Closed-form Expressions For Spectral Efficiency Research Articles

Wireless Information and Power Transfer Enabled Massive MIMO Multi-Way Relaying

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.

Cell-Free Massive MIMO With Mixed-Resolution ADCs and I/Q Imbalance Over Rician Spatially Correlated Channels

The practical deployment of cell-free massive multiple-input multiple-output (CF mMIMO), a promising technology empowering the sixth-generation with multitudinous access points (APs). This paper considers a CF mMIMO system over Rician spatially correlated fading channels with the single-antenna user equipments (UEs) and multi-antenna APs, where the phase-shift induced by the UEs' movement exists at the line-of-sight path. Though the low-resolution analog-to-digital converters (ADCs) can effectively address the expensive hardware cost and power-hungry problems, complicated data processing algorithms are of vital importance to be well designed to compensate for the performance gap compared with the real scenarios since the hardware impairments. However, the novel mixed-ADC architecture could solve the above challenges with better performance. So, we investigate the effect of mixed-resolution ADCs deploying at APs and the in-phase and quadrature-phase imbalance (IQI) on the CF mMIMO systems. Furthermore, the achievable uplink spectral efficiency (SE) is analyzed considering IQI and quantization loss based on a two-layer decoding scheme. Moreover, the novel closed-form SE expression with the maximum ratio (MR) combining is derived. And we find the relationship between the SE performance and different combining schemes, quantization bits, and IQI parameters. Finally, the numerical results reveal the mixed-resolution ADCs show a great advantage in boosting the SE performance, and increasing the number of APs is an effective means to promote the system performance.

Broadband Connectivity for Handheld Devices via LEO Satellites: Is Distributed Massive MIMO the Answer?

Significant efforts are being made to integrate satellite and terrestrial networks into a unified wireless network. One major aspect of such an integration is the use of unified user terminals (UTs), which work for both networks and can switch seamlessly between them. However, supporting broadband connectivity for handheld UTs directly from low Earth orbit (LEO) satellite networks is very challenging due to link budget reasons. This paper proposes using distributed massive multiple-input multiple-output (DM-MIMO) techniques to improve the data rates of handheld devices with a view to supporting their broadband connectivity by exploiting the ultra-dense deployment of LEO satellites and high-speed inter-satellite links. In this regard, we discuss DM-MIMO-based satellite networks from different perspectives, including the channel model, network management, and architecture. In addition, we evaluate the performance of such networks theoretically by deriving closed-form expressions for spectral efficiency and using extensive simulations based on actual data from a Starlink constellation. The performance is compared with that of collocated massive MIMO connectivity (CMMC) and single-satellite connectivity (SSC) scenarios. The simulation results validate the analytical results and show the superior performance of DM-MIMO-based techniques compared to CMMC and SSC modes for improving the data rates of individual users.

Uplink Performance of Cell-Free Massive MIMO Over Spatially Correlated Rician Fading Channels

We consider a practical cell-free massive multiple-input-multiple-output (MIMO) system with multi-antenna access points (APs) and spatially correlated Rician fading channels. The significant phase-shift of the line-of-sight component induced by the user equipment movement is modeled randomly. Furthermore, we investigate the uplink spectral efficiency (SE) with maximum ratio (MR)/local minimum mean squared error (L-MMSE) combining and optimal large-scale fading decoding based on the phase-aware MMSE, phase-aware element-wise MMSE and linear MMSE (LMMSE) estimators. Then new closed-form SE expressions with MR combining are derived. Numerical results validate our derived expressions and show that the SE benefits from the spatial correlation. It is important to observe that the performance gap between L-MMSE and MR combining increases with the number of antennas per AP and the SE of the LMMSE estimator is lower than that of other estimators due to the lack of phase-shifts knowledge.

