We provide an overview of the extensive results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For time-varying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for single-user MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends on the available channel information at either the receiver or transmitter, the channel signal-to-noise ratio, and the correlation between the channel gains on each antenna element. We then focus attention on the capacity region of the multiple-access channels (MACs) and the largest known achievable rate region for the broadcast channel. In contrast to single-user MIMO channels, capacity results for these multiuser MIMO channels are quite difficult to obtain, even for constant channels. We summarize results for the MIMO broadcast and MAC for channels that are either constant or fading with perfect instantaneous knowledge of the antenna gains at both transmitter(s) and receiver(s). We show that the capacity region of the MIMO multiple access and the largest known achievable rate region (called the dirty-paper region) for the MIMO broadcast channel are intimately related via a duality transformation. This transformation facilitates finding the transmission strategies that achieve a point on the boundary of the MIMO MAC capacity region in terms of the transmission strategies of the MIMO broadcast dirty-paper region and vice-versa. Finally, we discuss capacity results for multicell MIMO channels with base station cooperation. The base stations then act as a spatially diverse antenna array and transmission strategies that exploit this structure exhibit significant capacity gains. This section also provides a brief discussion of system level issues associated with MIMO cellular. Open problems in this field abound and are discussed throughout the paper.

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Capacity limits of MIMO channels

Spatial modulation (SM) is a recently developed transmission technique that uses multiple antennas. The basic idea is to map a block of information bits to two information carrying units: 1) a symbol that was chosen from a constellation diagram and 2) a unique transmit antenna number that was chosen from a set of transmit antennas. The use of the transmit antenna number as an information-bearing unit increases the overall spectral efficiency by the base-two logarithm of the number of transmit antennas. At the receiver, a maximum receive ratio combining algorithm is used to retrieve the transmitted block of information bits. Here, we apply SM to orthogonal frequency division multiplexing (OFDM) transmission. We develop an analytical approach for symbol error ratio (SER) analysis of the SM algorithm in independent identically distributed (i.i.d.) Rayleigh channels. The analytical and simulation results closely match. The performance and the receiver complexity of the SM-OFDM technique are compared to those of the vertical Bell Labs layered space-time (V-BLAST-OFDM) and Alamouti-OFDM algorithms. V-BLAST uses minimum mean square error (MMSE) detection with ordered successive interference cancellation. The combined effect of spatial correlation, mutual antenna coupling, and Rician fading on both coded and uncoded systems are presented. It is shown that, for the same spectral efficiency, SM results in a reduction of around 90% in receiver complexity as compared to V-BLAST and nearly the same receiver complexity as Alamouti. In addition, we show that SM achieves better performance in all studied channel conditions, as compared with other techniques. It is also shown to efficiently work for any configuration of transmit and receive antennas, even for the case of fewer receive antennas than transmit antennas.

Spatial Modulation

We present an experiment-based characterization of passive suppression and active self-interference cancellation mechanisms in full-duplex wireless communication systems. In particular, we consider passive suppression due to antenna separation at the same node, and active cancellation in analog and/or digital domain. First, we show that the average amount of cancellation increases for active cancellation techniques as the received self-interference power increases. Our characterization of the average cancellation as a function of the self-interference power allows us to show that for a constant signal-to-interference ratio at the receiver antenna (before any active cancellation is applied), the rate of a full-duplex link increases as the self-interference power increases. Second, we show that applying digital cancellation after analog cancellation can sometimes increase the self-interference, and thus digital cancellation is more effective when applied selectively based on measured suppression values. Third, we complete our study of the impact of self-interference cancellation mechanisms by characterizing the probability distribution of the self-interference channel before and after cancellation.

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Experiment-Driven Characterization of Full-Duplex Wireless Systems

Mathematica--A System for Doing Mathematics by Computer.

