Continuous aperture arrays (CAPAs) provide a theoretical upper bound on the performance of densely packed antenna arrays, but their analysis is limited by the lack of closed-form signal-to-noise ratio (SNR) distributions under realistic fading conditions. This paper derives accurate analytical expressions for the matched-filter SNR distribution of one-dimensional CAPAs in correlated Rayleigh environments under both the sinc and Jakes correlation models using the Karhunen–Loève expansion. By applying a truncated hypoexponential model, we obtain accurate approximations for the probability density function and cumulative distribution function of the SNR that closely match simulations, including the outage probability region where precise characterization is critical. Compared to a standard gamma approximation, our approach provides significantly improved accuracy in this regime. Additionally, the CAPA system considered is shown to outperform discrete antenna arrays. The derived expressions enable tractable and accurate evaluation of CAPAs under practical channel models.

Phase selection design for reconfigurable intelligent surfaces (RISs) is a significant research challenge, as a closed-form optimal solution for a multi-user (MU) system is believed to be intractable. While existing methods achieve strong near-optimal performance, they typically entail high computational complexity. In this work, we take a different approach and propose a practical method that achieves competitive performance while substantially reducing computational complexity. To do so, we consider a RIS divided into subsurfaces. Each subsurface is designed specifically for one user, who is served on their own frequency band. The other subsurfaces (those not designed for this user) provide additional uncontrolled scattering. We derive the exact closed-form expression for the mean signal-to-noise ratio (SNR) for the proposed subsurface design (SD) when all channels experience correlated Ricean fading. We simplify this to find the mean SNR for line-of-sight (LoS) channels and channels experiencing correlated Rayleigh fading. An iterative SD (ISD) process is proposed, where subsurfaces are designed sequentially, and the phases that are already set are used to enhance the design of the remaining subsurfaces. This is extended to a converged ISD (CISD), where the ISD process is repeated multiple times until the SNR increases by less than a specified tolerance. The ISD and CISD both provide a performance improvement over SD, which increases as the number of RIS elements increases. The SD is significantly simpler than the lowest complexity MU method we know of, and despite each user having less bandwidth, the SD outperforms the existing method in some key scenarios. The SD is more robust to strongly LoS channels and clustered users, as it does not rely on spatial multiplexing like other MU methods. Combined with the complexity reduction, this makes the SD an attractive phase selection method.

Motivated by the constant modulus property of frequency shift keying (FSK) based waveforms and the stabilisation of its radar performance with an increase in the number of subpulses, in this paper an FSK-based dynamic subpulse number joint communications and radar waveform design is proposed. From a communications point of view, the system operates based on traditional FSK modulation. From a sensing point of view, although the subpulses are continuously generated and transmitted, radar waveforms are dynamically formed by monitoring the flatness of the spectrum which in return guarantees the accuracy of the delay estimation. Other constraints on the waveform length are used to ensure satisfactory values of the root mean square time duration, ambiguity function sidelobe levels and prevent overly long waveforms. To provide an estimation of the probability of generating extremely long waveforms, the distribution of the number of subpulses is approximated using a Brownian motion process and an existing result on its one-sided exit density. Numerical examples are provided to evaluate the accuracy of the approximate distribution, as well as the ambiguity function sidelobe levels and the delay and Doppler shift estimation performance of the transmitted waveforms.

Motivated by the ideal peak-to-average-power ratio and radar sensing capability of traditional frequency-coded radar waveforms, this paper considers the frequency shift keying (FSK) based waveform for joint communications and radar (JCR). An analysis of the probability distributions of its ambiguity function (AF) sidelobe levels (SLs) and peak sidelobe level (PSL) is conducted to study the radar sensing capability of random FSK. Numerical results show that the independent frequency modulation introduces uncontrollable AF PSLs. In order to address this problem, the initial phases of waveform sub-pulses are designed by solving a min-max optimisation problem. Numerical results indicate that the optimisation-based phase design can effectively reduce the AF PSL to a level close to well-designed radar waveforms while having no impact on the data rate and the receiver complexity. For large numbers of waveform sub-pulses and modulation orders, the impact on the error probability is also insignificant.

A key challenge facing reconfigurable intelligent surfaces (RISs) is channel state information acquisition. Passive RISs cannot generate pilot signals or process data, making rapid temporal changes in the channel problematic. Additionally, the impact of spatial changes in RIS channels has not been thoroughly investigated. Therefore, in this work, we use second order statistics to investigate the spatio-temporal behaviour of a single-user (SU) RIS system. Assuming a line-of-sight (LoS) RIS to base station (BS) link, we derive an exact expression for the level crossing rate (LCR) of the RIS link (user equipment (UE)-RIS-BS path) and propose a numerically stable approximation for the LCR of the global UE-BS channel. Each LCR expression attained is then utilised to find the corresponding average fade duration (AFD). The temporal signal-to-noise ratio (SNR) correlation is also derived assuming an LoS RIS-BS link. Assuming a Ricean RIS-BS link, expressions for the spatial correlation matrix of the global channel and the mean SNR loss due to channel ageing are derived. All of the analyses are verified by simulation, and the impact of key system parameters is investigated. We show that the use of an RIS does not significantly amplify changes in the channel.

We consider a single-user (SU) continuous fluid antenna system (CFAS) employing matched filtering (MF) operating over a Ricean fading channel. Focusing on the upper tail of the received signal-to-noise ratio (SNR) distribution (the high SNR probability (HSP)), we derive accurate approximations for the HSP in 1, 2, and 3 dimensions using the expected Euler characteristic (EEC), presenting the first analytical results for a CFAS in a Ricean environment. In the process, we provide the first closed-form expression for the Euler characteristic density of a non-central $\chi _2^2$ random field. We then examine the impact of the Ricean K-factor on the CFAS performance, emphasizing the critical role of channel variations in achieving a strong HSP.

We consider a reconfigurable intelligent surface (RIS) that can implement a phase rotation continuously over the whole surface rather than via a finite number of discrete elements. Such an RIS can be considered a design for future systems where advances in metamaterials make such an implementation feasible or as the limiting case where the number of elements in a traditional RIS increases in a given area. We derive the optimal RIS design for the single-user (SU) scenario assuming a line-ofsight (LoS) from the RIS to the base station (BS) and correlated Rayleigh fading for the other links. We also derive the associated optimal signal-to-noise ratio (SNR) and its mean, a bound on the mean spectral efficiency (SE), an approximation to the SNR outage probability and an approximation to the coefficient of variation for the investigation of channel hardening.

Recent developments in Multiple-Input-Multiple-Output (MIMO) technology include packing a large number of antenna elements in a compact array to access the bandwidth benefits provided by higher mutual coupling (MC). The resulting super-wideband (SW) systems require a circuit-theoretic framework to handle the MC and channel models which span extremely large bands. Hence, in this paper, we make two key contributions. First, we develop a physically-consistent Rician channel model for use with SW systems. Secondly, we express the circuit-theoretic models in terms of a standard MIMO model, so that insights into the effects of antenna layouts, MC, and bandwidth can be made using standard communication theory. For example, we show the bandwidth widening resulting from the new channel model. In addition, we show that MC distorts line-of-sight paths which has beamforming implications. We also highlight the interaction between spatial correlation and MC and show that tight coupling reduces spatial correlations at low frequencies.

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.

We analyse the level crossing rate (LCR) of an uplink single-user (SU) reconfigurable intelligent surface (RIS) aided system. It is assumed that the RIS to base station (RIS-BS) channel is deployed as line-of-sight (LoS), and the user (UE)-RIS and UE-BS channels are correlated Rayleigh. For the optimal RIS reflection matrix, we derive a novel and exact analytical LCR expression for when the direct (UE-BS) channel is blocked, i.e. the RIS-only channel. Also, the existing exact expression for the direct-only channel (equivalent to classical maximal-ratio-combining (MRC)) suffers from extreme numerical precision problems when the BS has many elements. Therefore, we propose a new stable and accurate approximation to the LCR of the direct channel. The approximation is based on replacing any small similar eigenvalues of the channel correlation matrix by their average. We show that increasing the number of elements at the RIS or BS and decreasing channel correlation makes the LCR drop more rapidly for thresholds away from the mean SNR. Crucially, we find that RIS systems do not significantly amplify temporal variations in the channel. This is particularly beneficial for RIS systems considering the difficulty in acquiring channel state information (CSI).

Building on recent trends in multiple-input multiple-output and reconfigurable intelligent surfaces, where densely spaced element arrays are considered, this paper focuses on con-tinuous antenna systems where the receive antenna is modelled as a continuous line (in the one-dimensional case) or a continuous surface (in the two-dimensional case). Considering a spatially-correlated Rayleigh process for the communication channel, we conduct an analytical investigation based on matched filtering. More specifically, we derive an approximated distribution for the instantaneous received signal-to-noise ratio (SNR) at the continuous surface. Furthermore, we derive approximations to the achievable rate, average symbol error rate for Mary phase shift keying (MPSK) and an upper bound for the achievable rate. We use extensive numerical examples to illustrate the accuracy of our approximation to the SNR distribution as well as the performance analysis.

Orthogonal time frequency space (OTFS) modulation has recently been identified as a suitable waveform for joint radar and communication systems. Focusing on the effect of data modulation on the radar sensing performance, we derive the ambiguity function (AF) of the OTFS waveform and characterize the radar global accuracy. We evaluate the behavior of the AF with respect to the distribution of the modulated data and derive an accurate approximation for the mean and variance of the AF, thus, approximating its distribution by a Rice distribution. Finally, we evaluate the global radar performance of the OTFS waveform with the OFDM waveform.

