a system with α ∈ [0, 1), the MRC-MRT precoder asymptotically cancels the multi-user interference (MUI) when the supremum and infimum of large-scale fading parameters are strictly nonzero and finite, respectively. Furthermore, its per-user pairwise error probability converges to that of an equivalent AWGN channel, as both N and the number of users 2M = [Nα] tend to infinity, with a relay power scaling of Pr= (2MEr/N) and Erbeing a constant. We also derive upper bounds for both the per-user rate and EE. We analytically show that the quantized MRC-MRT precoder requires as few as B = 2 bits to yield a BER, EE, and per-user rate close to the respective unquantized counterparts. Finally, we show that the analysis developed herein to derive a bound on α for MUI cancellation is applicable both to Gaussian as well as to any arbitrary non-Gaussian complex channels.

We design a precoder for non-concurrent two-way relaying (ncTWR) where a base station (BS) serves a transmitonly user equipment (TUE) in the uplink and a receive-only user equipment (RUE) in the downlink. The RUE experiences backpropagating interference (B!). The proposed precoder is designed such that it not only cancels the B! experienced by the RUE but more importantly, enables receive data decoding with high diversity. The high diversity precoder is designed by deriving the closed-form pairwise error probability (PEP) expressions, and by optimizing the precoder elements to minimize the PEP. We analytically show that with Nr-antenna relay, Nb-antenna BS, and Nu-antenna TUE and RUE, both BS and RUE decode their respective data with a diversity order of min(Nu2, (Nr- Nu)Nb) at high receive signal-to-noise ratio. We also numerically show that the proposed design has lower bit error rate than the existing state-of-the-art ncTWR designs.

We consider two-way amplify-and-forward relaying, where multiple full-duplex user pairs exchange information via a shared full-duplex massive multiple-input multiple-output (MIMO) relay. Most of the previous massive MIMO relaying works maximize the spectral efficiency (SE). By contrast, we maximize the non-convex energy efficiency (EE) metric by approximating it as a pseudo-concave problem, which is then solved using the classic Dinkelbach approach. We also maximize EE of the least energy-efficient user relying on the max-min approach. We also compare SE and EE of the proposed design with existing full-duplex systems and quantify the significant improvement achieved by the proposed algorithm. We also compare EE of the proposed full-duplex system to that of its half-duplex counterparts, and characterize the self-loop and inter-user interference regimes, for which the proposed full-duplex system outperforms the half-duplex ones.

We consider two-way amplify and forward relaying, where multiple full-duplex user pairs exchange information via a shared full-duplex massive multiple-input multiple-output (MIMO) relay. We derive closed-form lower bound for the spectral efficiency with zero-forcing processing at the relay, by using minimum mean squared error channel estimation. The zero-forcing lower bound for the system model considered herein, which is valid for arbitrary number of antennas, is not yet derived in the massive MIMO relaying literature. We numerically demonstrate the accuracy of the derived lower bound and the performance improvement achieved using zero-forcing processing. We also numerically demonstrate the spectral gains achieved by a full-duplex system over a half-duplex one for various antenna regimes.

We investigate a limited feedback precoder based on symbol pairwise error probability (PEP) for a block-faded K×ntdownlink multiple-input multiple-output (MIMO) channel. In the considered system, K = ⌊ntα⌋ single-antenna users feedback quantized channel state information to the nt-antenna transmitter using B bits per-transmit-antenna per user. We analytically show that for αt→ ∞, both symbol PEP and achievable rate of each of the K downlink users almost surely converge to the symbol PEP and achievable rate of K parallel additive white Gaussian noise (AWGN) channels, respectively. We show that the encoding complexity of the precoder is O(ntK). We also show that if channel coefficients estimated by the user are corrupted by AWGN noise, the symbol PEP and achievable rate of each user almost surely converge to the symbol PEP and achievable rate in a scaled AWGN channel with B > 1 and nt→ ∞. For correlated channels, we derive a condition, which enables the proposed precoder almost surely to cancel multi-user interference for large ntvalues. Finally, we numerically compare the bit error rate, encoding complexity, and per-user achievable rate of the proposed scheme with the existing designs.

