We propose low-complexity long-term two-stage beamforming techniques for uplink distributed MU-MIMO systems. Stage one involves analog (A) or digital (D) maximal ratio combining (MRC), followed by long-term decoding (LT) in stage two, denoted as A-LT and D-LT. We derive an approximate expected signal-to-interference-plus-noise-ratio (SINR) for A-LT and D-LT, considering correlation, channel estimation errors, and various base station layouts. These novel analytical results can be used to evaluate the performance of wireless communication systems under different scenarios without the need for extensive simulations or experiments. Our findings indicate that as the number of antennas increases, the performance gap between ALT, D-LT, and A-D, D-D diminishes. A-D and D-D necessitate accurate channel state information (CSI), while A-LT and DLT solely rely on channel statistics, significantly alleviating the channel estimation overhead. This suggests that A-LT and DLT show promise for scalable, cost-effective massive distributed MU-MIMO systems.

In this paper, we derive an exact mean SNR expression for the optimal single user Reconfigurable Intelligent Surface (RIS) design in the presence of imperfect channel state information (CSI). It is assumed that the user (UE)-RIS and UE- base station (BS) channels experience correlated Rayleigh fading and the RIS-BS link is line of sight (LOS). We present simplified versions of the derived mean SNR expression for the correlation extremes (no correlation and full correlation) in the UE-RIS and UE-BS channels. The derived mean SNR expression is then leveraged to analytically characterise the impact of error variances from the channel estimation process on the mean SNR. We show that as the error variances increase, the mean SNR expression reduces to that of a system with randomly selected RIS phases. Consequently, the growth in mean SNR reduces from$\mathcal {O}(N^{2}) $to$ \mathcal {O}(N)$. Numerical results validate the analysis.

In this paper we focus on phase dependent loss (PDL), an important aspect of reconfigurable intelligent surfaces (RIS) where the signals reflected from the RIS elements are attenuated by varying amounts depending on the phase rotation provided by the element. To evaluate the effects of PDL, we analyse the SNR of a SIMO RIS-aided wireless link. We assume that the channel between the base station (BS) and RIS is a rank-1 LOS channel, while the user (UE)-BS and UE-RIS are correlated Rayleigh channels. The RIS design is optimal in the absence of PDL and maximizes the SNR in this scenario. Specifically, we derive an exact expression for the mean SNR in the presence of PDL. The attenuation function used for PDL was developed from a detailed circuit analysis of RIS elements. Leveraging the derived results, we analytically characterise the impact of PDL on the mean SNR. Numerical results are conducted to validate the derived expressions and verify the analysis.

The objective of this paper is to develop simple techniques to bound the optimal uplink sum-rate of multi-user RIS-aided wireless systems. Specifically, we develop a novel technique called channel separation which provides a new understanding as to how the RIS phases affect the sum-rate. Leveraging channel separation, we derive upper and lower bounds on the optimal sum-rate. In addition, we propose a low-complexity alternating optimization algorithm to obtain near-optimal sum-rate results. Numerical results demonstrate the tightness of the bounds and show that the alternating optimization approach delivers sum-rate values similar to the results of a full numerical optimization procedure. Furthermore, in practical scenarios where hardware limitations cause the RIS phases to be quantized, our lower bound can still be applied and shows that the sum-rate is robust to quantization, even with low resolution.

We present an analysis of the optimal SNR of a SIMO Reconfigurable Intelligent Surface (RIS)-aided wireless link. We assume that the channel between base station (BS) and RIS is a rank-1 LOS channel while the user (UE)-RIS and UE-BS channels are correlated Ricean. For the optimal RIS matrix, which maximizes the SNR, we derive an exact closed form expression for the mean SNR and an approximation for the SNR variance leading to an accurate gamma approximation to the distribution of the SNR. Using the gamma distribution to approximate the SNR, we derive expressions for the mean rate and outage rate. Furthermore, we analytically characterise the effects of correlation and the Ricean K-factor on SNR, showing that increasing the K-factor and correlation in the UE-BS channel can have negative effects on the mean SNR, while increasing the K-factor and correlation in the UE-RIS channel improves system performance. We also present favourable and unfavourable channel scenarios which provide insight into the sort of environments that improve or degrade the mean SNR. We also show that the relative gain in the mean SNR when transitioning from an unfavourable to a favourable environment saturates to$(4-\pi)/\pi $as$N \rightarrow \infty $.

We propose a two-stage channel estimation procedure for a multi-antenna base station (BS) assisted by a reconfigurable intelligent surface (RIS). In Stage 1, the BS estimates the direct link from the user to BS and the UE-to-RIS link using partial knowledge of the RIS-to-BS channel. To reduce pilot overhead, the UE-to-RIS channel state information (CSI) is interpolated from channel estimates for a subset of active RIS elements. CSI obtained in Stage 1 is then used to inform the RIS phase design and form an initial estimate of the global channel, which is refined with more pilot symbols in Stage 2 and subsequently used to perform uplink processing during data transmission. We examine the normalised mean squared error of the global channel estimate from Stage 1 under various channel conditions, and the spectral efficiency (SE) following Stage 2. Using physically-motivated models, we are able to study the impact of ray angular spread, RIS size, and inter-element spacing on the global channel estimation accuracy, and reveal the detrimental effect of errors in the RIS-to-BS channel knowledge. The SE following Stage 2 approaches the performance achieved with perfect CSI, revealing the greater importance of CSI accuracy for processing as opposed to RIS design.