This paper focuses on waveform design for joint radar and communication systems and presents a new subset selection process to improve the communication error rate performance and global accuracy of radar sensing of the permutation based random stepped frequency radar waveform. An optimal communication receiver based on integer programming is proposed to handle any subset of permutations followed by a more efficient sub-optimal receiver based on the Hungarian algorithm. Considering optimal maximum likelihood detection, the block error rate is analyzed under both additive white Gaussian noise and correlated Rician fading. We propose two methods to select a permutation subset with an improved block error rate and an efficient encoding scheme to map the information symbols to selected permutations under these subsets. From the radar perspective, the ambiguity function is analyzed with regards to the local and the global accuracy of target detection. Furthermore, a subset selection method to reduce peak-to-sidelobe ratio (PSLR) is proposed by extending the properties of Costas arrays. Finally, the process of remapping the frequency tones to the symbol set used to generate permutations is introduced as a method to improve both the communication and radar performances of the selected permutation subset.

Arrays with a large number of antennas can achieve outstanding performance for both communication and radar sensing. This motivates us to investigate the transmit beamforming design for massive multiple-input multiple-output integrated sensing and communications (mMIMO-ISAC) systems. Inspired by the facts that linear precoding methods can provide very good performance in mMIMO and that a dual-function ISAC transmit beamformer should be suitable for both communication and radar sensing, we propose an implementation-friendly mMIMO-ISAC transmit beamformer as a weighted combination of a linear precoder and a pre-designed array beamformer. The weights are selected and adjusted through the powers allocated to the beamformers, while the design problem is formulated as a total transmit power minimization, while satisfying the requirements for both sensing and communication. Leveraging the use-and-then-forget strategy, simplified performance metrics for communication and sensing under the proposed mMIMO-ISAC transmit model are derived, which yields linear programming (LP) problems for the design. It is shown that analytical solutions can be obtained and, hence, the proposed design is computationally very attractive. Simulations are carried out to demonstrate the effectiveness and performance of the proposed methods.

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 consider the problem of transmit beamforming design for massive multiple-input multiple-output integrated sensing and communications (MMIMO-ISAC) systems. Different from the existing designs for regular MIMO-ISAC systems, which directly optimize the dual-function beamformer matrix and are computationally expensive especially for large-scale antenna arrays, we propose to construct the beamformer as a weighted sum of the maximum ratio precoder and a desired sensing beamformer. This is motivated by the fact that maximum ratio precoding schemes are simple, and performs well in MMIMO systems. The weights involved in the beamformer are adjusted via optimizing the powers allocated to the users and sensing. A linear programming (LP) problem, which minimizes the total transmit power subject to the performance constraints of communication and sensing, is thus formulated. It is shown that the LP problem can be analytically solved. Therefore, the proposed transmit beamforming design has very low computational complexity. Its effectiveness and performance are illustrated by simulations.

The wireless propagation environment between the transmitter and the receiver plays a major role in wireless communication. It is this environment that gives rise to the multipath. In contrast to the conventional wisdom, the impact of this multipath on wireless communication is now considered as something that can be changed. Instead of introducing foreign objects like "reflective surfaces" to physically alter the wireless environment, in this paper we study an emerging area of study known as "mediumband wireless communication", that can statistically manipulate the effect of the wireless propagation environment. The unique bimodal nature of the probability density function (PDF) of the desired fading factor in mediumband channels means this new class of channels have the potential to reduce the deep fading considerably. In this paper, we propose an accurate PDF in analytically convenient form to capture this bimodal nature, and analyse the extent of the effect of deep fading avoidance. The objective is to enable further analysis and simulation of mediumband channels and also to ease the study of the wider impact of mediumband wireless communication for future wireless communication.

Distributed massive multiple-input multiple-output (mMIMO) is a key technology for improving the performance of future wireless communication systems. As an alternative to channel estimation in mMIMO systems, non-coherent detection offers several advantages. In this paper, we present a comprehensive analysis of non-coherent detection for distributed mMIMO systems. We obtain novel expressions for the signal-to-interference-and-noise ratio (SINR) for differential detection. Building upon a theoretical basis, we show that under non-coherent detection, cooperation is always beneficial in noise-limited conditions. We further investigate scenarios where the gains of cooperation are most evident. We then obtain useful error rate results by deriving expressions for the symbol error probability (SEP) when using differential detection. The results are illustrated by numerical examples and simulations.

In this paper, we analyse the performance of a reconfigurable intelligent surface (RIS) aided system where the RIS is divided into subsurfaces. Each subsurface is designed specifically for one user, who is served on their own frequency band. The other subsurfaces (those not designed for this user) provide additional uncontrolled scattering. A new subsurface RIS design is developed based on the optimal single-user design for a pure line-of-sight (LoS) base station (BS) to RIS channel. This is also extended to arbitrary BS-RIS channels. For our method, exact closed form solutions for the mean SNR and a mean rate upper bound are derived for the BS-RIS LoS scenario. For each user, the designed subsurface performs optimally in LoS conditions and is remarkably robust to non-LoS conditions. The system design drives down complexity to extremely low levels, reducing RIS design and receiver processing complexity and reducing the channel estimation requirements. We also quantify the complexity-performance trade-off for the new design relative to multi-user approaches.

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 propose a new partial joint processing architecture for distributed massive multiple-input multiple-output (MIMO) networks. As opposed to the traditional full-joint processing architecture, where the channel coefficients of all the users within the cooperating cluster are learnt at the base stations, in the proposed architecture, we allow each base station to learn the channel coefficients only of the users that maintain a strong average received signal-to-noise ratio to that base station based on a predefined threshold. This threshold provides extra flexibility, trading-off channel estimation for performance. We assume a zero-forcing receiver at the central processing unit using estimated channels and unknown terms are set to zero. We then derive an accurate approximation for the instantaneous received signal-to-interference-and-noise ratio of an arbitrary user. We use this approximation to derive closed-form expressions for the achievable rate and symbol error probability of an arbitrary user. Numerical examples are used to illustrate the accuracy of the analysis.

This paper presents a new joint radar and communication technique based on the classical stepped frequency radar waveform. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. A new signaling scheme is proposed in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. Considering the optimum maximum likelihood detection, the union bound and the nearest neighbour approximation on the communication block error probability is derived for communication in an additive white Gaussian noise channel. The results are further extended to incorporate the Rician fading channel model, of which the Rayleigh fading channel is presented as a special case. Furthermore, an efficient communication receiver implementation is discussed based on the Hungarian algorithm which achieves optimum performance with much less operational complexity when compared to an exhaustive search. From the radar perspective, two key analytical tools, namely, the ambiguity function and the Fisher information matrix are derived. Furthermore, accurate approximations to the Cramer-Rao lower bounds on the delay and Doppler estimation errors are derived based on which the range and velocity estimation accuracy of the waveform is analysed.

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.

This paper presents a new waveform that is suitable for simultaneous data transmission and radar sensing. The approach considers a classical random stepped frequency radar waveform that is suitable for the emerging automotive radar application. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. More specifically, we propose a new Lehmer code based signaling model that modulates data based on the selection of the permutation. Considering maximum likelihood detection, the union bound on the communication block error probability is derived for baseband communication both in an additive white Gaussian noise (AWGN) channel and Rayleigh fading channel. Using the Hungarian Algorithm, an efficient implementation method for the communications receiver is also presented. From the radar perspective, we derive the ambiguity function, which is a key analytical tool in radar waveform design, and characterize the behavior of the Lehmer code based random stepped frequency radar waveform. Numerical examples are used to illustrate the performance of the proposed waveform.

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.

In multiuser multiple-input multiple-output (MU-MIMO) systems, channel correlation is detrimental to system performance. We demonstrate that widely used, yet overly simplified, correlation models that generate identical correlation profiles for each terminal tend to severely underestimate the system performance. In sharp contrast, more physically motivated models that capture variations in the power angular spectra across multiple terminals, generate diverse correlation patterns. This has a significant impact on the system performance. Assuming correlated Rayleigh fading and downlink zero-forcing precoding, tight closed-form approximations for the average signal- to-noise-ratio, and ergodic sum spectral efficiency are derived. Our expressions provide clear insights into the impact of diverse correlation patterns on the above performance metrics. Unlike previous works, the correlation models are parameterized with measured data from a recent 2.53 GHz urban macrocellular campaign in Cologne, Germany. Overall, results from this paper can be treated as a timely re-calibration of performance expectations from practical MU-MIMO systems.

Fifth generation cellular networks must support dense user environments where close proximity users and highly correlated channels are prevalent. This study presents a novel decorrelating zero‐forcing (DZF) scheme. It improves downlink zero‐forcing (ZF) performance over multi‐user multiple‐input multiple‐output channels when highly correlated users are present. DZF groups correlated users into pairs where the stronger user is labelled ‘near’ and the weaker user, ‘far’. For the far and unpaired users, the proposed design is similar to conventional ZF (CZF) in that the base station performs traditional ZF and the users employ the leading left singular vectors of the channel for processing. In contrast, the near users employ the second strongest left singular vector which decorrelates their effective channel with the paired far user. This reduces the noise inflation inherent in ZF for correlated channels. From simulations and analysis the authors demonstrate that DZF has both rate and fairness advantages over CZF when highly correlated users are present. Furthermore, they design a hybrid ZF (HZF) scheme, which harnesses the advantages of both CZF and DZF, hence providing robustness against the joint scheduling of semi‐orthogonal and highly correlated users with very little additional complexity. Simulations clearly demonstrate that HZF has higher rates than CZF and DZF.

