We address the problem of removing specular ground surface reflections and leakage/cross-talk from downward looking stepped frequency ground-penetrating radar (GPR) data. A new model for the ground-bounce and the leakage/cross-talk is introduced. An algorithm that jointly estimates these effects from collected data is presented. The algorithm has the sound foundation of a nonlinear least squares (LS) fit to the presented model. The minimization is performed in a cyclic manner where one step is a linear LS minimization and the other step is a non-linear LS minimization where the optimum can efficiently be found using, e.g., the chirp-transform algorithm. The results after applying the algorithm to measured GPR data, collected at a US army test range, are also shown
A method for the computationally efficient sliding window time-updating of the Capon and APES spectral estimators based on the time-variant displacement structure of the data covariance matrix is presented. The proposed algorithm forms a natural extension of the computationally most efficient algorithm to date, and offers a significant computationalgain as compared to the computational complexity associated with the batch re-evaluation of the spectral estimates for each time-update.
In this paper, we present a computationally efficient sliding window time updating of the Capon and amplitude and phase estimation (APES) matched filterbank spectral estimators based on the time-variant displacement structure of the data covariance matrix. The presented algorithm forms a natural extension of the most computationally efficient algorithm to date, and offers a significant computational gain as compared to the computational complexity associated with the batch re-evaluation of the spectral estimates for each time-update. Furthermore, through simulations, the algorithm is found to be numerically superior to the time-updated spectral estimate formed from directly updating the data covariance matrix.
Simultaneous wireless information and power transfer techniques for multiway massive multiple-input multiple-output (MIMO) relay networks are investigated. By using two practically viable relay receiver designs, namely 1) the power splitting receiver and 2) the time switching receiver, asymptotic signal-to-interference-plus-noise ratio (SINR) expressions are derived for an unlimited number of antennas at the relay. These asymptotic SINRs are then used to derive asymptotic symmetric sum rate expressions in closed form. Notably, these asymptotic SINRs and sum rates become independent of radio frequency-to-direct current (RF-to-DC) conversion efficiency in the limit of infinitely many relay antennas. Moreover, tight average sum rate approximations are derived in closed form for finitely many relay antennas. The fundamental tradeoff between the harvested energy and the sum rate is quantified for both relay receiver structures. Notably, the detrimental impact of imperfect channel state information (CSI) on the MIMO detector/precoder is investigated, and thereby, the performance degradation caused by pilot contamination, which is the residual interference due to nonorthogonal pilot sequence usage in adjacent/cochannel systems, is quantified. The presence of cochannel interference (CCI) can be exploited to be beneficial for energy harvesting at the relay, and consequently, the asymptotic harvested energy is an increasing function of the number of cochannel interferers. Notably, in the genie-aided perfect CSI case, the detrimental impact of CCI for signal decoding can be cancelled completely whenever the number of relay antennas grows without bound. Nevertheless, the pilot contamination severely degrades the sum rate performance even for infinitely many relay antennas.
In this paper we deal with the problem of the joint optimization of the precoders, equalizers and relay beamformer of a multiple-input multiple-output interfering relay channel. This network can be regarded az a generalized model for both one-way and two-way relay channels with/without direct interfering links. Unlike the conventional design procedures, we assume that the Channel State Information (CSI) is not known perfectly. The imperfect CSI is described using the norm bounded error framework. We use a system-wide Sum Mean Square Error (SMSE) based problem formulation which is constrained using the transmit power of the terminals and the relay node. The problem at hand, from a worst-case design perspective, is a multilinear, and hence, a nonconvex problem which is also semiinfinite in its constraints. We use a generalized version of the Peterson’s lemma to handle the semi-infiniteness and reduce the original problem to a single Linear Matrix Inequality (LMI). However, this LMI is not convex, and to resolve this issue we propose an iterative algorithm based on the alternating convex search methodology to solve the aforementioned problem. Finally simulation results, i.e., the convergence of the proposed algorithm and the SMSE properties, are included to asses the performance of the proposed algorithm.