In this paper, we present an analysis of the optimal uplink SNR of a SIMO Reconfigurable Intelligent Surface (RIS)-aided wireless link. We assume that the channel between base station and RIS is a rank-1 LOS channel while the user (UE)-RIS and UE-base station (BS) channels are correlated Rayleigh. We derive an exact closed form expression for the mean SNR and an approximation for the SNR variance leading to an accurate gamma approximation to the distribution of the UL SNR. Furthermore, we analytically characterise the effects of correlation on SNR, showing that correlation in the UE-BS channel can have negative effects on the mean SNR, while correlation in the UE-RIS channel improves system performance. For systems with a large number of RIS elements, correlation in the UE-RIS channel can cause an increase in the mean SNR of up to 27.32% relative to an uncorrelated channel.

Massive multiple-input multiple-output (MIMO) has gained a tremendous amount of attention as a key enabler of fifth-generation cellular systems. The majority of the vast literature on massive MIMO is based on fully digital processing, where each antenna element in the massive array is equipped with an up/down-conversion chain. Unlike previous works, we present a suite of greedy algorithms using pure analog processing which approach the performance of uplink digital zero-forcing (ZF) combining. Based on successive nulling and amplification processing (SNAP), the proposed techniques are evaluated in a multi-user context over a range of heterogeneous channel models. Rigorous comparisons are then made to other benchmark analog techniques, digital ZF and an upper bound on analog processing. The most promising approach is shown to have very low-complexity and robustness against a variety of channel conditions, while providing useful performance gains.

We present a flexible family of 3D mobility models suitable for unmanned aerial vehicles (UAV). Based on stochastic differential equations, the models offer a unique property of explicitly incorporating the mobility control mechanism and environmental perturbation, while enabling tractable steady state solutions for properties such as position and connectivity. Specifically, motivated by UAV flight data, for a symmetric mobility model with an arbitrary control mechanism, we derive the steady state distribution of the distance from the target position. We provide closed form expressions for the special cases of the Ornstein-Uhlenbeck (OU) process and on-off control (OC). We extend the model to incorporate imperfect positioning and asymmetric control. For a practically relevant scenario of partial symmetry (such as in the x-y plane), we present steady state position results for the OU control. Building on these results, we derive UAV connectivity probability results based on a SNR criterion in a Rayleigh fading environment.

We examine the favorable propagation (FP) behavior of a massive multi-user multiple-input-multiple-output (MU-MIMO) system equipped with a uniform linear array (ULA), horizontal uniform rectangular array (HURA) or uniform circular array (UCA) using a ray-based channel model with user cluster sharing. We demonstrate FP for these systems and provide analytical expressions for the mean-squared distance (MSD) of the FP metric from its large-system limit for each of the aforementioned topologies. We use these results to examine the detrimental effects of user cluster sharing on FP behavior, and demonstrate the superior performance of the ULA as compared to the UCA and the HURA with equal inter-element spacing. Although cluster sharing has a negative impact on FP for finite arrays, we additionally examine the asymptotic rate of convergence to FP as a function of array size and show that this rate is unchanged with or without user cluster sharing.

Favorable propagation (FP) and channel hardening (CH) are desired properties in massive multiple-input multiple-output (MIMO) systems. To date, these properties have primarily been analyzed for classical statistical channel models, or ray-based models with very specific angular parameters and distributions. This paper presents a thorough mathematical analysis of the asymptotic system behavior for ray-based channels with arbitrary ray distributions, and considers two types of antenna array structures at the cellular base station: a uniform linear array (ULA) and a uniform planar array (UPA). In addition to FP and channel hardening, we analyze the large system potential (LSP) which measures the asymptotic ratio of the expected power in the desired channel to the expected total interference power when both the antenna and user numbers grow. LSP is said to hold when this ratio converges to a positive constant. The results demonstrate that while FP is guaranteed in ray-based channels, CH may or may not occur depending on the nature of the model. Furthermore, we demonstrate that LSP will not normally hold as the expected interference power grows logarithmically for both ULAs and UPAs relative to the power in the desired channel as the system size increases. Nevertheless, we identify some fundamental and attractive properties of massive MIMO in this limiting regime.

The energy detector and the sphericity test are two widely used spectrum sensing techniques that utilize different properties of the signal received at the secondary user terminal. In this paper we use meta analysis to combine these two techniques and derive two novel mixture detectors that outperform both techniques. Since the spectrum sensing capability of the energy detector is limited by the uncertain knowledge of the noise power, first, we analyze the performance of the energy detector with estimated noise power. We derive analytical expressions for the false alarm and the detection probabilities when the secondary user terminal is equipped with multiple antennas. Next, we apply meta analysis to combine the outputs of the energy detector and the sphericity test to derive two mixture detectors, namely, Fisher's method and the weighted z-transform method. Furthermore, we extend our analysis to consider cooperative spectrum sensing where multiple secondary user terminals cooperatively detect the presence of primary users. Based on the mixture detectors, we propose two new cooperative spectrum sensing techniques and derive simple analytical expressions for false alarm probabilities. Extensive numerical examples are used to illustrate the accuracy of our analysis and to highlight the performance gains obtained by the mixture detectors.

Favorable propagation (FP) and channel hardening are desired properties in massive multiple-input and multiple-output (MIMO) systems, where nearly optimal performance is achieved with linear processing techniques, such as maximal-ratio combining. To date, these properties have primarily been analyzed for statistical channel models, or ray-based models with very specific angular parameters and distributions. This paper presents a thorough mathematical analysis of the asymptotic system behavior for ray-based channels with arbitrary ray distributions and a uniform linear array at the base station. In addition to FP and channel hardening, we analyze the large system potential (LSP) which measures the asymptotic signal-to-interference ratio when both the antenna and user numbers grow at an equal rate. The results demonstrate that while FP is guaranteed in ray-based channels, channel hardening may or may not occur depending on the nature of the model. Furthermore, we demonstrate that LSP will not normally hold as the interference power grows logarithmically relative to the signal as the array size increases. Nevertheless, we identify some fundamental and attractive properties of massive MIMO in this limiting regime.