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.

Connectivity questions for mobile D2D networks are often approached by considering steady state performance metrics. This is due to the difficulty in handling a finite time horizon with random mobility. Hence, in this paper we create a framework to evaluate connectivity time in closed form over a finite time horizon for mobile devices. The basic metric is the mean proportion of time devices are connected over a finite period. The methodology is shown to deliver closed form results for a variety of deterministic and random mobility models in both fading and non-fading scenarios. This allows a comparison of mobility types and an understanding of the underlying parameters. In addition, an approach is developed which allows different mobility types to be compared on the basis of a single 'equivalent' speed and also the overall framework allows the energy requirements of certain mobility control mechanisms to be evaluated.

In this paper, we take a fundamental look at the interference characteristics of a lens-based millimeter-wave (mmWave) multiuser multiple-input multiple-output system (MU-MIMO) system. We consider a hybrid architecture, implemented via a bank of radio-frequency (RF) switches which perform beam selection followed by low-complexity uplink maximum-ratio combining (MRC) at baseband. Considering a Rotman lens antenna array in line- of-sight (LoS) propagation, we derive tight analytical approximations to the average (expected) interference power of an arbitrary terminal, with and without the presence of RF switching. The analytical expressions show that without RF switching, the Rotman lens losses its benefits and collapses to a conventional uniform linear array. Our numerical results demonstrate that the expected interference power to a given terminal decreases significantly with RF switching, due to beam selection separating the uplink direction-of-arrivals (DoAs), in contrast to the case without RF switching, which relaxes the beam selection constraint and thus allows very similar DoAs. Overall, the results in this paper emphasize the necessity of RF switching in order to obtain superior performance with lens arrays, over conventional phased arrays.

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.

Non-orthogonal multiple access based zero-forcing beamforming (NOMA-ZFBF) systems require both semi- orthogonal users (SU) in beams and highly correlated (HC) users within a beam to maximize the spectral efficiency of the system. Hence, channel models where different users are likely to experience both similar and near-orthogonal channel vectors are likely to give good NOMA performance. In order to explore this, we analyze the variance of the interference power between two users, where a large variance indicates this channel behavior is more likely. Moreover, we have compared the Rician and Rayleigh channels in correlated and independent and identically distributed (I.I.D.) environments in order to provide some new insights into the role of line- of-sight (LoS) and correlated components with respect to NOMA beam formation and clustering of HC users. Analysis and numerical results show that correlated channels with similar channel statistics result in a higher variance that in turn increases the cluster percentage and enhances the cluster rate.

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.

In this paper, we present a new theoretical analysis of the performance of a distributed antenna system (DAS) with a constraint on the number of RF chains. We consider a cooperating network model with receiver sites distributed across the network. Each receive site is equipped with a limited number of RF chains that picks the best set of antennas based on the channel between the transmitter and the receiver. Considering a hybrid generalized selection/maximal ratio combining (GS/MRC) scheme, we derive new expressions for three important performance measures, namely, the achievable rate, symbol error probability (SEP) and outage probability. Our expressions are based on closed-form expressions we derive for the moment generating function (MGF) of the received signal-to-noise-ratio (SNR). We further analyse the high SNR error performance to accurately characterize the diversity order and the array gain of the system. Numerical examples demonstrate that our analytical results accurately reflect the simulations for a wide range of network scenarios. We highlight that the DAS with GS/MRC requires fewer RF chains and introduces a lower hardware complexity when compared to conventional MRC.

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.

This paper analyzes the performance of a multi-user multihop relay network using a low complexity decentralized relay selection (DRS) scheme for decode-and-forward cooperative networks. We carry out a rigorous diversity order analysis, with Nakagami-m fading and pathloss and show that the DRS scheme achieves full diversity while maintaining a complexity that is quadratic in the number of users, quadratic in the number of relays and independent of the number of hops. For a special case of two-user networks we derive exact closed-form expressions for the outage probability by considering the order statistics. Furthermore, we extend our analysis to consider interfering relay networks and derive an accurate lower bound on the outage of an arbitrary network user. Based on the lower bound we also show how the outage probability saturates in the high signal-to-interference-plus-noise ratio regime. Extensive numerical examples are used to illustrate the accuracy of the analysis and to highlight the use of the DRS scheme in multi-user multihop relay networks.

We analyze topological entropy in wireless networks that are subject to local scattering and macroscopic shadowing effects. To this end, we model a network as a random geometric graph with probabilistic pair connections (due to channel randomness) and define uncertainty as the Shannon entropy of the underlying graph ensemble. We present new bounds on topological entropy that are functionals of the underlying composite fading distributions and use these to show that different fading models lead to very different network entropies under certain conditions, a result that has significant implications for self-organization and storage of the network state. We also study the behavior of the entropy bounds as the number of nodes n in the network grows large while the typical connection range r0varies monotonically with n. This analysis leads to two key results that quantify the rate of growth or decay of r0, as a function of the number of nodes n, that must be obeyed in order for the entropy bounds to converge to a positive limit. Although the contributions of this paper are theoretical, they have applications in systems such as ad hoc networks employing opportunistic routing and device-to-device (D2D) networks for future cellular communication.

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.

There is considerable pressure to define the key requirements of 5G, develop 5G standards, and perform technology trials as quickly as possible. Normally, these activities are best done in series but there is a desire to complete these tasks in parallel so that commercial deployments of 5G can begin by 2020. 5G will not be an incremental improvement over its predecessors; it aims to be a revolutionary leap forward in terms of data rates, latency, massive connectivity, network reliability, and energy efficiency. These capabilities are targeted at realizing high-speed connectivity, the Internet of Things, augmented virtual reality, the tactile internet, and so on. The requirements of 5G are expected to be met by new spectrum in the microwave bands (3.3-4.2 GHz), and utilizing large bandwidths available in mm-wave bands, increasing spatial degrees of freedom via large antenna arrays and 3-D MIMO, network densification, and new waveforms that provide scalability and flexibility to meet the varying demands of 5G services. Unlike the one size fits all 4G core networks, the 5G core network must be flexible and adaptable and is expected to simultaneously provide optimized support for the diverse 5G use case categories. In this paper, we provide an overview of 5G research, standardization trials, and deployment challenges. Due to the enormous scope of 5G systems, it is necessary to provide some direction in a tutorial article, and in this overview, the focus is largely user centric, rather than device centric. In addition to surveying the state of play in the area, we identify leading technologies, evaluating their strengths and weaknesses, and outline the key challenges ahead, with research test beds delivering promising performance but pre-commercial trials lagging behind the desired 5G targets.

There are rapid developments towards the deployment of 5G and hardly a day goes by without the release of a major announcement concerning 5G. Many of these developments are happening in parallel as there is a race against time for 5G deployment. Various test beds have been established, laboratory trials and proof of concept trials of individual building blocks of 5G are already underway or have been completed, large scale system trials are also happening or are planned and standardisation efforts in the ITU, 3GPP, IEEE, etc. are also in progress. In the case of ITU/3GPP, the standards are expected to be completed by 2019. Many candidate bands for 5G in the centimetric and mm wave range were identified by the World Radio Conference (WRC) 2015 and are expected to be finalized by WRC 2019, while coexistence studies of 5G and existing systems in the new candidate bands are underway.

This is the second part of the papers in this special issue on deployment issues and performance challenges for 5G. The papers have been divided into five categories:•Massive MIMO•Co existence•Signal Processing and New Waveforms•Cloud RAN•Field Trials

Reconfigurable antenna arrays provide a means for efficient use of the spatial domain in wireless communication systems. Despite its potential, the topic is only briefly explored in the literature. In this paper, we present a comprehensive theoretical analysis of the performance of reconfigurable systems. We consider a receiver equipped with multiple reconfigurable antennas that pick the best state based on the channel between the transmitter and the receiver. For such a system, we derive a new expression for the moment generating function (MGF) of the received signal-to-noise ratio by employing maximal ratio combining. Based on the MGF, we analyze three important performance measures, specifically, achievable rate, error probability, and outage probability. Furthermore, we conduct an asymptotic analysis incorporating the correlation between reconfigurable states and show that a reconfigurable system can achieve a diversity order of the number of antennas times the number of reconfigurable states. Finally, we discuss the applicability of reconfigurable antennas in novel wireless networks with large antenna arrays and distributed antenna systems, highlighting the performance gains and requirement for fewer RF chains.

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.

This paper investigates the achievable spectral efficiency (SE) of millimeter wave downlink cellular systems accounting for both small and large-scale fading effects. The base station (BS) employs a uniform linear array (ULA) and maximal ratio transmission. We derive the expectation of the squared inner product for different channel links under the assumption that the users are randomly distributed within a circular-shaped cell. Using this result, a new lower bound on the achievable SE, valid for arbitrary numbers of antennas is derived. The analytical results show that the achievable SE increases with the number of BS antennas, whilst it converges to a saturated value in the high signal-to-noise ratio (SNR) regime and larger inter- antenna spacing.