In this paper, we deal with the problem of joint optimization of the source precoder, the relay beamformer and the destination equalizer in a nonregenerative relay network with only a partial knowledge of the Channel State Information (CSI).
We model the partial CSI using a deterministic norm bounded error model, and we use a system-wide mean square error performance measure which is constrained based on the transmit power regulations for both source and relay nodes.
Most conventional designs employ the average performance optimization, however, we solve this problem from a worst-case design perspective.
The original problem formulation is a semi-infinite trilinear optimization problem which is not convex.
To solve this problem we extend the existing theories to deal with the constraints which are semi-infinite in different independent complex matrix variables.
We show that the equivalent approximate problem is a set of linear matrix inequalities, that can be solved iteratively.
Finally simulation results assess the performance of the proposed scheme.
We formally generalize the sign-definiteness lemma to the case of complex-valued matrices and multiple norm-bounded uncertainties. This lemma has found many applications in the study of the stability of control systems, and in the design and optimization of robust transceivers in communications. We then present three different novel applications of this lemma in the area of multi-user multiple-input multiple-output (MIMO) robust transceiver optimization. Specifically, the scenarios of interest are: (i) robust linear beamforming in an interfering adhoc network, (ii) robust design of a general relay network, including the two-way relay channel as a special case, and (iii) a half-duplex one-way relay system with multiple relays. For these networks, we formulate the design problems of minimizing the (sum) MSE of the symbol detection subject to different average power budget constraints. We show that these design problems are non-convex (with bilinear or trilinear constraints) and semiinfinite in multiple independent uncertainty matrix-valued variables. We propose a two-stage solution where in the first step the semi-infinite constraints are converted to linear matrix inequalities using the generalized signdefiniteness lemma, and in the second step, we use an iterative algorithm based on alternating convex search (ACS). Via simulations we evaluate the performance of the proposed scheme.
This paper deals with the problem of discriminating samples that contain only noise from samples that contain a signal embedded in noise. The focus is on the case when the variance of the noise is unknown. We derive the optimal soft decision detector using a Bayesian approach. The complexity of this optimal detector grows exponentially with the number of observations and as a remedy, we propose a number of approximations to it. The problem under study is a fundamental one and it has applications in signal denoising, anomaly detection, and spectrum sensing for cognitive radio. We illustrate the results in the context of the latter.
In this paper, we create a unified framework for spectrum sensing of signals which have covariance matrices with known eigenvalue multiplicities. We derive the generalized likelihood-ratio test (GLRT) for this problem, with arbitrary eigenvalue multiplicities under both hypotheses. We also show a number of applications to spectrum sensing for cognitive radio and show that the GLRT for these applications, of which some are already known, are special cases of the general result.
We point out an error in a derivation in the recent paper [1], and provide a correct and much shorter calculation of the result in question. In passing, we also connect the results in [1] to the literature on array signal processing and on principal component analysis, and show that the main findings of [1] follow as special cases of standard results in these fields.
We consider spectrum sensing of signals encoded with an orthogonal space-time block code (OSTBC). We propose a CFAR detector based on knowledge of the eigenvalue multiplicities of the covariance matrix which are inherent owing to the OSTBC and derive theoretical performance bounds. In addition, we show that the proposed detector is robust to a carrier frequency offset, and propose a detector that deals with timing synchronization using the detector for the synchronized case as a building block. The proposed detectors are shown numerically to perform well.
We consider spectrum sensing of a second-order cyclostationary signal receivedat multiple antennas. The proposed detector exploits both the spatial andthe temporal correlation of the received signal, from knowledge of thefundamental period of the cyclostationary signal and the eigenvaluemultiplicities of the temporal covariance matrix. All other parameters, suchas the channel gains or the noise power, are assumed to be unknown. The proposeddetector is shown numerically to outperform state-of-the-art detectors forspectrum sensing of anOFDM signal, both when using a single antenna and with multiple antennas.