The performance of linear multi-user multiple-input multiple-output (MU-MIMO) systems has been extensively studied for classical statistical channel models. In contrast, there is little analysis for ray-based models, which are physically motivated, feature prominently in standards and have been experimentally validated. Thus, we present a novel analytical framework for zero forcing (ZF) and maximal ratio combining (MRC) applicable to such models. Specifically, using a central result for averaging in the angular domain, we derive accurate expressions for ZF signal-to-noise ratio and MRC signal, interference and noise powers. The remarkably simple expressions offer the following insights into the effects of the propagation environment. While ZF is robust to parameters such as cluster and subray angular spreads, MRC interference is highly sensitive to them. We show that the performance scales linearly with the number of antennas, and that it degrades with narrow angular spreads and as the propagation moves toward the antenna end-fire. Finally, by evaluating the variance of the MRC interference, we observe that an approximation to the MRC SINR widely used for classical statistical models, is inaccurate in ray-based channels.

We consider spectrum sensing in a cognitive radio network with arbitrary numbers of primary and secondary users. Based on the sphericity test, we first analyze the centralized spectrum sensing where all the data available at the secondary users are combined for the signal detection of primary users. We derive accurate approximations for the false alarm and detection probabilities that are also compared against the approximations already available in the literature. Next, we analyze the distributed spectrum sensing where only partial data from each secondary user are used in the signal detection of primary users. Two novel techniques, namely, the multisample sphericity test and metaanalysis, are proposed and analyzed. Instead of sending all the raw data received at the secondary user terminals, in the multisample sphericity test and metaanalysis, only one or two real numbers are required to be sent to a central processor to make a decision about the presence of primary users. Accurate analytical expressions on the false alarm and detection probabilities are derived, and numerical examples are provided to verify their accuracy. Receiver operating characteristic curves are also presented to compare the performance of the proposed methods.

We consider a massive multiple-input multiple- output system with minimum-mean-squared-error processing on the uplink. A novel analytical framework is proposed to approximate the instantaneous signal-to-interference-plus-noise- ratio (SINR) of an arbitrary user terminal, as well as, the system sum spectral efficiency. Unlike previous studies, our methodology considers spatially correlated Ricean fading, with unequal Ricean K-factors, spatial correlation matrices and link gains across all terminals. Under this fully heterogeneous setting, we demonstrate that the SINR of a terminal can be tightly approximated by a linear combination of non-central chi-squared random variables, where the scaling depends on the individual link gains, K-factors, and eigenvalues of the terminal specific correlation matrices. Our approximations remain tight across the considered spatial correlation models, K-factor models, average uplink signal-to-noise-ratios and number of receive antennas. Leveraging the general form of the SINR and sum spectral efficiency, an analytical method to approximate their statistical moments is presented utilizing the moment generating function. The generality of the aforementioned analytical results is demonstrated via several special cases of practical relevance.

Spatial correlation across an antenna array is known to be detrimental to the terminal signal-to- interference-plus-noise-ratio (SINR) and system spectral efficiency. For a downlink multiuser multiple-input multiple-output system (MU-MIMO), we show that the widely used, yet overly simplified, correlation models which generate fixed correlation patterns for all terminals tend to underestimate the system performance. This is in contrast to more sophisticated, yet physically motivated, remote scattering models that generate variations in the correlation structure across multiple terminals. The remote scattering models are parameterized with measured data from a recent 2.53 GHz urban macrocellular channel measurement campaign in Cologne, Germany. Assuming spatially correlated Ricean fading, with maximum-ratio transmission precoding, tight closed-form approximations to the expected (average) SINR, and ergodic sum spectral efficiency are derived. The expressions provide clear insights into the impact of variable correlation patterns on the above performance metrics. Our results demonstrate the sensitivity of the MU-MIMO performance to different correlation models, and provide a cautionary tale of its impact.

Millimeter-wave channel models are fundamental for evaluating the performance of technologies for 5G. In this paper, we present two kinds of millimeter-wave channel measurements, fixed point measurements and virtual measurements, in an indoor open office. A correlation sounder with a bandwidth of 600 MHz is used to carry out these measurements. Then, channel parameters, e.g., the path loss, shadow fading, root mean square (RMS) delay spread (DS), K-factor, delay-cluster number and angular spread, are extracted and modelled. These extracted models will enable the generation of an impulse response for the indoor hotspot environment. Differences between our measurement-based channel model parameters and the International Telecommunication Union (ITU) channel model are discussed. The impact of differences on capacity are investigated by simulations. We find that the ITU channel model is optimistic about capacity. These results can help researchers to use millimeter-wave channel models for indoor office scenarios when evaluating 5G performance.

We consider distributed spectrum sensing in cognitive radio networks with multiple primary and secondary user terminals. Two novel techniques based on the sphericity test, namely, the multisample sphericity test and meta analysis, are analysed in such a scenario. Instead of sending all the raw data received at the secondary user terminals, as in the case with centralized spectrum sensing, in the multisample sphericity and meta analysis tests only one or two real numbers are required to be sent to the central processor to make a decision about the presence of primary users. Accurate analytical expressions on the false alarm probability are derived for both techniques and numerical examples are provided to verify their accuracy. Receiver operating characteristic (ROC) curves are also presented to compare the performance of the proposed methods and other simple fusion techniques.

There has been a rejuvenated interest in the use of non-equally spaced (irregular) constellations after promising performance results were demonstrated compared with the conventional lattice constellations. This paper investigates the use of the irregular constellations in convolutionally coded systems. To enable the use of such irregular constellations in the presence of convolutional encoders, we derive a bit-error-rate (BER) upper bound expression for the downlink of the coded transmit maximum ratio combining systems operating in Nakagami-m fading environments. In addition, the analysis is extended to turbo trellis-coded modulation scenarios in which the convolutional encoders are used as the constituent codes. We demonstrate, via simulation, that commonly used performance analysis techniques in the literature fail to provide a valid BER bound in coded cases where quasi-regularity is not satisfied. In contrast, the technique proposed herein does not require the chosen pair of constellation and encoder to be quasi-regular. Furthermore, the system model includes a provision for multiple orthogonal transmission stages with different numbers of transmit antennas. Antenna correlation as well as distributed transmission is also supported by the model. Simulation results demonstrate the accuracy of the derived analytical results for a wide range of system scenarios.