In this study, a reconfigurable antenna codebook feedback (FB) scheme is investigated to reduce precoding codebook loss without increasing the number of FB bits. Analysis and simulations show that increasing the number of receive antenna states ( S ) has the same effect as codebook size expansion when the codeword and state selection is based on minimising the distance between channel and codeword. In addition, the authors propose an optimum selection approach. The signal to noise ratio (SNR) and rates achieved with perfect FB in a traditional non‐reconfigurable antenna system, can be exceeded with only S = 2, using the proposed optimum selection. In fact doubling S gives an approximate SNR gain of 40% compared with S = 1. The authors also consider the effects of channel estimation errors and correlated antenna states. The authors show that the performance losses due to correlation can be quantified with a simple closed form result.

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.

We derive closed-form expressions to approximate the distribution of detection delay for a time-invariant cumulative sum detector. In addition, we derive approximations for the distribution of detection delay for the general case, which can be applied to any independent and identically distributed channel. We also employ random walk and Brownian motion theory to derive approximate expressions. The validity of these expressions is verified using simulations. We also approximate the probability of missed detection and investigate the probability of long detection delays via analysis and simulations. Numerical results show that different signal-to-noise ratio and detection delay conditions require different approaches to achieve good approximations of the detection delay distribution. Results also illustrate that the remarkably simple Brownian motion approach provides the best approximation for longer delays and the type of fading channel has very little impact on long detection delays.

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 a novel class of space time trellis codes based on super quasi-orthogonal space time codes for a reconfigurable antenna system. We call them space time state trellis codes (STSTCs). We design for 4 trellis states and both 2 and 4 branch trellis structures for BPSK and QPSK constellations. The proposed codes take advantage of the additional degrees of diversity offered by reconfigurable antennas and changing propagation states. They achieve full rate, full diversity and high coding gain. Simulation results demonstrate their good performance. STSTCs achieve the diversity order expected of four transmit antennas while using only two reconfigurable transmit antennas. Our code out performs the existing super orthogonal space time trellis code, which fails to achieve full diversity in a reconfigurable antenna system. The proposed 4 trellis state STSTC is designed based on the following performance criteria: minimum coding gain distance of the minimum return path (CGD MRP), performance factor (PF), rank of the partial valid path (RPVP) on top of traditional minimum coding gain distance of parallel path (CGD PP). We show through analysis and simulations that minimum CGD PP is not a sufficient criteria and that additional performance gains are provided by considering the CGD MRP.

Pilot contamination occurs when cells simultaneously transmit the same pilot sequences, creating interference. Unsynchronizing the pilots can reduce pilot contamination, but it can produce data to pilot interference. In this paper, we investigate the impact of pilot contamination and other interference, namely data to pilot interference, on the performance of finite massive MIMO systems with synchronized and unsynchronized pilots. Two unsynchronized pilot schemes are considered. The first is based on an existing time-shifted pilot scheme, where pilots overlap with downlink data from nearby cells. The second time-shifted method overlaps pilots with uplink data from nearby cells. Results show that if there are small numbers of users, the first time-shifted method provides the best sum rate performance. However, for higher numbers of users, the second time-shifted method has advantage compared to other methods. We also show that time-synchronized pilot is not necessarily the worst case scenario in term of sum rate performance when shadowing effect are considered.

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.

Pilot contamination is an issue affecting massive MIMO systems. It is known that a time-shifted pilot method can be used to reduce pilot contamination from neighboring cells when the number of antennas at the base station is infinitely large [1]. In our research, we analyze the effect of a finite number of antennas on the sum rate of the time-shifted method. Numerical results show that the time-shifted pilot method can improve uplink and downlink transmission rate compared to time-synchronized method for small number of spatial multiplexing users. However, for higher number of spatial multiplexing users, the time-shifted method will need more antennas at the base station in order to have noticeable improvement over the time-synchronized method.

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 deal with the deployment of full-duplex relaying in amplify-and-forward (AF) cooperative networks with multiple-antenna terminals. In contrast to previous studies, which focus on the spatial mitigation of the loopback interference (LI) at the relay node, a joint precoding/decoding design that maximizes the end-to-end (e2e) performance is investigated. The proposed precoding incorporates rank-1 zero-forcing (ZF) LI suppression at the relay node and is derived in closed-form by solving appropriate optimization problems. In order to further reduce system complexity, the antenna selection (AS) problem for full-duplex AF cooperative systems is discussed. We investigate different AS schemes to select a single transmit antenna at both the source and the relay, as well as a single receive antenna at both the relay and the destination. To facilitate comparison, exact outage probability expressions and asymptotic approximations of the proposed AS schemes are provided. In order to overcome zero-diversity effects associated with the AS operation, a simple power allocation scheme at the relay node is also investigated and its optimal value is analytically derived. Numerical and simulation results show that the joint ZF-based precoding significantly improves e2e performance, while AS schemes are efficient solutions for scenarios with strict computational constraints.

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 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 a novel class of space time trellis codes based on super quasi-orthogonal space time codes for a reconfigurable antenna system. We call them Space Time State Trellis Codes (STSTCs). The proposed codes are capable of taking advantage of the additional degrees of diversity offered by reconfigurable antennas and changing propagation states. They achieve full rate, full diversity and high coding gain. Simulation results demonstrate their good performance. STSTCs achieve the diversity order expected for four transmit antennas while using only two reconfigurable transmit antennas. Our code out performs the existing super orthogonal space time trellis code, which fails to achieve full diversity in a reconfigurable antenna system.

This paper presents a new analytical solution for the cumulative distribution function of the throughput of an adaptive MIMO-OFDM system in Rayleigh fading channels. We derive novel results on the distribution of the eigenvalues and hence compute the mean and variance of the number of bits transmitted per OFDM block. We compare the performance of the adaptive MIMO-SVD scheme with that of an adaptive modulation system employing MMSE receivers and demonstrate the effect of reduced feedback on the LTE system performance.

The performance of maximal ratio combining (MRC) in Rayleigh channels with co-channel interference (CCI) is well-known for receive arrays which are co-located. Recent work in network MIMO, edge-excited cells and base station collaboration is increasing interest in macrodiversity systems. Hence, in this paper we consider the effect of macrodiversity on MRC performance in Rayleigh fading channels with CCI. We consider the uncoded symbol error rate (SER) as our performance measure of interest and investigate how different macrodiversity power profiles affect SER performance. This is the first analytical work in this area. We derive approximate and exact symbol error rate results for M-QAM/BPSK modulations and use the analysis to provide a simple power metric. Numerical results, verified by simulations, are used in conjunction with the analysis to gain insight into the effects of the link powers on performance.

The prospect of base station cooperation leading to joint combining at widely separated antennas has led to increased interest in macrodiversity systems, where both sources and receive antennas are geographically distributed. In this scenario, analytical investigation of channel capacity is extremely challenging for finite-size systems since the channel matrices have a very general form where each path may have a different power. Hence, in this paper, we consider the ergodic sum capacity of a macrodiversity multiple-input multiple-output system with arbitrary numbers of sources and receive antennas operating over Rayleigh fading channels. For this system, we compute the exact ergodic capacity for a system with at most two transmit antennas and a compact approximation for the general system, which is shown to be very accurate over a wide range of cases. Finally, we compare our results with previous asymptotic results and bounds. Results are verified by Monte Carlo simulations and the impact on capacity of various channel power profiles is investigated.

Consider a multiuser system where an arbitrary number of users communicate with a distributed receive array over independent Rayleigh fading paths. The receive array performs minimum mean squared error (MMSE) or zero forcing (ZF) combining and perfect channel state information is assumed at the receiver. This scenario is well-known and exact analysis is possible when the receive antennas are located in a single array. However, when the antennas are distributed, the individual links all have different average signal to noise ratio (SNRs) and this is a much more challenging problem. In this paper, we provide approximate distributions for the output SNR of a ZF receiver and the output signal to interference plus noise ratio (SINR) of an MMSE receiver. In addition, simple high SNR approximations are provided for the symbol error rate (SER) of both receivers assuming M-PSK or M-QAM modulations. These high SNR results provide array gain and diversity gain information as well as a remarkably simple functional link between performance and the link powers.

The performance of linear receivers in the presence of co-channel interference (CCI) in Rayleigh channels is a fundamental problem in wireless communications. Performance evaluation for these systems is well-known for receive arrays which are co-located. In contrast, there are almost no analytical results available for macrodiversity systems (such as network MIMO) where both the sources and receive antennas are widely separated. In general, this appears to be an extremely difficult problem. However, progress is possible for the two-user scenario. In this paper, we derive closed form results for the probability density function (pdf) and cumulative distribution function (cdf) of the output signal to interference plus noise ratio (SINR) and signal to noise ratio (SNR) of minimum mean squared error (MMSE) and zero forcing (ZF) receivers in independent Rayleigh channels with arbitrary numbers of receive antennas. The results are verified by Monte Carlo simulations. The results enable further system analysis such as the evaluation of outage probabilities, bit error rate (BER) and capacity.

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.

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.

The prospect of base station cooperation has led to increased interest in macrodiversity systems, where both sources and receive antennas are geographically distributed. In this scenario, little is known about channel capacity since the channel matrices have a very general form where each path may have a different power. Hence, in this paper we consider the ergodic sum capacity of a macrodiversity MIMO system with arbitrary numbers of sources and antennas operating over Rayleigh fading channels. For this system, we compute a compact approximation to ergodic sum capacity, which is shown to be very accurate over a wide range of cases. Finally, we develop a highly simplified upper-bound which leads to insights into the relationship between capacity and the channel powers.