We consider spectrum sensing of OFDM signals in an AWGN channel. For the case of completely unknown noise and signal powers, we derive a GLRT detector based on empirical second-order statistics of the received data. The proposed GLRT detector exploits the non-stationary correlation structure of the OFDM signal and does not require any knowledge of the noise power or the signal power. The GLRT detector is compared to state-of-the-art OFDM signal detectors, and shown to improve the detection performance with 5 dB SNR in relevant cases.
For the case of completely known noise power and signal power, we present a brief derivation of the optimal Neyman-Pearson detector from first principles. We compare the optimal detector to the energy detector numerically, and show that the energy detector is near-optimal (within 0.2 dB SNR) when the noise variance is known. Thus, when the noise power is known, no substantial gain can be achieved by using any other detector than the energy detector.
We consider spectrum sensing of OFDM signals in an AWGN channel. For the case of completely known noise and signal powers, we set up a vector-matrix model for an OFDM signal with a cyclic prefix and derive the optimal Neyman-Pearson detector from first principles. The optimal detector exploits the inherent correlation of the OFDM signal incurred by the repetition of data in the cyclic prefix, using knowledge of the length of the cyclic prefix and the length of the OFDM symbol. We compare the optimal detector to the energy detector numerically. We show that the energy detector is near-optimal (within 1 dB SNR) when the noise variance is known. Thus, when the noise power is known, no substantial gain can be achieved by using any other detector than the energy detector.
For the case of completely unknown noise and signal powers, we derive a generalized likelihood ratio test (GLRT) based onempirical second-order statistics of the received data. The proposed GLRT detector exploits the non-stationary correlation structure of the OFDM signal and does not require any knowledge of the noise power or the signal power. The GLRT detector is compared to state-of-the-art OFDM signal detectors, and shown to improve the detection performance with 5 dB SNR in relevant cases.
We consider detection of signals encoded with orthogonal space-time block codes (OSTBC), using multiple receive antennas. Such signals contain redundancy and they have a specific structure, that can be exploited for detection. We derive the optimal detector, in the Neyman-Pearson sense, when all parameters are known. We also consider unknown noise variance, signal variance and channel coefficients. We propose a number of GLRT based detectors for the different cases, that exploit the redundancy structure of the OSTBC signal. We also propose an eigenvalue-based detector for the case when all parameters are unknown. The proposed detectors are compared to the energy detector. We show that when only the noise variance is known, there is no gain in exploiting the structure of the OSTBC. However, when the noise variance is unknown there can be a significant gain.
In this work, we consider spectrum sensing of Gaussian signals with structured covariance matrices. We show that the optimal detector based on the probability distribution of the sample covariance matrix is equivalent to the optimal detector based on the raw data, if the covariance matrices are known. However, the covariance matrices are unknown in general. Therefore, we propose to estimate the unknown parameters using covariance matching estimation techniques (COMET). We also derive the optimal detector based on a Gaussian approximation of the sample covariance matrix, and show that this is closely connected to COMET.
Cognitive radio is a new concept of reusing a licensed spectrum in an unlicensed manner. The motivation for cognitive radio is various measurements of spectrum utilization, that generally show unused resources in frequency, time and space. These "spectrum holes" could be exploited by cognitive radios. Some studies suggest that the spectrum is extremely underutilized, and that these spectrum holes could provide ten times the capacity of all existing wireless devices together. The spectrum could be reused either during time periods where the primary system is not active, or in geographical positions where the primary system is not operating. In this paper, we deal primarily with the concept of geographical reuse, in a frequency-planned primary network. We perform an analysis of the potential for communication in a geographical spectrum hole, and in particular the achievable sum-rate for a secondary network, to some order of magnitude. Simulation results show that a substantial sum-rate could be achieved if the secondary users communicate over small distances. For a small number of secondary links, the sum-rate increases linearly with the number of links. However, the spectrum hole gets saturated quite fast, due to interference caused by the secondary users. A spectrum hole may look large, but it disappears as soon as someone starts using it.