Closed-form approximations to the expected perterminal signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency of a large multiuser multiple-input multiple-output system are presented. Our analysis assumes correlated Ricean fading with maximum ratio combining on the uplink, where the base station (BS) is equipped with a uniform linear array (ULA) with physical size restrictions. Unlike previous studies, our model caters for the presence of unequal correlation matrices and unequal Rice factors for each terminal. As the number of BS antennas grows without bound, with a finite number of terminals, we derive the limiting expected perterminal SINR and ergodic sum spectral efficiency of the system. Our findings suggest that with restrictions on the size of the ULA, the expected SINR saturates with increasing operating signal-to-noise-ratio (SNR) and BS antennas. Whilst unequal correlation matrices result in higher performance, the presence of strong line-of-sight (LoS) has an opposite effect. Our analysis accommodates changes in system dimensions, SNR, LoS levels, spatial correlation levels and variations in fixed physical spacings of the BS array.

Results of recent measurement campaigns demonstrate a significant increase in the degrees of freedom introduced by the elevation domain, and consequently, a large capacity gap as predicted by 3D and 2D MIMO channel models. To gain further insight into the effects of the elevation domain on MIMO system performance, we derive new spatial correlation (SC) expressions for 3D and 2D channel models, given rectangular arrays of cross-polarized antennas. The main result relates 3D SC to the 2D counterpart, allowing us to quantify the effects of the elevation domain on SC. Furthermore, our result allows us to derive the following three simple relationships between 2D and 3D correlations. We show that for a small elevation angle spread, the difference between 2D and 3D SCs grows quadratically in both vertical separation and angle spread. For the case of small vertical spacings, we derive a bound on the above correlation gap. Furthermore, we show that the elevation effects on correlation can be accurately decoupled, allowing us to express the 3D SC matrix as a Hadamard product of a 2D SC matrix and an elevation component. Collectively, our results demonstrate the need for accurate channel modeling when evaluating the performance of 3D MIMO systems.

The range of candidate bands considered for 5G wireless systems extends from 6-100 GHz. In this paper we examine the impact of key parameters of millimeter-wave (mmWave) and microwave channel models on various system performance metrics, e.g., spectral efficiency, eigenvalue structure and convergence to massive multiple-input multiple-output (MIMO) properties. We consider 6 spatial channel model (SCM) based scenarios, including 3GPP SCM at 2.6 GHz and those derived from recent measurement campaigns at 6 GHz, 28 GHz and 73 GHz. We define and evaluate an effective degrees of freedom metric (EDOF), demonstrating a dramatic EDOF reduction in mmWave bands compared to microwave, unless serving multiple users, where the antenna separation increases the effective rank of the composite channel. Furthermore, we analytically derive the covariance matrix of two SCM structures showing the impact of modelling choice on the channel correlations.

General analysis of expected per-terminal signal-to-interference-plus-noise-ratio (SINR) and ergodic per-cell sum spectral efficiency for a multi-cellular system with coordinated regularized zero-forcing (RZF) precoding is presented. An application to two-tier small-cell networks is considered, assuming independent and identically distributed (i.i.d.) and semi-correlated Rayleigh fading channels, with spatial correlation at the base station. Our analysis caters for equal and unequal correlation matrices for each terminal. For the i.i.d. case and when each terminal is assigned an equal correlation matrix, our expressions are averaged over the eigenvalue densities of the channel correlation matrices, which follow an uncorrelated and correlated complex central Wishart distribution. With unequal correlation matrices, we exploit the high signal-to-noise-ratio (SNR) convergence of RZF precoding to zero-forcing (ZF) precoding and use a second-order Neumann series expansion to derive closed-form approximations to the expected RZF SINR and ergodic sum spectral efficiency, via the expected ZF SNR and ergodic sum spectral efficiency. Our numerical results show the adverse effects of intercellular interference, along with the improvements in the above-mentioned performance metrics with network-wide coordination over cell-wide and macro-only coordination strategies. The derived expressions are robust to changes in system dimensions, operating SNRs, and correlation levels.

A general framework for the analysis of expected per-user signal-to-interference-plus-noise-ratio (SINR) of a multiuser multiple-input-multiple-output system is presented. Our analysis assumes spatially correlated Rayleigh fading channels with regularized zero-forcing precoding on the downlink. Unlike previous works, our analytical expressions are averaged over the eigenvalue densities of the complex Wishart distributed channel correlation matrix. To aid the derivation of the expected per-user SINR, we derive a closed-form expression for the joint density of two arbitrary eigenvalues of the complex Wishart matrix. In the high signal-to-noise-ratio (SNR) regime, with zero-forcing precoding, we derive analytical expressions to approximate the instantaneous per-user SNR and show that it is approximately gamma distributed. The generality of the approximations is validated with numerical results over a wide range of system dimensions, spatial correlation and SNR levels.