Multi-user downlink MIMO communication has the potential to increase throughput using efficient beamforming. However, the precoding criteria assume perfect knowledge of the beamforming matrices at the base station (BS). This requires a user to transmit its complete channel information to the BS, a task that entails significant overhead. Limited feedback precoding, a part of LTE standardization now, needs only limited information be fed back to the BS. This paper studies the capacity loss incurred by using LTE codebooks, under different power allocation schemes with varying degrees of optimality. The sub-optimal power allocation schemes also ensure a better throughput-fairness trade-off. It is observed that using LTE codebooks results in a significant loss and that there is a need to develop codebooks which offer better adaptation to channel variations.

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.

This paper investigates the following general problem relating to ordered random processes: givennindependent but not necessarily identical random processes, how frequently, on average, does any given process become one of thepth (p=1,2,...,n-1) largest processes? This is a fundamental problem arising in the design and analysis of contemporary multidimensional wireless communication systems (e.g., multiantenna, multiuser) employing opportunistic selection. We formulate this problem as one involving the level crossing rate (LCR) of a carefully defined ordered random process across the zero threshold, which we solve by developing a new mathematical framework based on the theory of permanents. For the case where the processes correspond to time-varying Rayleigh fading channels, we present exact closed-form formulas for the LCR, simplified tight upper bounds, as well as asymptotic results fornandpapproaching infinity but with fixed ratio. These results reveal interesting fundamental limits for the LCR, and are shown to given meaningful insight even for small values ofnandp. We further use our mathematical framework to characterize the required per-branch and overall switching rate of a generalized selection combining diversity receiver, allowing for different average powers for each branch. With the aid of majorization theory, we demonstrate that the overall switching rate is maximized when the power delay profile is uniform.

The performance of linear receivers in the presence of co-channel interference in Rayleigh channels is a fundamental problem in wireless communications. Performance evaluation for these systems is well-known for receive arrays where the antennas are close enough to experience equal average SNRs from a source. In contrast, almost no analytical results are available for macrodiversity systems where both the sources and receive antennas are widely separated. Here, receive antennas experience unequal average SNRs from a source and a single receive antenna receives a different average SNR from each source. Although this is an extremely difficult problem, progress is possible for the two-user scenario. In this paper, we derive closed form results for the probability density function (pdf) and cumulative distribution function (cdf) of the output signal to interference plus noise ratio (SINR) and signal to noise ratio (SNR) of minimum mean squared error (MMSE) and zero forcing (ZF) receivers in independent Rayleigh channels with arbitrary numbers of receive antennas. The results are verified by Monte Carlo simulations and approximations and high SNR analysis are also derived. The results enable further system analysis such as the evaluation of outage probability, bit error rate (BER) and capacity.

This paper focuses on the relay selection problem in amplify-and-forward (AF) cooperative communication with full-duplex (FD) operation. Different relay selection schemes assuming the availability of different instantaneous information are studied. We consider optimal relay selection that maximizes the instantaneous FD channel capacity and requires global channel state information (CSI) as well as several sub-optimal relay selection policies that utilize partial CSI knowledge such as a) source-relay and relay-destination links b) loop interference c) source-relay links and loop interference. To facilitate comparison, exact outage probability expressions and asymptotic approximations of these policies that show a zero diversity order are derived. In addition, an optimal relay selection procedure that incorporates a hybrid relaying strategy, which dynamically switches between FD and half-duplex relaying according to the instantaneous CSI, is also investigated.

This paper analyzes the exact average symbol error rate (SER) performance of beamforming in spatially correlated multiple-input single output (MISO) systems with channel estimation error and feedback delay. We derive the joint distribution function of two quadratic forms and employ the result to obtain an expression for the cumulative distribution function (cdf) of the received signal-to-noise ratio (SNR). Using this cdf expression, we investigate the exact SER applicable for a large number of modulation schemes. The results show that the average SER performance is sensitive to feedback delay, channel estimation and spatial correlation at the transmitter. Furthermore, feedback delay causes an error floor and has the most degrading impact on performance. We also present Monte Carlo simulation results as verification of our analytical results.

Given n independent but not necessarily identical random processes, this paper investigates the general problem of determining how frequently, on average, any given process becomes at least the p-th (p = 1, 2, . . . , n - 1) largest among all processes. This problem requires determining the level crossing rate (LCR) of a carefully defined ordered process, which we solve by developing a general mathematical framework based on the theory of permanents. Our results are very general and may be applicable for a wide range of engineering applications which involve ordered random processes. To demonstrate the applicability to wireless communications, we present closed-form formulas for the LCR for the case where the processes correspond to time-varying Rayleigh fading channels, and use these to characterize the required switching rate for a particular branch of a generalized selection combining diversity receiver.

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.

This paper analyzes the exact average symbol error rate (SER), outage probability and ergodic capacity performance of beamforming in spatially correlated multiple-input single output systems with channel estimation error and feedback delay. We derive the joint distribution function of two correlated quadratic forms and employ the result to obtain expressions for the cumulative distribution function, probability density function, moment generating function and moments of the signal-to-noise ratio. Using these expressions, we investigate the exact SER applicable for a large number of modulation schemes, outage probability and the ergodic capacity of the system. The results show that the average SER performance is sensitive to both feedback delay, channel estimation and spatial correlation at the transmitter. Furthermore, feedback delay causes an error floor and has the most degrading impact on performance. We also present Monte Carlo simulation results as verification of our analytical results.

In this paper, we propose two solutions to the problem of joint transmit-receive antenna selection in a multiple-input multiple-output (MIMO) cognitive radio (CR) system. Our objective is to maximize CR data rates and satisfy interference constraints at the primary user (PU) receiver(s). In the first we approximate the original non-convex optimization problem using an iterative approach solving a series of smaller convex problems. Second we present a novel, norm-based transmit receive antenna selection technique that simultaneously improves throughput while maintaining the PU interference constraints. We show that this approach yields near optimal results with massive complexity reductions. We make a performance comparison between the proposed approaches and the optimal exhaustive search approach. We provide an analysis of the exhaustive search and relate selection gains to system parameters such as the shadow fading standard deviation, the path loss exponent and the number of PUs per square kilometer. Our results establish that antenna selection is a promising option for future MIMO CR devices in sparse PU environments.

We consider the effects of the frequency variation of frequency selective fading channels on adaptive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The magnitude of this variation has important effects on system performance and design as well as applications to temporal variation, feedback delay and channel estimation.We first examine the variation of the eigenvalues and eigenvalue sums across the frequency bins of a MIMO OFDM system focusing on the changes in the ordered eigenvalues and the eigenvalue sum or link gain between two distinct frequency bins. Here we derive distributions and moments for changes in the link gain and maximum eigenvalue and autocorrelation functions for the link gain and maximum eigenvalue as well as simple approximate results for the ordered eigenvalue differences. We then consider variations in performance via the level crossing rates (LCRs) of the bit error rates (BERs) across the frequency bins of the MIMO OFDM system operating over a Rayleigh fading channel. Each eigenmode constitutes a random process in the frequency domain and we compute the LCR for the BER of transmission down the eigenchannels of the MIMO OFDM channel. We finally verify our analysis using Monte Carlo simulations.

Antenna selection schemes offer a good complexity versus performance tradeoff for amplify-and-forward (AF) relay network implementation. In this paper, we consider a dual-hop channel state information assisted AF relay network with a direct source-destination link and investigate the performance of two antenna selection schemes (one optimal and another suboptimal). We derive analytical expressions for the systems' rate outage probabilities and the average bit error rate (BER) that match perfectly with simulation based results in the medium to high signal-to-noise ratio (SNR) regimes. We also investigate the channel capacity of the two schemes by deriving tight upper bounds. In order to gain further insights, simple high SNR approximations for the outage probability and the average BER have also been developed. Our theoretical analysis shows that the performance gap between the optimal and suboptimal schemes largely diminishes in the high SNR regime by increasing the number of antennas at the source. Since the suboptimal scheme has a near optimal performance as well as low signaling overhead compared to the optimal scheme, it seems to be a promising solution for implementing future cellular networks expecting to support relay based communications.

The standard condition number (SCN) is a fundamental metric in the context of multiple-input multiple-output communication systems, linear detection and classical linear algebra. Hence, in this paper we propose a novel generic framework for the SCN distribution of three different classes of Wishart matrices which leads to new results and insights. In particular, our analysis covers both central and non-central Wishart distributions of arbitrary dimension and therefore is applicable to uncorrelated/semi-correlated Rayleigh fading and Ricean fading scenarios. For the special case of dual semi-correlated central Wishart matrices, we derive exact and asymptotic polynomial expressions for the SCN distributions. All analytical results are validated via Monte-Carlo simulations with the attained accuracy being excellent in all cases. The impact of the model parameters on channel conditioning is also investigated in detail.

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.

With the ever increasing interest in multiple-input multiple-output (MIMO) cognitive radio (CR) systems, reducing the costs associated with RF-chains at the radio front end becomes a very important factor. In this paper, we propose two solutions to the problem of joint transmit-receive antenna selection with the objective of maximizing data rates and satisfying interference constraints at the primary user (PU) receiver. In the first method we approximate the original non-convex optimization problem with an iterative way of solving a series of smaller convex problems. Then we present a novel, norm-based transmit receive antenna selection technique that simultaneously improves throughput while maintaining the PU interference constraints. We show that this simple approach yields near optimal results with massive complexity reductions. In addition to making a performance comparison between the proposed approaches and the optimal exhaustive search approach, we establish that antenna selection is a promising option for future MIMO CR devices.