This paper considers approximations of marginalization sums thatarise in Bayesian inference problems. Optimal approximations ofsuch marginalization sums, using a fixed number of terms, are analyzedfor a simple model. The model under study is motivated byrecent studies of linear regression problems with sparse parametervectors, and of the problem of discriminating signal-plus-noise samplesfrom noise-only samples. It is shown that for the model understudy, if only one term is retained in the marginalization sum, thenthis term should be the one with the largest a posteriori probability.By contrast, if more than one (but not all) terms are to be retained,then these should generally not be the ones corresponding tothe components with largest a posteriori probabilities.
In this paper we deal with spoofing detection in GNSS receivers. We derive the optimal genie detector when the true positions are perfectly known, and the observation errors are Gaussian, as a benchmark for other detectors. The system model considers three dimensional positions, and includes correlated errors. In addition, we propose several detectors that do not need any position knowledge, that outperform recently proposed detectors in many interesting cases.
We present a survey of state-of-the-art algorithms for spectrum sensing in cognitive radio. The algorithms discussed range from energy detection to sophisticated feature detectors. The feature detectors that we present all have in common that they exploit some known structure of the transmitted signal. In particular we treat detectors that exploit cyclostationarity properties of the signal, and detectors that exploit a known eigenvalue structure of the signal covariance matrix. We also consider cooperative detection. Specifically we present data fusion rules for soft and hard combining, and discuss the energy efficiency of several different sensing, sleeping and censoring schemes in detail.
The ever-increasing demand for higher data rates in wireless communications in the face of limited or underutilized spectral resources has motivated the introduction of cognitive radio. Traditionally, licensed spectrum is allocated over relatively long time periods and is intended to be used only by licensees. Various measurements of spectrum utilization have shown substantial unused resources in frequency, time, and space [1], [2]. The concept behind cognitive radio is to exploit these underutilized spectral resources by reusing unused spectrum in an opportunistic manner [3], [4]. The phrase cognitive radio is usually attributed to Mitola [4], but the idea of using learning and sensing machines to probe the radio spectrum was envisioned several decades earlier (cf., [5]).
The computational complexity of optimum decoding for an orthogonal space-time block code is quantified. Four equivalent techniques of optimum decoding which have the same computational complexity are specified. Modifications to the basic formulation in special cases are calculated and illustrated by means of examples.
The computational complexity of optimum decoding for an orthogonal space-time block code {cal G}_N satisfying {cal G}_N^H{cal G}_N=c(∑_{k=1}^Kos_ko^2)I_N where c is a positive integer is quantified. Four equivalent techniques of optimum decoding which have the same computational complexity are specified. Modifications to the basic formulation in special cases are calculated and illustrated by means of examples. This paper corrects and extends and unifies them with the results from the literature. In addition, a number of results from the literature are extended to the case c>1.
We present a survey of some recent developments for decompositions of multi-way arrays or tensors, with special emphasis on results relevant for applications and modeling in signal processing. A central problem is how to find lowrank approximations of tensors, and we describe some new results, including numerical methods, algorithms and theory, for the higher order singular value decomposition (HOSVD) and the parallel factors expansion or canonical decomposition (CP expansion).
Tensor modeling and algorithms for computing various tensor decompositions (the Tucker/HOSVD and CP decompositions, as discussed here, most notably) constitute a very active research area in mathematics. Most of this research has been driven by applications. There is also much software available, including MATLAB toolboxes [4]. The objective of this lecture has been to provide an accessible introduction to state of the art in the field, written for a signal processing audience. We believe that there is good potential to find further applications of tensor modeling techniques in the signal processing field.