Analytical expressions to approximate the expected per-user signal-to-interference-plus-noise-ratio (SINR) and ergodic sum-rate of a multiuser multiple-input-multiple-output system are presented. Our analysis assumes uncorrelated Ricean fading channels with regularized zero-forcing precoding on the downlink. The derived expressions are averaged with respect to the previously unknown arbitrary eigenvalue densities of the complex non-central Wishart distributed channel correlation matrix. To aid the derivation of the expected SINR, we derive analytical expressions for the joint density of two arbitrary eigenvalues of the complex non-central Wishart matrix. Unlike previous studies, our model caters to the presence of a unique Rice factor for each user terminal, making it suitable for analysis of modern systems, such as small cells and millimeter-wave. Our findings suggest that while the presence of strong line-of-sight has an adverse effect on the expected SINR and ergodic sum-rates, increasing the variability of Rice factors enhances the peak rate performance of the system. Our analysis can be applied to arbitrary system dimensions and is seen to remain tight across the signal-to-noise-ratio range considered.

There has been a rejuvenated interest in the use of arbitrary constellations (non-equally spaced) after promising performance results were demonstrated compared to conventional grid and circular constellations. To enable the development of such constellations, in this contribution we derive an upper bound bit-error-rate (BER) expressions for coded transmit maximum ratio combining (TMRC) systems operating in Nakagami-\textit{m} fading environments with arbitrary constellations and encoder types. Unlike most existing works on error performance analysis for coded systems, a chosen pair of constellation and encoder need not be quasi-regular. Furthermore, the system model includes a provision for multiple orthogonal transmission phases with different number of transmit antennas. Simulation results demonstrate the accuracy of the derived analytical results for a range of system scenarios.

In this study, the authors investigate the impact of cooperation in an interference limited downlink cellular network. The authors identify the areas in which the transmissions of adjacent cells overlap in a 19 cell network for urban and suburban environments. They assume that the cooperative users are located in these overlapping areas and thus can receive channel information from neighbouring base stations (BSs) to cancel intercell interference. They also study the performance of such systems with various types of precoding techniques. They demonstrate that they can improve the system performance employing precoders that maximise signal‐to‐leakage‐noise ratios for each user. They also consider imperfect cross channel state information (CCSI) between cooperative users and interfering BSs. Furthermore, they analytically derive the additional intercell interference that is caused by imperfect CCSI at the receivers. The results demonstrate that the system can achieve better sum rates with cooperation, however this improvement is susceptible to the accuracy of the CCSI. They show that imperfect CCSI degrades the cooperation gains drastically.

Approximate expressions for the spatial correlation of cylindrical and uniform rectangular arrays (URA) are derived using measured distributions of angles of departure (AOD) for both the azimuth and zenith domains. We examine massive multiple-input-multiple-output (MIMO) convergence properties of the correlated channels by considering a number of convergence metrics. The per-user matched filter (MF) signal-to-interference-plus-noise ratio (SINR) performance and convergence rate, to respective limiting values, of the two antenna topologies is also explored.

We present the results of a 3 dimensional (3D) multiple-input multiple-output (MIMO) channel impulse response (CIR) measurement conducted in China and New Zealand (NZ) for an outdoor-to-indoor (O2I) urban macro environment. Key channel parameters are computed from the measured data using the space-alternating generalized expectation-maximization (SAGE) algorithm, and are used to re-construct the 16 × 16 3D MIMO CIR according to the guidelines given in the 3GPP 3D MIMO channel model. The CIR is then used to evaluate the channel capacity for four different antenna configurations. These different topologies, along with different antenna spacings, allow us to study the characteristics of the MIMO channel with different spatial correlation structures.

We investigate the prediction of wideband MIMO spatial channels. We propose a two-stage long range parametric prediction scheme that exploits the temporal, spatial and frequency correlations in a realistic cluster based fading channel. The proposed scheme utilizes the frequency correlation in an ESPRIT-like approach to estimate the cluster delays and scattering coefficients. The spatial and temporal correlations are then used to jointly estimate the angles of arrival, angles of departure and Doppler shifts via a 3D ESPRIT algorithm. Simulation results using the standardized 3GPP/WINNER II spatial channel model show that the proposed algorithm offers improved prediction performance over previous methods and can achieve longer prediction range.

In this paper we examine convergence properties of massive MIMO systems with the aim of determining the number of antennas required for massive MIMO gains. We consider three characteristics of a channel matrix and study their asymptotic behaviour. Furthermore, we derive ZF SNR and MF SINR for a scenario of unequal receive powers. In our results we include the effects of spatial correlation. We show that the rate of convergence of channel metrics is much slower than that of the ZF/MF precoder properties.

We propose a novel combined receiver which applies zero forcing (ZF) to null the dominant interferers, followed by minimum-mean-square-error (MMSE) processing to reduce the effect of the remaining interference and noise. The receiver is used in conjunction with an interference alignment (IA) scheme in a multicell environment. Simulation results considering a range of interferer profiles show that the combined receiver outperforms an MMSE receiver, due to its ability to eliminate the dominant interferers. The complete nulling of many dominant interferers in a multi-user, multicell case requires a large number of receive antennas. If the antennas are closely located in a compact array, then spatial correlation is important and its impact on the IA scheme is also considered.

A novel prediction scheme for polarized narrowband MIMO channels is proposed in this paper. The prediction scheme is based on estimation of the parameters of a double directional polarized propagation model. The proposed algorithm transforms the channel impulse response matrix in such a manner that a multidimensional extension of the ESPRIT algorithm can be utilized to jointly estimate the angles of arrival, angles of departure, Doppler shifts and complex polarimetric weights of the dominant multipath components. Simulation results show that the proposed algorithm outperforms repeated application of one dimensional ESPRIT based approach with similar computational complexity.

In this letter, we derive simple expressions for the lower bound on the prediction error variance for narrowband MIMO channel with uniform linear array at both ends of the link. The derived bounds show the relationship between the achievable prediction performance and prediction algorithm design parameters, thereby providing useful insights into the development of fading channel prediction algorithms.