Transceiver designs for multiple-input multiple-output (MIMO) two-way relaying are being actively explored. Most of the state-of-the-art studies optimize a system-wide objective function subject to the transmit power constraints on the two source nodes and the relay. Transceiver designs with quality-of-service (QoS) constraints have lacked attention in two-way relaying literature. In this paper, we study a MIMO transceiver design, based on the generalized singular value decomposition, that allocates power at the source and relay nodes to optimize the following per-stream rate-constrained objectives: 1) network transmit power, and 2) sum-rate. In addition, we also maximize the rate of the transmit stream with the worst signal-to-noise ratio. Through extensive numerical evaluations, we demonstrate the superior performance of proposed design over the existing ones, not only with QoS constraints but also without them.

We investigate a joint design of linear precoders and receivers for multiple-input multiple-output non-simultaneous two-way relaying (NS-TWR). Unlike conventional two-way relaying, the base station in NS-TWR performs two-way relaying with two different users-a transmit-only user and a receive-only user (RUE). The RUE experiences back-propagating interference (BI). The proposed design cancels this BI and provides beamforming gain over existing designs. For NS-TWR, we maximize the weighted sum-rate (WSR) through joint power allocation, by solving a sequence of geometric programs. The precoder and the receiver designs as well as the power allocation program are then extended for a multi-user system with multiple transmit-only and receive-only users. With exhaustive simulations, we show that the proposed design provides significantly better WSR than the existing ones. The proposed design is also evaluated in a cellular framework using realistic path loss models, to assess the system-level performance gain achievable.

In conventional two-way relaying (TWR), it is assumed that a user has data to send and receive simultaneously from the base station (BS) via a relay. In cellular systems, data flow between the BS and a user is usually not simultaneous, e.g., a transmit-only user (say, TUE) may have uplink data to send in the multiple access (MAC) phase, but may not have downlink data to receive in the broadcast (BC) phase. Such one-way data flow will reduce TWR to spectrally inefficient one-way relaying. The multiple-input-multiple-output (MIMO) asymmetric TWR (ATWR) protocol considered here restores the two-way data flow via a relay. In ATWR, the BC phase following the MAC phase of a TUE is used to send downlink data to a receive-only user (say, RUE). However, the RUE will not be able to cancel the back-propagating interference. We design a structured precoder at the relay to cancel this interference. The proposed precoder also triangularizes the end-to-end MIMO channels. The channel triangularization reduces the weighted sum-rate maximization and relay power minimization problems to power allocation problems, which are then cast as geometric programs. Simulation results illustrate the effectiveness of the proposed precoder when compared with conventional solutions.

Two-way relaying reduces the loss in spectral efficiency caused in a conventional half-duplex relay due to two channel uses per data unit transmitted to the destination. Two-way relaying is possible when two nodes exchange data simultaneously through a relay. In the case of cellular systems, data exchange between base station (BS) and users (UE) is usually not symmetric, e.g., a user (UE1) might have uplink data to transmit during multiple access (MAC) phase, but might not have downlink data to receive during broadcast (BC) phase. This asymmetry in data exchange will reduce the gains of two-way relaying. In the case of infrastructure relays, where there are multiple users communicating through a relay, we propose that the BC phase following the MAC phase of UE1be used by the relay to transmit downlink data to a second user (UE2). Conventional two-way relaying with symmetric MAC and BC phases must now be modified to asymmetric MAC (BS → RS ← UE1) and BC phases (BS ← RS → UE2), respectively. This will result in UE2not being able to cancel the back-propagating interference in the usual way. We design precoders using conventional zero-forcing and linear minimum-mean-square-error criteria to mitigate the back-propagating interference at UE2for an amplify-and-forward (AF) relay. We also propose a novel precoder appropriate for the asymmetric two-way relaying. The sum-rate performance of the proposed precoder is shown to be better than the conventional precoders.