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.

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multiple-output (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading.

In this paper we consider the capacity of the cognitive radio (CR) channel in different fading environments under a "low interference regime". First we derive the probability that the "low interference regime" holds under shadow fading as well as Rayleigh and Rician fast fading conditions. We demonstrate that this is the dominant case, especially in certain practical CR deployment scenarios. The capacity of the CR channel depends critically on a power loss parameter, ¿, which governs how much transmit power the CR dedicates to relaying the primary message. We derive a simple, accurate approximation to ¿ in Rayleigh and Rician fading environments which gives considerable insight into system capacity. We also investigate the effects of system parameters and propagation environment on ¿ and the CR capacity. In all cases, the use of the approximation is shown to be extremely accurate.

The future deployment of cognitive radios (CRs) is critically dependent on the fact that the incumbent primary user (PU) system must remain as oblivious as possible to their presence. This in turn heavily relies on the fluctuations of the interfering CR signals. In this letter we compute the level crossing rates (LCRs) of the cumulative interference created by the CRs. We derive analytical formulae for the LCRs in Rayleigh and Rician fast fading conditions. We approximate Rayleigh and Rician LCRs using fluctuation rates of gamma and scaled noncentral x2processes respectively. The analytical results and the approximations used in their derivations are verified by Monte Carlo simulations and the analysis is applied to a particular CR allocation strategy.

Cognitive radio design aims to increase spectrum utilization by allowing the secondary users (SUs) to coexist with the primary users (PUs) as long as the interference caused by the SUs to each PU is properly regulated. At the SU, channel state information (CSI) between its transmitter and the PU receiver is used to calculate the maximum allowable SU transmit power to limit the interference. We assume that this PU-SU CSI is imperfect as it is the practical case. In addition to a peak received interference power constraint, an upper limit to the SU transmit power constraint is also considered. We derive a closed-form expression for the mean SU capacity under this scenario. Due to imperfect CSI, the SU can not always satisfy the received peak interference power constraint at the PU and has to back off its transmit power. The resulting capacity loss for the SU is quantified using the cumulative distribution function of the interference at the PU. Additionally, we investigate the impact of CSI quantization. Our results are confirmed through comparison with simulations.

This paper presents an ergodic capacity analysis of an amplify-and-forward multiple-input, multiple-output two-hop system including the source to destination (direct) link. We first derive an expression for the probability density function of an unordered eigenvalue of the system. Then, using this result, a closed form expression for the ergodic capacity of the system is derived. The ergodic capacity expression has one integral that needs to be evaluated numerically. The results produced are valid for all SNR values and for arbitrary numbers of antennas at the source, relay and destination. We also present simulation results to validate our analysis. The results show that the analysis exactly matches the simulations and quantifies the improvements in capacity due to the diversity offered by the direct link.

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.

Single-user, multiuser, and network MIMO performance is evaluated for downlink cellular networks with 12 antennas per site, sectorization, universal frequency reuse, scheduled packet-data, and a dense population of stationary users. Compared to a single-user MIMO baseline system with 3 sectors per site, network MIMO coordination is found to increase throughput by a factor of 1.8 with intra-site coordination among antennas belonging to the same cell site. Intra-site coordination performs almost as well as a highly sectorized system with 12 sectors per site. Increasing the coordination cluster size from 1 to 7 sites increases the throughput gain factor to 2.5.

In real wireless communication environments, it is highly likely that different channels associated with a relay network could experience different fading phenomena. In this paper, we investigate the end-to-end performance of a dual-hop fixed gain relaying system when the source-relay and the relay-destination channels experience Rayleigh/Rician and Rician/Rayleigh fading scenarios respectively. Analytical expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio are derived and used to evaluate the outage probability and the average bit error probability of M-QAM modulations. Numerical and simulation results are presented to illustrate the impact of the Rician factor on the end-to-end performance. Furthermore, these results confirm that the system exhibits an improved performance in a Rician/Rayleigh (source-relay link/relay-destination link) environment compared to a Rayleigh/Rician environment.

In this paper we consider an adaptive modulation system with multiple-input multiple-output (MIMO) antennas in conjunction with orthogonal frequency division multiplexing (OFDM) operating over frequency selective Rayleigh fading environments. In particular, we consider a type of beamforming with a maximum ratio transmission, maximum ratio combining (MRT-MRC) transceiver structure. For this system we derive a central limit theorem for various block-based performance metrics. This motivates an accurate Gaussian approximation to the system data rate and the number of outages per OFDM block. In addition to data rate and outage distributions, we also consider the subcarrier SNR as a random process in the frequency domain and compute level crossing rates (LCRs) and average fade bandwidths (AFBs). Hence, we provide fundamental but novel results for the MIMO OFDM channel. The accuracy of these results is verified by Monte Carlo simulations, and applications to both performance analysis and system design are discussed.

Cognitive radio technology is an innovative radio design concept which aims to increase spectrum utilization by exploiting unused spectrum in dynamically changing environments. By extending previous results, we investigate the capacity gains achievable with this dynamic spectrum approach in asymmetric fading channels. More specifically, we allow the secondary-to- primary and secondary-to-secondary user channels to undergo Rayleigh or Rician fading, with arbitrary link power. In order to compute the capacity, we derive the distributions of ratios of Rayleigh and Rician variables. Compared to the symmetric fading scenario, our results indicate several interesting features of the capacity behaviour under both average and peak received power constraints. Finally, the impact of multiple primary users on the capacity under asymmetric fading has also been studied.

The 17 papers in this special issue focus on MIMO systems and applications: field experience, practical aspects, limitations and challenges. The papers are summarized here.

This communication considers the distribution of the mutual information of frequency-selective spatially uncorrelated Rayleigh fading multiple-input–multiple-output (MIMO) channels. Results are presented for orthogonal frequency-division multiplexing (OFDM)-based spatial multiplexing. New exact closed-form expressions are derived for the variance of the mutual information. In contrast to previous results, our new expressions apply for systems with both arbitrary numbers of antennas and arbitrary-length channels. Simplified expressions are also presented for high and low signal-to-noise ratio (SNR) regimes. The analytical variance results are used to provide accurate analytical approximations for the distribution of the mutual information, and the outage capacity.

In this paper we consider transmit and receive selection methods designed to achieve high channel capacities in a single-user MIMO link. A variety of radio channels are considered, including i.i.d. Rayleigh, correlated Rayleigh and Ricean fading environments. Also considered is the presence of imperfect channel state information (CSI) and a simplified waterfllling scheme. In all cases, we evaluate the performance of optimal selection, simple norm-based selection and other benchmark selection techniques. The major contribution is a general approach to analyzing the capacity of the norm-based selection schemes via a simple power scaling factor. We are able to assess the impact of different channels, imperfect CSI and power allocation using this power scaling factor. Furthermore, the analysis is valid for all scenarios: transmit selection, receive selection and joint transmit-receive selection. Results are shown which compare the capacity performance over a wide range of cases. A notable conclusion is that optimal selection, which is computationally intensive, is outperformed at low signal-to-noise- ratios by the simple norm-based approach with power allocation.

For MIMO broadcast systems the effects of shadowing on the channel capacity and the fairness of the system in sharing the resources amongst multiple users are important issues that need to be addressed. In this paper we consider a variety of capacity-approaching algorithms for MIMO broadcast channels. We compare the performance of these algorithms in terms of their ability to approach the sum-capacity and their fairness in sharing the channel resources amongst the multiple users. We also model distance-based attenuation effects and shadowing, yielding valuable insights into the relative performances of the algorithms under varying SNR conditions. Using a novel approach of mapping the broadcast channel to an "equivalent' single-user channel followed by power scaling, we derive closed-form analytical approximations for the capacity of MIMO broadcast channels. For the more evenly distributed SNR case our approximations are quite accurate, suggesting an analytical lower bound for the well known iterative waterfilling solution. Finally, our Monte Carlo simulations comparing the algorithms point to an inherent tradeoff between sum-capacity and fairness.

In most wireless communications research, the channel models considered experience less severe fading than the classic Rayleigh fading case. In this work, however, we investigate MIMO channels where the fading is more severe. In these environments, we show that the coefficient of variation of the channel amplitudes is a good predictor of the link mutual information, for a variety of models. We propose a novel channel model for severely fading channels based on the complex multivariate t distribution. For this model, we are able to compute exact results for the ergodic mutual information and approximations to the outage probabilities for the mutual information. Applications of this work include wireless sensors, RF tagging, land-mobile, indoor-mobile, ground-penetrating radar, and ionospheric radio links. Finally, we point out that the methodology can also be extended to evaluate the mutual information of a cellular MIMO link and the performance of various MIMO receivers in a cellular scenario. In these cellular applications, the channel itself is not severely fading but the multivariate t distribution can be applied to model the effects of inter-cell interference.

We derive new analytic approximations to the capacity distribution of frequency-selective Rayleigh fading MIMO channels. The results apply specifically to OFDM-based spatial multiplexing. In particular, we present a new closed-form Gaussian approximation which yields very high accuracy in many scenarios. For the low SNR regime, we also present a new simpler closed-form Gamma approximation, which we show to be even more accurate than Gaussian in this case. Our approximations are based on new exact closed-form expressions which we derive for the variance of the mutual information which, in contrast to previous results, apply for systems with both arbitrary numbers of antennas and arbitrary-length channel delay profiles.