We consider a cognitive radio (CR) relay network consisting of a cognitive source, a cognitive destination and a number of cognitive relay nodes that share spectrum with a primary transmitter and receiver. Due to poor channel conditions, the cognitive source is unable to communicate directly with the cognitive destination and hence employs the cognitive relays for assistance. We assume that perfect channel state information (CSI) for all links is not available to the CR. Under the assumption of partial and imperfect CSI at the CR system, we propose new robust CR cooperative relay beamformers where either the total relay transmit power or the cognitive destination signal-to-interference-and-noise ratio (SINR) is optimized subject to a constraint on the primary receiver outage probability. We formulate the robust total relay power minimisation and the cognitive destination SINR maximisation optimisation problems as a convex second order cone program and a semidefinite program, respectively. Cumulative distribution functions of primary receiver and cognitive destination receiver SINR for Rayleigh fading channels are presented.

In multi-antenna systems the use of multiple antennas at one end or both ends of the link produces multiple channels. A useful, although ill-defined, metric for such a link is the number of independent channels provided. In this paper, we discuss several candidate metrics and compare their utility in the Rayleigh fading, single-input multiple-output case. We show that most of the metrics available in the literature have limitations and can exhibit non-physical behaviour. In order to improve on their performance, we develop two novel measures for the number of independent channels based on the statistical construction of the channel and channel capacity. These two measures are then extended to multiple-input multiple-output systems, Rician channels and arbitrary channel models.

In this paper, we present a differential codebook design by modifying the Grassmannian codebook for a single-cell multiuser (MU) multiple-input single-output (MISO) system operating under spatially and temporally correlated channels. The differential codebook design involves scaling and rotation methods that help a codebook to track the slow varying channel. We propose an adaptive scaling technique that improves the performance of the system in correlated channels without any additional feedback information. Monte Carlo simulations show that the proposed differential codebook reduces quantization errors and improves sum-rate performance as compared to other differential codebooks designed for spatially and temporally correlated MISO channels.

We consider a cognitive radio (CR) relay network consisting of a cognitive source, a cognitive destination and a number of cognitive relay nodes that share spectrum with a primary transmitter and receiver. Due to poor channel conditions, the cognitive source is unable to communicate directly with the cognitive destination and hence employs the cognitive relays for assistance. We assume that the CR has a very loose cooperation with the primary network and therefore, only partial channel state information is available. Under these assumptions, we propose a new statistically robust CR cooperative relay beamformer where either the total relay transmit power or the cognitive destination signal-to-interference-and-noise ratio (SINR) is optimised subject to primary receiver outage probability constraint. We formulate the robust total relay power and the cognitive destination SINR optimisation problems as a convex second order cone program and a convex feasibility problem, respectively, that provide near optimum results. We also present efficient iterative algorithms that provide the optimum results.

We investigate the efficiency of interference alignment for 2 × 2 × 2 interference networks formed by concatenation of two user interference channels under the assumption of imperfect channel state information. We show that, as a result of cumulative noise in zero forcing receivers, aligned interference neutralisation is not practical when perfect channel state information is not available. We give analytical SNR and SINR expressions at relays and receivers and also provide some simulation results using a channel estimation error model.

In this paper, we propose an ESPRIT-based parametric prediction scheme for narrowband MIMO systems that fully exploits both temporal and spatial correlations in realistic MIMO channels. The proposed predictor uses a vector transmit spatial signature model and two-dimensional ESPRIT for the estimation of the channel parameters. The proposed scheme outperforms existing algorithms and is well suited to both two dimensional azimuth only and three dimensional MIMO spatial channel models.

The author presents the design and analysis of low‐complexity symbol timing error detectors (TEDs) for timing synchronisation in quasi‐orthogonal space–time block code (QOSTBC) receivers. The estimators operate on data symbols and approximate decision variables, producing timing error measurements which are shown to be robust to channel fading. In evaluating the detector S‐curve for the general form of the estimator, the author shows that the result is independent of the constellation rotation angle employed by the code. The expressions for the estimation error variance and TED signal‐to‐noise ratio are also obtained, with the analysis carried out under the assumptions of perfect data and channel knowledge at the receiver. Through system simulations, the effects of decision errors on the detector characteristics are examined, and the overall system performance is evaluated, where the proposed TEDs are incorporated into the receiver timing loop. Receivers with perfect channel knowledge and pilot‐based channel estimation are considered. Symbol error rate results show timing synchronisation loss of less than 0.5 dB for a receiver with perfect channel information. In addition, it is shown that the receiver is able to track the timing variations two orders of magnitude faster than required by the present‐day hardware oscillators.

Interference modeling is central to the analysis of many interference limited systems. The aggregate interference due to many individual interferers is often very difficult to characterize exactly, especially when lognormal shadowing and path loss is considered. Some results are available for homogeneous sources where the individual components have the same distribution, but many more detailed studies involve heterogeneous sources. Hence, in this paper we build upon previous models for homogeneous sources to develop three general purpose approaches to modeling the aggregate interference from heterogeneous sources which include both shadowing and path-loss. These models are the inverse gamma, inverse generalized gamma and extreme value distributions. These models are motivated by prior work as well as by three distinct interference scenarios relating to cognitive radio systems, digital television and femtocells. The models are fitted to these wide ranging examples and numerical results show good agreement, both for interference and SINR distributions.

We consider a cognitive radio system with N secondary user (SU) pairs and a pair of primary users (PU). The SU power allocation problem is formulated as a rate maximisation problem under PU and SU quality of service and SU peak power constraints. We show our problem formulation is a geometric program and can be solved with convex optimisation techniques. We examine the effect of PU transmissions in our formulations. Solutions for both low and high signal-to-interference-and-noise ratio (SINR) scenarios are provided. We show that including the PU rate in the optimisation problem leads to increased PU performance while not significantly degrading SU rate. Achievable rate cumulative distribution functions for various Rayleigh fading channels are produced.