Uplink Channel Estimation With Hardware Imperfections, Antenna Position Error and Channel Correlation for Nested and Linear Array Antennas

In this treatise, we have proposed an uplink channel estimation algorithm for nested and linear array antennas with hardware imperfections, antenna position error, and channel correlation in a multi-cell, multi-user wireless system with a one-ring scattering channel model. Hardware impairments and antenna position errors assume special importance in modern wireless system due to their severe impacts on system performance. With the increase of radio frequency (RF) in the modern wireless system and the subsequent usage of a large number of antennas for beamforming and meeting ever-increasing data rates, those errors are much relevant today. We have considered a sparse nested array (NA) and uniform linear array (ULA) for array geometry at the base station (BS). In this work, closed-form expression and bounds on the mean square error (MSE) of the linear minimum mean square error (LMMSE) channel estimate are derived. We have also analyzed the spectral efficiency (SE) of a simplified system with ULA and NA at the BS, given the model with hardware distortion and antenna position error. Two cases for (a) perfect channel side information (CSI) and (b) estimated channel are evaluated and compared in terms of their SEs, while the closed-form expression for SE with ULA at the BS considering perfect CSI is derived and verified. Numerical simulations are conducted to verify the accuracies of our derived results.

Local Partial Zero-Forcing Precoding for Cell-Free Massive MIMO

Cell-free Massive MIMO (multiple-input multiple-output) is a promising distributed network architecture for 5G-and-beyond systems. It guarantees ubiquitous coverage at high spectral efficiency (SE) by leveraging signal co-processing at multiple access points (APs), aggressive spatial user multiplexing and extraordinary macro-diversity gain. In this study, we propose two distributed precoding schemes, referred to as \textit{local partial zero-forcing} (PZF) and \textit{local protective partial zero-forcing} (PPZF), that further improve the spectral efficiency by providing an adaptable trade-off between interference cancelation and boosting of the desired signal, with no additional front-hauling overhead, and implementable by APs with very few antennas. We derive closed-form expressions for the achievable SE under the assumption of independent Rayleigh fading channel, channel estimation error and pilot contamination. PZF and PPZF can substantially outperform maximum ratio transmission and zero-forcing, and their performance is comparable to that achieved by regularized zero-forcing (RZF), which is a benchmark in the downlink. Importantly, these closed-form expressions can be employed to devise optimal (long-term) power control strategies that are also suitable for RZF, whose closed-form expression for the SE is not available.

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

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.

Adaptive Spatial Modulation over MmWave Channel with UPA

Spatial modulation (SM) utilizes the transmit antenna index and a quadrature amplitude modulation (QAM) symbol chosen from a constellation diagram to improve spectral efficiency (SE) comparing to conventional modulation scheme. However, in the conventional SM system, the modulation mode applied to the active antenna is fixed, which degrades the bits error rates (BER) and spectral efficiency (SE) performance. Moreover, a large number of researches on SM systems focus on the utilization of the uniform linear array (ULA) for transmission, which only considers the transmission on the horizontal domain while ignoring that on the vertical domain. Therefore, in this paper, we propose an adaptive spatial modulation (ASM) scheme with uniform planar array (UPA) over millimeter wave (mmWave) channels, which combines SM with adaptive modulation (AM) to enhance the performance of SE. To further improve the bits error rates (BER) performance, we develop an UPA-based ASM scheme with transmit antenna selection (TAS). We then analyse the BER and SE performance of both the two ASM scheme and obtain the closed-form expression for SE of the UPA-based ASM scheme with TAS algorithm. The simulations demonstrate that the proposed ASM schemes can achieve a considerable SE and a relatively low BER.