The automatic recognition of the modulation format of a detected signal, the intermediate step between signal detection and demodulation, is a major task of an intelligent receiver, with various civilian and military applications. Obviously, with no knowledge of the transmitted data and many unknown parameters at the receiver, such as the signal power, carrier frequency and phase offsets, timing information and so on, blind identification of the modulation is a difficult task. This becomes even more challenging in real-world scenarios with multipath fading, frequency-selective and time-varying channels. With this in mind, the authors provide a comprehensive survey of different modulation recognition techniques in a systematic way. A unified notation is used to bring in together, under the same umbrella, the vast amount of results and classifiers, developed for different modulations. The two general classes of automatic modulation identification algorithms are discussed in detail, which rely on the likelihood function and features of the received signal, respectively. The contributions of numerous articles are summarised in compact forms. This helps the reader to see the main characteristics of each technique. However, in many cases, the results reported in the literature have been obtained under different conditions. So, we have also simulated some major techniques under the same conditions, which allows a fair comparison among different methodologies. Furthermore, new problems that have appeared as a result of emerging wireless technologies are outlined. Finally, open problems and possible directions for future research are briefly discussed.

Survey of automatic modulation classification techniques: classical approaches and new trends

The distribution of the local average power at a mobile is usually considered to be lognormal in terrestrial and satellite channels. However, the mathematical form of the lognormal distribution is not convenient for analytic calculations. In this paper, we show the utility of the gamma distribution for shadow fading, in both terrestrial and satellite channels, using empirical data. Furthermore, we show that the application of the gamma model of shadow fading results in closed-form and mathematically-tractable solutions for key system performance measures such as the average symbol error rate of different modulations with a variety of diversity combining techniques.

A Comparative Study of Two Shadow Fading Models in Ultrawideband and Other Wireless Systems

In mobile communications the strength of a line of sight component measured by the K factor of the Ricean received envelope distribution has significant impact on system performance analysis and link budget calculations. In this paper, we study the performance of moment-based estimators for the Ricean K-factor as less complex alternatives to the maximum likelihood estimator. Our asymptotic analysis reveals that the estimators that rely on lower-order moments have a better asymptotic performance for moderate/large values of K. We also illustrate, by Monte Carlo simulations, that the fading correlation among the envelope samples deteriorates the estimator performance. The simplest estimator, which can be expressed in closed form in terms of the second- and fourth-order sample moments offers a good compromise between statistical performance and computational simplicity.

Performance analysis of moment-based estimators for the K parameter of the Rice fading distribution

We introduce a comprehensive statistical characterization of the multipath wireless channel built as a superposition of a number of scattered waves with random phases. We consider an arbitrary number $N$ of specular (dominant) components plus other diffusely propagating waves. Our approach covers the cases on which the specular components have constant amplitudes, as well as when these components experience random fluctuations. These propagation scenarios are found in different use cases of 5G networks, as well as in the context of large intelligent surface based communications. We show that this class of fading models can be expressed in terms of a continuous mixture of an underlying Rician (or Rician shadowed) fading model, averaged over the phase distributions of the specular waves. It is shown that the fluctuations of the specular components have a detrimental impact on performance, and the best performance is obtained when there is only one specular component.

Stochastic Fading Channel Models with Multiple Dominant Specular Components for 5G and Beyond.

In this letter, a novel low-complexity optimal channel estimator using uncorrelated periodic complementary sets of binary sequences is proposed for multiple-input multiple-output (MIMO) intersymbol interference (ISI) channels. The estimator is optimal since it attains the minimum possible Crameacuter-Rao lower bound (CRLB). Moreover, it can be implemented with very low complexity via ASIC/FPGA, which makes it suitable and ready for practical MIMO systems

Low-Complexity Optimal Estimation of MIMO ISI Channels With Binary Training Sequences

In this paper we propose a new shadowed Rice model for land mobile satellite channels. In this model the amplitude of the line-of-sight is characterized by the Nakagami distribution. The model provides closed-form mathematically-tractable expressions for the fundamental channel statistics such as envelope probability density function and envelope-squared moment generating function. The model is very convenient for analytical and numerical performance prediction of complex narrowband and wideband land mobile satellite systems, with different types of uncoded/coded modulations, with or without diversity. Comparison of the new model with published channel data demonstrates the flexibility of the model in characterizing a variety of channel conditions and propagation mechanisms.

Ali Abdi

Papers

A Comparative Study of Two Shadow Fading Models in Ultrawideband and Other Wireless Systems

Performance analysis of moment-based estimators for the K parameter of the Rice fading distribution

Stochastic Fading Channel Models with Multiple Dominant Specular Components for 5G and Beyond.

Low-Complexity Optimal Estimation of MIMO ISI Channels With Binary Training Sequences

A new simple model for land mobile satellite channels