In this paper, we evaluate the capacity gains offered by MIMO systems relative to SISO by using two metrics: the ratio between the expected value of the two capacities and a weighted difference between the two capacities. We present results for these metrics for the case of a general channel, where fading could be iid, correlated Rayleigh, or any other type. We derive limiting values of the capacity metrics for low and high SNR and show via simulation their behavior at other values of SNR. These simulations provide valuable insight into the variation of the capacity metrics in the important SNR range from -5 dB to 20 dB which is commonly observed in cellular systems.

We investigate the performance of femto cell networks in both closed and open access regimes. Specifically, we analyse the typical user capacity as well as the sum capacity of all users in a macro cell with a Poisson field of femto base stations. The closed access results demonstrate that while the system sum capacity initially increases with the density of femto cells, this gain comes with a significant performance penalty suffered by an individual macro user. In open access mode, we show via analytical derivations that macro users only benefit from access to the available femto base stations for impractically high densities. Furthermore, we derive limiting sum capacity results showing that while the mean sum capacity initially increases linearly with femto density, sum capacity will eventually decay to zero in the limiting case as the femto density approaches infinity.

In limited feedback multiple-input multiple-output (MIMO) systems, it is important that the codebooks used provide a good approximation to the channel. Any mismatch between the codebook entries and the actual channel creates a non zero chordal distance (or subspace angle) between the codebook element and the corresponding columns of the right singular matrix of the channel. As a result, the system exhibits a capacity loss. We evaluate and quantify the amount of this capacity loss with long term evolution (LTE) and Grassmannian codebooks in the case of Layer 1 (L1) and Layer 2 (L2) transmission using linear receivers in three different channel models. We evaluate the distribution of the minimum distance for LTE and Grassmannian codebooks via simulations. We also derive capacity loss approximations for zero forcing (ZF), minimum mean-squared error (MMSE) and singular value decomposition (SVD) receivers. We find that the capacity loss approximations for L1 transmission are accurate for all receivers and lead to an extremely simple relationship between capacity loss and minimum distance.

The authors deal with the issues of statistical modelling of the aggregate interference because of cognitive radios (CRs) at primary users and the deployment of CR systems in real world environments. The authors explore the possibilities of modelling the interference by two- and three-parameter log-normal distributions. The authors find that the traditional approach of using a two-parameter log normal is not a suitable option on account of the massive skewness difference between the actual interference and the log-normal variable used for fitting purposes. Similarly, the authors observe that the recently proposed three-parameter log-normal approximation works only under specific scenarios. While probing these issues, the authors also arrive at a considerably simpler way of deriving the cumulants of the total interference. Owing to analytical difficulties, the authors resort to simulations to assess different CR deployment schemes. Based on CRs equipped with a priori knowledge of the radio environment map (REM), the authors compare various CR system design parameters achieved by the proposed techniques. Furthermore, the authors describe the effect of imperfections in the REM information on the performance of CR systems. Via analysis and simulations the authors explore the relationship between the required precision of the REM and various system properties.

Limited feedback precoding is part of the LTE standard. Despite standardization, important fundamental questions, especially relating to the performance due to the use of codebooks and receiver processing techniques, remain to be explored. In order to understand these questions, we consider a single user in a single cell employing single or multi-stream transmission using a variety of codebooks and a choice of different receiver types. We derive expressions for capacity loss relative to perfect feedback due to the limited size of codebook. When multistream transmission is deployed, we show that codebook feedback manifests itself as inter-stream interference resulting in a capacity loss for all receiver types. In the case of SVD receivers, this interference results in a capacity floor. We define a precoding matrix index (PMI) coherence time and bandwidth and show how these parameters are respectively related to channel coherence time and bandwidth. The PMI coherence parameters shed new light on how often feedback is required, both in time and frequency domains, and help us to determine the capacity penalty if feedback is delayed beyond the coherence parameters. Finally, we show the distribution of PMI and also show that this is environment dependent. This supports the need for codebooks that are adaptable to different environments and are not strictly tied to i.i.d. channels.

We examine the impact of channel knowledge on the secondary user (SU) in a cognitive radio system. Under a minimum signal-to-interference-and-noise ratio (SINR) constraint for the primary user (PU) receiver, we determine the SU capacity under four channel knowledge scenarios. We derive analytical expressions for the capacity cumulative distribution functions which are verified by means of simulations. We show that the lack of exact knowledge of the PU-PU channel gain by the SU-Tx either prohibits SU transmission or necessitates high interference level at the PU. We also show that the lack of exact knowledge of the SU-Tx to PU-Rx link has little or no impact on SU capacity.

In a receive diversity system the use of multiple antennas at one end of the link produces multiple channels. A useful, although ill-defined, metric for such a link is the number of independent channels provided. In this letter we discuss several candidate metrics and compare their utility. We show that most of the metrics available in the literature have limitations and can exhibit non-physical behaviour. In order to improve on their performance, we develop two novel measures for the number of independent channels based on the statistical construction of the channel and channel capacity.

In this paper we describe a model for calculating the aggregate interference encountered by primary receivers in the presence of randomly placed cognitive radios (CRs). We show that incorporating the impact of distance attenuation and lognormal fading on each constituent interferer in the aggregate, leads to a composite interference that cannot be satisfactorily modeled by a lognormal. Using the interference statistics we determine a number of key parameters needed for the deployment of CRs. Examples of these are the exclusion zone radius, needed to protect the primary receiver under different types of fading environments and acceptable interference levels, and the numbers of CRs that can be deployed. We further show that if the CRs have apriori knowledge of the radio environment map (REM), then a much larger number of CRs can be deployed especially in a high density environment. Given REM information, we also look at the CR numbers achieved by two different types of techniques to process the scheduling information.