Energy Efficiency of the Cell-Free Massive MIMO Uplink With Optimal Uniform Quantization

A cell-free Massive multiple-input multiple-output (MIMO) uplink is considered, where the access points (APs) are connected to a central processing unit (CPU) through limited-capacity wireless microwave links. The quantized version of the weighted signals are available at the CPU, by exploiting the Bussgang decomposition to model the effect of quantization. A closed-form expression for spectral efficiency is derived taking into account the effects of channel estimation error and quantization distortion. The energy efficiency maximization problem is considered with per-user power, backhaul capacity and throughput requirement constraints. To solve this non-convex problem, we decouple the original problem into two sub-problems, namely, receiver filter coefficient design, and power allocation. The receiver filter coefficient design is formulated as a generalized eigenvalue problem whereas a successive convex approximation (SCA) and a heuristic sub-optimal scheme are exploited to convert the power allocation problem into a standard geometric programming (GP) problem. An iterative algorithm is proposed to alternately solve each sub-problem. Complexity analysis and convergence of the proposed schemes are investigated. Numerical results indicate the superiority of the proposed algorithms over the case of equal power allocation.

Uplink Spectral Efficiency Analysis for a Massive MIMO Primary Network

Faster development of smart electronic devices in recent years along with significant increase in demanding higher data rates has made cognitive radio networks (CRNs) to be taken into consideration as a promising technology. A CRN has the ability to increase spectral efficiency (SE) of communication systems by opportunistically using unused spectrums. Furthermore, Massive multiple-input multiple-output is a major candidate to be used in next generation cellular systems in light of its great capabilities to improve system performance from spectral as well as energy efficiency standpoint. In this paper, we propose a CRN whose base station, as well as the primary base station (PBS) are equipped with large numbers of antennas. We derive closed-form expressions for SE in the uplink of primary users for three different scenarios. In these scenarios perfect and imperfect channel state information are considered separately. In addition, the impact of pilot contamination due to the correlation among users’ pilot signals on sum SE of primary network is examined. For the first two scenarios, minimum number of antennas (MNA) at the PBS to achieve a specified SE is derived in a closed-form expression. MNA is analyzed numerically for the third scenario.

Threshold-Based Substream Selection for Closed-Loop Spatial Multiplexing

We propose a low-complexity closed-loop spatial multiplexing method with limited feedback over multi-input-multi-output (MIMO) fading channels. The transmit adaptation is simply performed by selecting transmit antennas (or substreams) by comparing their signal-to-noise ratios to a given threshold with a fixed nonadaptive constellation and fixed transmit power per substream. We analyze the performance of the proposed system by deriving closed-form expressions for spectral efficiency, average transmit power, and bit error rate (BER). Depending on practical system design constraints, the threshold is chosen to maximize the spectral efficiency (or minimize the average BER) subject to average transmit power and average BER (or spectral efficiency) constraints, respectively. We present numerical and Monte Carlo simulation results that validate our analysis. Compared to open-loop spatial multiplexing and other approaches that select the best antenna subset in spatial multiplexing, the numerical results illustrate that the proposed technique obtains significant power gains for the same BER and spectral efficiency. We also provide numerical results that show improvement over rate-adaptive orthogonal space-time block coding, which requires highly complex constellation adaptation. We analyze the impact of feedback delay using analytical and Monte Carlo approaches. The proposed approach is arguably the simplest possible adaptive spatial multiplexing system from an implementation point of view. However, our approach and analysis can be extended to other systems using multiple constellations and power levels.

Comparison of adaptive beamforming and orthogonal STBC with outdated feedback

We compare the achievable performance of adaptive beamforming (A-BF) and adaptive orthogonal space time block coding (A-OSTBC) with outdated channel feedback. We extend our single user setup to multiuser diversity systems employing adaptive modulation, and illustrate the impact of feedback delay on the multiuser diversity gain with either A-OSTBC or A-BF. Using closed-form expressions for spectral efficiency and average BER of a multiuser diversity system derived in this paper, we prove that the A-BF scheme outperforms the A-OSTBC scheme with no feedback delay. However, when the feedback delay is large, the A-OSTBC scheme achieves better performance due to the reduced diversity advantage of A-BF. We observe that more transmit antennas bring higher spectral efficiency for BF. With small feedback delay, this becomes inverted using OSTBC, due to the effect of channel-hardening. Interestingly, however, we show that A-OSTBC with multiple users enjoys improved spectral efficiency when the number of transmit antennas is increased and the feedback delay is significant