Massive MIMO-systems have received considerable attention in recent years as an enabler in future wireless communication systems. As the idea is based on having a large number of antennas at the base station it is important to have both a scalable and distributed realization of such a system to ease deployment. Most work so far have focused on the theoretical aspects although a few demonstrators have been reported. In this work, we propose a base station architecture based on connecting the processing nodes in a K-ary tree, allowing simple scalability. Furthermore, it is shown that most of the processing can be performed locally in each node. Further analysis of the node processing shows that it should be enough that each node contains one or two complex multipliers and a few complex adders/subtracters operating at some hundred MHz. It is also shown that a communication link of some Gbps is required between the nodes, and, hence, it is fully feasible to have one or a few links between the nodes to cope with the communication requirements.
Wireless networks with many antennas at the base stations and multiplexing of many users, known as Massive MIMO systems, are key to handle the rapid growth of data traffic. As the number of users increases, the random access in contemporary networks will be flooded by user collisions. In this paper, we propose a reengineered random access protocol, coined strongest-user collision resolution (SUCR). It exploits the channel hardening feature of Massive MIMO channels to enable each user to detect collisions, determine how strong the contenders channels are, and only keep transmitting if it has the strongest channel gain. The proposed SUCR protocol can quickly and distributively resolve the vast majority of all pilot collisions.
The massive multiple-input multiple-output (MIMO) technology has great potential to manage the rapid growth of wireless data traffic. Massive MIMO achieves tremendous spectral efficiency by spatial multiplexing many tens of user equipments (UEs). These gains are only achieved in practice if many more UEs can connect efficiently to the network than today. As the number of UEs increases, while each UE intermittently accesses the network, the random access functionality becomes essential to share the limited number of pilots among the UEs. In this paper, we revisit the random access problem in the Massive MIMO context and develop a reengineered protocol, termed strongest-user collision resolution (SUCRe). An accessing UE asks for a dedicated pilot by sending an uncoordinated random access pilot, with a risk that other UEs send the same pilot. The favorable propagation of massive MIMO channels is utilized to enable distributed collision detection at each UE, thereby determining the strength of the contenders signals and deciding to repeat the pilot if the UE judges that its signal at the receiver is the strongest. The SUCRe protocol resolves the vast majority of all pilot collisions in crowded urban scenarios and continues to admit UEs efficiently in overloaded networks.
This paper considers three aspects of Massive MIMO (multiple- input multiple-output) communication networks that have received little attention in previous works, but are important to understand when designing and implementing this promising wireless technology. First, we analyze how bursty data traffic behaviors affect the system. Using a probabilistic model for intermittent user activity, we show that the spectral efficiency (SE) scales gracefully with reduced user activity. Then, we make an analytic comparison between synchronous and asynchronous pilot signaling, and prove that the choice between these has no impact on the SE. Finally, we provide an analytical and numerical study of the SE achieved with random network deployment.
Massive MIMO is a promising technique for increasing the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas M than scheduled users K because the users channels are likely to be near-orthogonal when M/K > 10. However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users K-star depends on M and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of K-star in the large-M regime is derived in closed form, while simulations are used to show what happens at finite M, in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal M/K is less than 10 in many cases of practical relevance. Interestingly, K-star depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same K.
Massive MIMO is a promising technique to increase the spectral efficiency of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent beamforming. A common rule-of-thumb is that these systems should have an order of magnitude more antennas, N, than scheduled users, K, because the users' channels are then likely to be quasi-orthogonal. However, it has not been proved that this rule-of-thumb actually maximizes the spectral efficiency. In this paper, we analyze how the optimal number of scheduled users, K*, depends on N and other system parameters. The value of K* in the large-N regime is derived in closed form, while simulations are used to show what happens at finite N, in different interference scenarios, and for different beamforming.