The condition number is a well known indicator of the spatial selectivity of a MIMO wireless channel. The objective of this paper is to examine the temporal behavior of this metric using a Markov model construction. Specifically, we have developed two methods to calculate analytically the transition probabilities between Markov states. These methods involve the joint density for the channel eigenvalues at two adjacent time instances and the level crossing rates (LCR) of the condition number. We then use our Markov model to investigate the behavior of dual-mode antenna selection schemes in an i.i.d. Rayleigh fading channel.

This letter provides a comprehensive overview and extension of recent results on outage probabilities and bit-error rates (BER) for optimal combiners in the presence of multiple interferers and additive noise. Desired signal and interferers are subject to flat Rayleigh fading and all channels are independent. In addition to summarizing previous work, this letter also derives the BER for a wider range of modulations than previously considered. We show that previous approximate results on the equal power interferer case where the number of interferers is less than the number of antenna elements can be made exact in a straightforward way. Finally we extend previous work on the single and double interferer case to the general case of arbitrary numbers of interferers.

For a power limited orthogonal frequency-division multiplexing (OFDM) system transmitting a large number N of subcarriers over a Rayleigh-fading channel, the distribution of the instantaneous capacity is shown to be approximately Gaussian. The mean and variance of the approximating distribution are derived. It is also shown that, in the limit as Nrarrinfin, the capacity approaches a constant value equal to the capacity of the infinite-bandwidth Gaussian channel

In this letter, the joint probability density function (PDF) for the eigenvalues of a complex Wishart matrix and a perturbed version of it are derived. The latter version can be used to model channel estimation errors and variations over time or frequency. As an example, the joint PDF is used to calculate the transition probabilities between modulation states in an adaptive MIMO system. This leads to a Markov model for the system. We then use the model to investigate the modulation state entering rates (MSER), the average stay duration (ASD), and the effects of feedback delay on the accuracy of modulation state selection in mobile radio systems. Other applications of this PDF are also discussed.

In this paper we develop a multiple input multiple output (MIMO) channel model and derive its spatial and temporal correlation properties. We present a generalized methodology to derive the spatial correlation when the angles of arrival (AoA) and angles of departure (AoD) are either independent or partly correlated. Our model therefore spans the full range from well-established single ring models, where AoA and AoD are fully correlated to complex industrial channel models where they are uncorrelated. It is shown that first order and second order approximations to the channel give rise to a single- Kroneckermodel and a sum-Kroneckermodel respectively. We compare our model to other MIMO channel models in terms of correlation structure and the ergodic mutual information (EMI) and study the effect of the non-Kronecker correlation structure.

Singular Value Decomposition (SVD) techniques are well-known for providing an elegant transceiver architecture, that can realize the intrinsic spatial links of a MIMO channel. Such a scheme is also referred to as eigen-beamforming or eigenmode transmission. The system performance is, however, closely related to the quality of the channel information at both ends of the link. Hence, we focus on the effect of feedback time delay, which causes the transmitter to use outdated channel information in timevarying fading channels. In this paper, we derive an analytical expression for the instantaneous SINR of eigenmode transmission with a feedback time delay T. Furthermore, this expression implies a novel metric that gauges the system performance sensitivity to time-variations of the steering vectors (eigenvectors of the channel correlation matrix) at the transmitter.

We derive closed-form expressions for the ergodic capacity and symbol error rate (SER) of MIMO beamforming with maximum ratio combining (MRC) receivers in uncorrelated and semi-correlated Rayleigh channels. Our results are exact, finite expressions, applying for arbitrary numbers of antennas, and all SNRs. Based on the analytical results, we examine the effect of spatial correlation on the capacity and SER.

Many channel models for MIMO systems have appeared in the literature. However, with the exception of a few recent results, they are largely focussed on two dimensional (2D) propagation, i.e., propagation in the horizontal plane, and the impact of elevation angle is not considered. The assumption of 2D propagation breaks down when in some propagation environments the elevation angle distribution is significant. Consequently, the estimation of ergodic capacity assuming a 2D channel coefficient alone can lead to erroneous results. In this paper, for cross polarized channels, we define a composite channel model and channel coefficient that takes into account both 2D and 3D propagation. Using this composite channel coefficient we assess the ergodic channel capacity and discuss its sensitivity to a variety of different azimuth and elevation power distributions and other system parameters.

In this paper we consider transmit and receive selection methods designed to achieve high channel capacities in a single-user MIMO link. A variety of radio channels are considered, including i.i.d. Rayleigh, correlated Rayleigh and Ricean fading environments. Also considered is the presence of imperfect channel state information (CSI) and a simplified waterfilling scheme. In all cases, we evaluate the performance of optimal selection, simple norm based selection and other benchmark selection techniques. The major contribution is a general approach to analyzing the capacity of the selection schemes via a simple power scaling factor. We are able to assess the impact of different channels, imperfect CSI and power allocation using this power scaling factor. Furthermore, the analysis is valid for all scenarios: transmit selection, receive selection and joint transmit-receive selection. Results are shown which compare the capacity performance over a wide range of cases. A notable conclusion is that optimal selection, which is computationally intensive, is outperformed at low SNR by the simple, norm based approach with power allocation.

Given digital transmission over two correlated Rician fading channels, we present a readily calculable expression for a tight approximation to the correlation between the probabilities of symbol error on each channel. For the Rayleigh fading channel the expression is exact. This correlation expression has applications in error performance analysis of fading systems, particularly multichannel systems and Markov modelling of error events. As an example we use these expressions to bound the block error rate of an OFDM system

This paper presents new statistical properties of complex noncentral matrix-variate quadratic forms. In contrast to previous results, the expressions do not involve infinite sums over partitions, or matrix-variate polynomials, and are easily and efficiently computable. These properties are used to derive new upper and lower bounds on the ergodic mutual information of double-sided correlated Rician MIMO channels with arbitrary-rank channel mean matrices. The bounds are shown to be tighter than previous reported bounds in the literature

In this paper, we are interested in evaluating the probability of adaptation error (PAE) in MIMO systems using adaptive modulation or transmission rate. We attack the problem from two distinct perspectives. Firstly, for a certain rate-feedback system, the PAE is computed by building a Markov model for the channel capacity. The transition probabilities between rate states during the feedback period are approximated using a novel analytical result for the level crossing rate (LCR) of MIMO capacity. Secondly, the impact of channel estimation error on adaptive modulation over eigenmodes is considered. By utilizing the joint dynamic statistics of the eigenvalues, the instantaneous probabilities of choosing inappropriate modulation schemes can be calculated

Fourth-generation (4G) systems are expected to support data rates of the order of 100 Mb/s in the outdoor environment and 1 Gb/s in the indoor/stationary environment. In order to support such large payloads, the radio physical layer must employ receiver algorithms that provide a significant increase in spectrum efficiency (and, hence, capacity) over current wireless systems. Recently, an explosion of multiple-input-multiple-output (MIMO) studies have appeared with many journals presenting special issues on this subject. This has occurred due to the potential of MIMO to provide a linear increase in capacity with antenna numbers. Environmental considerations and tower loads will often restrict the placing of large antenna spans on base stations (BSs). Similarly, customer device form factors also place a limit on the antenna numbers that can be placed with a mutual spacing of 0.5 wavelength. The use of cross-polarized antennas is widely used in modern cellular installations as it reduces spacing needs and tower loads on BSs. Hence, this approach is also receiving considerable attention in MIMO systems. In order to study and compare various receiver architectures that are based on MIMO techniques, one needs to have an accurate knowledge of the MIMO channel. However, very few studies have appeared that characterize the cross-polarized MIMO channel. Recently, the third-generation partnership standards bodies (3GPP/3GPP2) have defined a cross-polarized channel model for MIMO systems but this model neglects the elevation spectrum. In this paper, we provide a deeper understanding of the channel model for cross-polarized systems for different environments and propose a composite channel impulse model for the cross-polarized channel that takes into account both azimuth and elevation spectrum. We use the resulting channel impulse response to derive closed-form expressions for the spatial correlation. We also present models to describe the dependence of cross-polarization discrimination (XPD) on distance, azimuth and elevation and delay spread. In addition, we study the impact of array width, signal-to-noise ratio, and antenna slant angle on the mutual information (MI) of the system. In particular, we present an analytical model for large system mean mutual information values and consider the impact of elevation spectrum on MI. Finally, the impact of multipath delays on XPD and MI is also explored.

This paper presents asymptotic bounds and limits for the mean channel capacity of MIMO systems under Ricean channel conditions. It is shown that the mean capacity per dimension decreases as the K factor increases in value and approaches a value equal to that of the underlying scattering channel when the number of antennas are large and the specular matrix has unit rank. The accuracy of the bounds is verified by simulations. In addition, a variety of results for the MIMO Ricean channel are brought together to give an overview of the current knowledge in this area. We also show that the variance of the capacity for a Ricean channel approaches that of the scattering channel for large numbers of antennas

In this paper we present an approximate closed form solution for dimensioning mixed service 3G wireless networks for defined service and quality constraints. Both Web-browsing services alone, as well as a mixture of Web and circuit voice services are considered. Dimensioning is achieved through knowledge of the distribution of the latency delay experienced by end users of the 3G network. The parameters defining the distribution are shown to be dependent on a range of network and service parameters. This allows the dimensioning of 3G wireless networks under a wide range of quality and service conditions.