A general framework for the design of low complexity timing error detectors (TEDs) for orthogonal space-time block code (OSTBC) receivers is proposed. Specifically, we derive sufficient conditions for a difference-of-threshold-crossings timing error estimate to be robust to channel fading. General expressions for the S-curve, estimation error variance and the signal-to-noise ratio are also obtained. As the designed detectors inherently depend on the properties of the OSTBC under consideration, we derive and evaluate the properties of TEDs for a number of known codes. Simulations are used to assess the system performance with the proposed timing detectors incorporated into the receiver timing loop operating in tracking mode. While the theoretical derivations assume a receiver with perfect channel state information and symbol decisions, simulation results include performance for pilot-symbol-based channel estimation and data symbol detection errors. For the case of frequency-flat Rayleigh fading and QPSK modulation, symbol-error-rate results show timing synchronization loss of less than 0.3 dB for practical timing offsets. In addition it is shown that the receiver is able to track timing drift with a normalized bandwidth of up to 0.001.

We analyze the properties of a class of low complexity timing error detectors for the purpose of timing error tracking in orthogonal space-time block coding receivers. For symmetrical signal constellations, under the assumptions of ideal data decisions and channel knowledge at the receiver, expressions for the S-curve, estimation error variance and the detector signal-to-noise ratio are derived. Simulations are used to confirm the analytical results and to evaluate the effects of data decision errors on the estimator properties. Symbol-error-rate performance is evaluated for a system operating in a frequency-flat Rayleigh fading environment, where the timing synchronization loss is found to be less than 0.3 dB. In addition to receiver with perfect channel state information, results for pilot-based channel estimation are included in order to examine the effects of channel estimation errors on timing synchronization.

Design and analysis of low complexity timing error detectors (TEDs) for quasi-orthogonal space-time block coding systems are presented. The detectors operate on data symbols and approximate decision variables, producing timing error measurement robust to channel fading. In addition to the estimator S-curve, we obtain the estimation error variance and TED SNR, with the analysis carried out under the assumptions of perfect data and channel knowledge at the receiver. Simulations are used to examine the effects of decision errors on the detector characteristics, and to evaluate the overall system performance, where the proposed TEDs are incorporated into the receiver timing loop. Receivers with perfect channel knowledge and pilot-based channel estimation are considered. Symbol error rate results show timing synchronization loss of less than 0.5 dB for a receiver with perfect channel information.

We present a method for the design of low complexity timing error detectors in orthogonal space-time block coding (OSTBC) receivers. A general expression for the S-curve of timing error detectors is derived. Based on this result, we obtain sufficient conditions for a difference of threshold crossings timing estimate that is robust to channel fading. A number of timing error detectors for 3- and 4-transmit antenna codes are presented. The performance is evaluated by examining their tracking capabilities within a timing loop of an OSTBC receiver. Symbol-error-rate results are presented showing negligible loss due to timing synchronization. In addition, we study the performance as a function of the timing drift and show that the receiver is able to track up to the normalized timing drift bandwidth of 0.001

We analyze the properties of a robust timing error detector for nT= 2 orthogonal space-time block coded M-PSK systems with an arbitrary number of receive antennas. The algorithm uses maximum-likelihood detection variables to estimate the timing error by examining the difference in threshold crossings. The S-curve of the detector is shown to be independent of the channel state, thus making it very robust in poor channel conditions. Furthermore, we derive a closed form expression for the variance of the estimator, and show that the estimation SNR peaks in the timing error region the receiver usually operates in. We evaluate the tracking performance in 1-, 2- and 4-receive antenna systems with randomly distributed timing drift. Complete channel state estimation is assumed throughout the paper

We propose a very low complexity timing error detector for n/sub T/ = 2 orthogonal space-time block coded M-PSK systems with an arbitrary number of receive antennas. The algorithm uses maximum-likelihood detection variables to estimate the timing error by examining the difference in threshold crossings, similarly to the Mueller and Muller detector. We show that the timing error estimation is independent of the channel state, thus making it very robust in poor channel conditions. The decision directed version of the detector is used to evaluate the tracking performance for BPSK and QPSK signaling in 1-, 2- and 4-receive antenna systems. Symbol error rate as well as mean square estimation error results are presented. We examine the performance as a function of the timing drift and show that the receiver is able to maintain lock up to a normalized timing bandwidth of B/sub T/T = 0.001. Complete channel state estimation is assumed throughout the paper.

e analyze the performance of a joint timing epoch tracking and PSAM-based channel estimation system in a frequency-flat Rayleigh fading MIMO channel. The receiver tracks a random timing drift via a timing error detector developed for nT= 2 orthogonal space-time block coded MPSK systems with an arbitrary number of receive antennas. The detector's S-curve has recently been shown to be independent of the channel state, resulting in system very robust in poor channel conditions. We evaluate the receiver's tracking capabilities in conjunction with channel estimation and study the effects of the delay inherent to PSAM interpolation systems. Symbol error rate performance for a QPSK system is presented, with the results showing negligible performance degrad.

An effective method for joint timing and channel estimation for receive diversity systems in a frequency-flat Rayleigh fading environment is presented. We implement nonsynchronous timing recovery using Gardner's timing error detector, whose insensitivity to phase errors allows for timing recovery prior to pilot symbol based channel estimation. By employing a polyphase filter bank in the timing loop, we are able to simultaneously carry out matched filtering and data interpolation, thus eliminating the need for a separate interpolation filter. In addition, selection diversity combining is used to select the input to the timing loop, thus improving the reliability of the signal used for timing recovery. Pilot assisted channel estimation is performed on the recovered data strobes. For normalized Doppler frequency of 0.01 the system's bit error rate (BER) performance is within 1 dB from the ideal timing and channel estimation error bound, with an additional drop of 1.5 dB for a nonoptimum channel interpolator. In deep fades, the receiver timing is held fixed. We show that the receiver maintains timing lock over such fades up to a normalized timing bandwidth of 1/spl times/10/sup -4/for normalized Doppler frequency up to 0.05.