Wireless communications is one of the most successful technologies in modern years, given that an exponential growth rate in wireless traffic has been sustained for over a century (known as Coopers law). This trend will certainly continue, driven by new innovative applications; for example, augmented reality and the Internet of Things. Massive MIMO has been identified as a key technology to handle orders of magnitude more data traffic. Despite the attention it is receiving from the communication community, we have personally witnessed that Massive MIMO is subject to several widespread misunderstandings, as epitomized by following (fictional) abstract: "The Massive MIMO technology uses a nearly infinite number of high-quality antennas at the base stations. By having at least an order of magnitude more antennas than active terminals, one can exploit asymptotic behaviors that some special kinds of wireless channels have. This technology looks great at first sight, but unfortunately the signal processing complexity is off the charts and the antenna arrays would be so huge that it can only be implemented in millimeter-wave bands." These statements are, in fact, completely false. In this overview article, we identify 10 myths and explain why they are not true. We also ask a question that is critical for the practical adoption of the technology and which will require intense future research activities to answer properly. We provide references to key technical papers that support our claims, while a further list of related overview and technical papers can be found at the Massive MIMO Info Point: http://massivemimo.eu
Distributed massive multiple-input multiple-output (MIMO) combines the array gain of coherent MIMO processing with the proximity gains of distributed antenna setups. In this paper, we analyze how transceiver hardware impairments affect the downlink with maximum ratio transmission. We derive closed-form spectral efficiencies expressions and study their asymptotic behavior as the number of the antennas increases. We prove a scaling law on the hardware quality, which reveals that massive MIMO is resilient to additive distortions, while multiplicative phase noise is a limiting factor. It is also better to have separate oscillators at each antenna than one per BS
In this work, we consider spectrum sensing of OFDM signals. We deal withthe inevitable problem of a carrier frequency offset, and propose modificationsto some state-of-the-art detectors to cope with that. Moreover, the (modified)detectors are implemented using GNU radio and USRP, and evaluated over aphysical radio channel. Measurements show that all of the evaluated detectorsperform quite well, and the preferred choice of detector depends on thedetection requirements and the radio environment.
EDGE (enhanced data rates for global evolution) is one of the future wireless communication systems, offering high bit rates and packet data services. For data services an increased link quality will directly translate into improved throughput. A well-known technique that improves link performance is antenna diversity. Antenna diversity also enables interference-cancellation methods, which are evaluated in this paper. The conclusion is that introducing interference rejection in a GSM/EDGE classic scenario could increase average user bit rate by 26%. In a TDMA/EDGE compact scenario the average bit rate increase could be as high as 46% due to the time synchronized structure
This paper studies the potential performance im- provement from cooperative diversity transmission in a cellular network. We consider a simpli ed coopera- tive relaying system which allows the mobile terminals to relay data packets from their partners. We obtain numerical results for the outage probability, taking into account log-distance path loss, spatially corre- lated shadowing and small-scale fading. A compari- son with conventional macrodiversity is performed for various scenarios of interest. The simulation results demonstrate the superiority of cooperative diversity transmission.
We consider the problem of minimizing the packet drop probability (PDP) under an average transmit power constraint for Chase combining (CC)-based hybrid-automatic repeat request (HARQ) schemes in correlated Rayleigh fading channels. We propose a method to find a solution to the non-convex optimization problem using an exact expression of the outage probability. However, the complexity of this method is high. Therefore, we propose an alternative approach in which we use an asymptotically equivalent expression for the outage probability and reformulate it as a geometric programming problem (GPP), which can be efficiently solved using convex optimization algorithms.