In this paper we derive a generalized method to compute the error probabilities of singular value decomposition-based receivers for a MIMO system with uncoded transmission. The method can be used for a wide class of flat fading environments, including i.i.d. and semi-correlated Rayleigh and i.i.d. Ricean channels. Although we apply the method to equal-power BPSK, it can easily be extended to higher order M-PSK and M-QAM signal constellations and adaptive "water-filling" schemes. The error probability curves derived from closed-form formulas and simulations demonstrate very close agreement. We also compare the error performances of CI, MMSE and ZF receivers with the SVD receiver.

MIMO systems using adaptive transmission down the eigenchannels require the level crossing rate of the eigenvalues to compute adaptation rates and possibly feedback rates. Examples of such systems include MIMO systems using singular value decomposition (SVD) transmission. Similarly, the average fade durations of the eigenvalues give the average length of time that a particular constellation is used in adaptive modulation. Other systems which require the minimum eigenvalue to be above a certain threshold (for example, channel inversion) can also use these level crossing rates in system analysis. Hence, in this paper we derive approximate level crossing rates for the eigenvalues in the baseline case of an uncorrelated Rayleigh fading channel. Our results are remarkably accurate and compact and further improvements are also discussed.

This paper presents asymptotic bounds and limits for the ergodic channel capacity of MIMO systems under Ricean channel conditions. It is shown that the ergodic capacity per dimension decreases as the K factor increases in value and approaches a value equal to that of the underlying scattering channel when the number of antennas is large. The accuracy of the hounds is verified by simulations. In addition, a variety of results for the MIMO Ricean channel are brought together to give an overview of the current knowledge in this area.

In recent years there have been a proliferation of channel models suggested for MIMO systems. In this paper we take a look at the impact of model complexity on channel behaviour and on performance measures of systems operating in these channels. In particular we investigate whether large increases in channel complexity are justified or if simple models will lead to similar results and conclusions. We take the simplest channel model, which gives both spatial and temporal correlation, and compare it to a complex industrial model developed by the 3GPP. We compare the two models in terms of the spatial and temporal correlation of the channel. In addition, we look at the temporal correlation level crossing rate and average fade duration of the link capacity in these channels. This gives us an opportunity to assess the impact of channel differences on a performance measure of interest.

In this letter, we derive the exact variance of the capacity of a multiple-input multiple-output (MIMO) system. This enables an investigation of the accuracy of a Gaussian approximation to the capacity foreshadowed by various central limit theorems. We confirm recent results which state that the capacity variance appears to converge to a limit independent of absolute antenna numbers, but dependent on the ratio of the numbers of receive to transmit antennas. The Gaussian approximation itself is surprisingly good, even in the worst cases giving satisfactory results.

It is well known that MIMO systems offer the promise of achieving very high spectrum efficiencies (many tens of bits/Hz) in a mobile environment. The gains in MIMO capacity are sensitive to the presence of spatial and temporal correlation introduced by the radio environment. In this paper we examine how MIMO capacity is influenced by a number of factors, e.g.: a) temporal correlation, b) various combinations of low/high spatial correlations at either end, c) combined spatial and temporal correlations, In all cases we compare the channel capacity that would be achievable under independent fading. We investigate the behaviour of "capacity fades", examine how often the capacity experiences the fades, develop a method to determine level crossing rates and average data durations and relate these to antenna numbers.

This paper presents an overview of progress in the area of multiple input multiple output (MIMO) space-time coded wireless systems. After some background on the research leading to the discovery of the enormous potential of MIMO wireless links, we highlight the different classes of techniques and algorithms proposed which attempt to realize the various benefits of MIMO including spatial multiplexing and space-time coding schemes. These algorithms are often derived and analyzed under ideal independent fading conditions. We present the state of the art in channel modeling and measurements, leading to a better understanding of actual MIMO gains. Finally, the paper addresses current questions regarding the integration of MIMO links in practical wireless systems and standards.

The primary contribution of this work lies in the derivation of the exact characteristic function (and hence, the mean and variance) of the capacity of multiple-input multiple-output (MIMO) systems for semicorrelated flat-fading channels. A Gaussian approximation to the exact capacity results is suggested and evaluated for its accuracy. We show that over a range of correlation levels this approximation is adequate even for moderate numbers of transmit and receive antennas.

We consider the capacity of a single user t /spl rarr/ /spl tau/ MIMO wireless system in a Rayleigh or Ricean fading environment. It is known that a certain central limit theorem exists which states (under certain conditions) that the distribution of the standardized capacity is asymptotically Gaussian as r /spl rarr/ /spl infin/, t /spl rarr/ /spl infin/ and /spl tau//t /spl rarr/ y for some constant y. However we demonstrate the surprising accuracy of a Gaussian approximation to the capacity for virtually all values of /spl tau/ and t. In order to investigate the accuracy of the Gaussian fit we derive the variance of the capacity in the Rayleigh fading case.

We derive an exact closed-form solution for the reliability of an ideal M-branch MMSE (minimum mean-squared error) diversity combiner operating in a Rayleigh-fading channel with N interferers, each having some specified average power. The reliability is defined as the probability, taken over fading of the desired and interfering signals, that the combiner's output signal-to-interference ratio (SINR) is greater than some specified threshold. This kind of metric is important in evaluating the potential capacity improvements of using diversity combining and adaptive array processing in interference-limited wireless systems. Our result is remarkably simple, fast, straightforward to compute, and numerically stable. We show a set of special cases, which relate to standard results and reveal valuable insights into how this type of array processing operates in interference-limited environments. We also present a set of numerical examples, which show that our calculated reliabilities agree with estimates from Monte Carlo simulation.

Importance sampling (IS) is a simulation technique which aims to reduce the variance (or other cost function) of a given simulation estimator. In communication systems, this usually, but not always, means attempting to reduce the variance of the bit error rate (BER) estimator. By reducing the variance, IS estimators can achieve a given precision from shorter simulation runs; hence the term "quick simulation." The idea behind IS is that certain values of the input random variables in a simulation have more impact on the parameter being estimated than others. If these "important" values are emphasized by sampling more frequently, then the estimator variance can be reduced. Hence, the basic methodology in IS is to choose a distribution which encourages the important values. This use of a "biased" distribution will, of course, result in a biased estimator if applied directly in the simulation. However, there is a simple procedure whereby the simulation outputs are weighted to correct for the use of the biased distribution, and this ensures that the new IS estimator is unbiased. Hence, the "art" of designing quick simulations via IS is entirely dependent on the choice of biased distribution. Over the last 50 years, IS techniques have flourished, but it is only in the last decade that coherent design methods have emerged. The outcome of these developments is that at the expense of increasing technical content, modern techniques can offer substantial run-time saving for a very broad range of problems. We present a comprehensive history and survey of IS methods. In addition, we offer a guide to the strengths and weaknesses of the techniques, and hence indicate which techniques are suitable for various types of communications systems. We stress that simple approaches can still yield useful savings, and so the simulation practitioner as well as the technical researcher should consider IS as a possible simulation tool.

Study Group XIII of the ITU-TS has recently approved a new performance recommendation G.826 which the ITU-R has recommended as a standard for satellite systems in recommendation S.1062. G.826 establishes guidelines on the performance levels of digital systems operating at or above primary rate. These performance levels are stated in terms of block error rates. We discuss the impact of the block-based error performance objectives on the performance of transport systems. However, the impact of G.826 is difficult to evaluate directly since the performance recommendations are not given in terms of bit-error rate (BER) values. Hence, we present a procedure to convect block error rates to BER. This conversion is based on the statistical modeling of the error process and includes an analysis of bursty errors as well as random errors. Rather than using the equivalent BER values as simple thresholds, we produce BER against time distributions which satisfy G.826 and can be used as masks for a comparison with measured data and also for route design. It is shown that these masks are a crucial tool in any study of G.826 and contain useful information for system design and planning. Indeed it is shown that false conclusions can be drawn if the masks are not used. Finally, the impact of G.826 is discussed with particular reference to apportionment strategies, system margins, signal processing, and error correction schemes.

We review the work on optical heterodyne binary-DPSK systems. In particular we show why the study of these systems has been so challenging and discuss the techniques which have been developed to analyse the standard DPSK receiver. Next we describe the methods used to develop and analyse improved receiver structures and comment on the impact of improved performance and lowered error rate floors. We discuss the work on suboptimal receivers and outline the current state of the search for a truly optimal receiver. This work include a considerable discussion of the modeling and analysis of laser phase noise since it is this noise which makes the study of coherent optical systems so complex. We describe the historical development of this work from early approximate techniques to the accurate approaches currently emerging in the literature. We also evaluate the contributions made and outline their strengths, weaknesses and areas of use.>

The author presents some numerical methods for the calculation of the distribution functions of certain random geometric series. The semicontraction mapping approach of A. Huzii and H. Sugiyama (Electron. Commun. Jap.., vol.53-A, p.21-30, 1970) is generalized to give a convergent solution for most cases of interest. Also, initial approximations are discussed based on the moments of the distribution. In particular, the normal approximation seems a useful candidate since it is easy to construct. An alternative technique is outlined based on the Fourier transforms of the density functions. This approach seems to be particularly useful when accurate results are required.>