Massive multiple-input multiple-output (MIMO) is an emerging technology for mobile communications, where a large number of antennas are employed at the base station to simultaneously serve multiple single-antenna terminals with very high capacity. In this paper, we study the potentials and challenges of utilizing massive MIMO for unmanned aerial vehicles (UAVs) communication. We consider a scenario where multiple single-antenna UAVs simultaneously communicate with a ground station (GS) equipped with a large number of antennas. Speci[1]cally, we discuss the achievable uplink (UAV to GS) capacity performance in the case of line-of-sight (LoS) conditions. We also study the type of antenna polarization that should be used in order to maintain a reliable communication link between the GS and the UAVs. The results obtained using a realistic geometric model show that massive MIMO is a potential enabler for high-capacity UAV network
We illustrate the potential of Massive MIMO for communication with unmanned aerial vehicles (UAVs). We consider a scenario, where multiple single-antenna UAVs simultaneously communicate with a ground station (GS) equipped with a large number of antennas. Specifically, we discuss the achievable uplink (UAV to GS) capacity performance in the case of line-of-sight conditions. We develop a realistic geometric model, which incorporates an arbitrary orientation, of the GS and UAV antenna elements to characterize the polarization mismatch loss, which occurs due to the movement and orientation of the UAVs. A closed-form expression for a lower bound on the ergodic rate for a maximum-ratio combining receiver with estimated channel state information is derived. The optimal antenna spacing that maximizes the ergodic rate achieved by an UAV is also determined for uniform linear and rectangular arrays. It is shown that when the UAVs are spherically uniformly distributed around the GS, the ergodic rate per UAV is maximized for an antenna spacing equal to an integer multiple of one-half wavelength.
We investigate the achievable ergodic rate of Massive multi-input-multi-output (MIMO) system in environments with high mobility and line-of-sight (LoS). A 3-dimensional geometric model with uniform rectangular array at the basestation (BS) is used for the investigation. We derive a closed formexpression for a lower bound on the uplink ergodic rate takinginto account imperfections of the channel state information,number of BS antennas, antenna spacing, and spatial distributionof user terminals. The results show that, in LoS Massive MIMO, when the terminals are spherically uniformly distributed around the BS, the ergodic rate is maximized for antenna spacing equal to integer multiples of one-half wavelength.
We analyze the outage capacity performance of the Massive MIMO uplink in a random line-of-sight (LoS) scenario. Considering a maximum-ratio combining receiver and assuming perfect channel state information at the base station (BS), we derive closed-form expressions for a lower bound on the outage capacity. It is shown that the outage capacity of Massive MIMO in the random LoS scenario logarithmically increases with the number of BS antennas due to the fact that the fluctuations in the total interference power become negligible (i.e., an interference hardening effect).
This paper considers the jointly optimal pilot and data power allocation in single cell uplink massive MIMO systems. A closed form solution for the optimal length of the training interval is derived. Using the spectral efficiency (SE) as performance metric and setting a total energy budget per coherence interval the power control is formulated as optimization problems for two different objective functions: the minimum SE among the users and the sum SE. The optimal power control policy is found for the case of maximizing the minimum SE by converting it to a geometric program (GP). Since maximizing the sum SE is an NP-hard problem, an efficient algorithm is developed for finding KKT (local maximum) points. Simulation results show the advantage of optimizing the power control over both pilot and data power, as compared to heuristic power control policies.
The effect of frequency offsets on the uplink sumrate performance of massive MIMO systems is studied in the case of flat fading with pilot assisted estimation. Both collocated and distributed antenna architectures are studied to determine if there is a fundamental preference for collocated or distributed architectures from the perspective of frequency synchronization and its effect on the rate performance in a high mobility environment.
For both maximum ratio transmission (MRT) and zero forcing (ZF) precoding schemes and given any specific rate requirement the optimal transmit power, number of antennas to be used, number of users to be served and number of pilots spent on channel training are found with the objective to minimize the total consumed power at the base station. The optimization problem is solved by finding closed form expressions of the optimal transmit power and then search over the remaining discrete variables. The analysis consists of two parts, the first part investigates the situation when only power consumed in the RF amplifiers is considered. The second part includes both the power consumed in the RF amplifiers and in other transceiver circuits. In the former case having all antennas active while reducing the transmit power is optimal. Adaptive scheme to switch off some of the antennas at the base stations is found to be optimal in the latter case.
We investigate the capacity of the multiple-input-multiple-output channel taking into account the consumed power in the power amplifiers. The mutual information is optimized with a limitation of total consumed power and per-antenna radiated power for a fixed channel with full channel state information at both the transmitter and receiver. The capacity is thus obtained by optimizing the input distribution to maximize the mutual information. Since the optimization problem is non-convex, direct computation of the capacity suffers from high computational complexity. Hence upper and lower bounds on the capacity are given as benchmarks for different ad-hoc schemes. An efficient suboptimal algorithm is also presented. Numerical results show that the suboptimal algorithm performs close to the capacity.
This paper considers the use of NOMA in multiuser MIMO systems in practical scenarios where CSI is acquired through pilot signaling. A new NOMA scheme that uses shared pilots is proposed. Achievable rate analysis is carried out for a pilot signaling scheme including both uplink and downlink pilots. The achievable rate of the proposed NOMA scheme with shared pilots in each NOMA group is compared with the traditional orthogonal access scheme with orthogonal pilots. Numerical results show that when estimated downlink CSI is available at the users, our proposed NOMA scheme outperforms orthogonal schemes. With increasing number of antennas at the base station, the gain from our proposed NOMA scheme is also increasing. This shows that there is a benefit of applying the proposed NOMA scheme in massive MIMO systems.
This paper considers the jointly optimal pilot and data power allocation in single-cell uplink massive multiple-input-multiple- output systems. Using the spectral efficiency (SE) as performance metric and setting a total energy budget per coherence interval, the power control is formulated as optimization problems for two different objective functions: the weighted minimum SE among the users and the weighted sum SE. A closed form solution for the optimal length of the pilot sequence is derived. The optimal power control policy for the former problem is found by solving a simple equation with a single variable. Utilizing the special structure arising from imperfect channel estimation, a convex reformulation is found to solve the latter problem to global optimality in polynomial time. The gain of the optimal joint power control is theoretically justified, and is proved to be large in the low-SNR regime. Simulation results also show the advantage of optimizing the power control over both pilot and data power, as compared to the cases of using full power and of only optimizing the data powers as done in previous work.
This paper considers the use of non-orthogonal-multiple-access (NOMA) in multiuser MIMO systems in practical scenarios where channel state information (CSI) is acquired through pilot signaling. A new NOMA scheme that uses shared pilots is proposed. Achievable rate analysis is carried out for different pilot signaling schemes, including both uplink and downlink pilots. The achievable rate performance of the proposed NOMA scheme with shared pilot within each group is compared with the traditional orthogonal access scheme with orthogonal pilots. Our proposed scheme is a generalization of the orthogonal scheme, and can be reduced to the orthogonal scheme when appropriate power allocation parameters are chosen. Numerical results show that when downlink CSI is available at the users, our proposed NOMA scheme outperforms orthogonal schemes. However with more groups of users present in the cell, it is preferable to use multi-user beamforming instead of NOMA.
In this paper, we study the effect of channel aging on the uplink and downlink performance of an FDD massive MIMO system, as the system dimension increases. Since the training duration scales linearly with the number of transmit dimensions, channel estimates become increasingly outdated in the communication phase, leading to performance degradation. To quantify this degradation, we first derive bounds on the mean squared channel estimation error. We use the bounds to derive deterministic equivalents of the receive SINRs, which yields a lower bound on the achievable uplink and downlink spectral efficiencies. For the uplink, we consider maximal ratio combining and MMSE detectors, while for the downlink, we consider matched filter and regularized zero forcing precoders. We show that the effect of channel aging can be mitigated by optimally choosing the frame duration. It is found that using all the base station antennas can lead to negligibly small achievable rates in high user mobility scenarios. Finally, numerical results are presented to validate the accuracy of our expressions and illustrate the dependence of the performance on the system dimension and channel aging parameters.
We present approximations of the LLR distribution for a class of fixed-complexity soft-output MIMO detectors, such as the optimal soft detector and the soft-output via partial marginalization detector. More specifically, in a MIMO AWGN setting, we approximate the LLR distribution conditioned on the transmitted signal and the channel matrix with a Gaussian mixture model (GMM). Our main results consist of an analytical expression of the GMM model (including the number of modes and their corresponding parameters) and a proof that, in the limit of high SNR, this LLR distribution converges in probability towards a unique Gaussian distribution.