Multiple-input Single-output Case Research Articles

Global terrestrial temperature modeling by using fractional models

Modeling the global climate system through the temperature output is a very challenging task. Knowing the fractional operator long memory property to well model diffusion phenomena with very few parameters, it is proposed in this paper to use fractional models for climate change modeling. System identification is applied for continuous-time system identification of multiple-input single-output (MISO) fractional order models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. Finally, the estimation with fractional models is carried out on real input/output data and provide a very good goodness fit of the global earth temperature.

The DMT of Real and Quaternionic Lattice Codes and DMT Classification of Division Algebra Codes

In this paper we consider the diversity-multiplexing gain tradeoff (DMT) of so-called minimum delay asymmetric space-time codes. Such codes are less than full dimensional lattices in their natural ambient space. Apart from the multiple input single output (MISO) channel there exist very few methods to analyze the DMT of such codes. Further, apart from the MISO case, no DMT optimal asymmetric codes are known. We first discuss previous criteria used to analyze the DMT of space-time codes and comment on why these methods fail when applied to asymmetric codes. We then consider two special classes of asymmetric codes where the code-words are restricted to either real or quaternion matrices. We prove two separate diversity-multiplexing gain trade-off (DMT) upper bounds for such codes and provide a criterion for a lattice code to achieve these upper bounds. We also show that lattice codes based on Q-central division algebras satisfy this optimality criterion. As a corollary this result provides a DMT classification for all Q-central division algebra codes that are based on standard embeddings. While the Q-central division algebra based codes achieve the largest possible DMT of a code restricted to either real or quaternion space, they still fall short of the optimal DMT apart from the MISO case.

System identification of MISO fractional systems: Parameter and differentiation order estimation

This paper deals with continuous-time system identification of multiple-input single-output (MISO) fractional differentiation models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. A new definition of structured-commensurability (or S-commensurability) is introduced to better cope with differentiation order estimation. Three variants of the algorithm are then proposed: (i) first, all differentiation orders are set as integer multiples of a global S-commensurate order, (ii) then, the differentiation orders are set as integer multiples of a local S-commensurate orders (one S-commensurate order for each subsystem), (iii) finally, all differentiation orders are estimated by releasing the S-commensurability constraint. The first variant has the smallest number of parameters and is used as a good initial hit for the second variant which in turn is used as a good initial hit for the third variant. Such a progressive increase of the number of parameters allows better performance of the optimization algorithm evaluated by Monte Carlo simulation analysis.

Power Efficient IRS-Assisted NOMA

In this paper, we propose a downlink multiple-input single-output (MISO) transmission scheme, which is assisted by an intelligent reflecting surface (IRS) consisting of a large number of passive reflecting elements. In the literature, it has been proved that nonorthogonal multiple access (NOMA) can achieve the same performance as computationally complex dirty paper coding, where the quasi-degradation condition is satisfied, conditioned on the users' channels fall in the quasi-degradation region. However, in a conventional communication scenario, it is difficult to guarantee the quasi-degradation, because the channels are determined by the propagation environments and cannot be reconfigured. To overcome this difficulty, we focus on an IRS-assisted MISO NOMA system, where the wireless channels can be effectively tuned. We optimize the beamforming vectors and the IRS phase shift matrix for minimizing transmission power. Furthermore, we propose an improved quasi-degradation condition by using IRS, which can ensure that NOMA achieves the capacity region with high possibility. For a comparison, we study zero-forcing beamforming (ZFBF) as well, where the beamforming vectors and the IRS phase shift matrix are also jointly optimized. Comparing NOMA with ZFBF, it is shown that, with the same IRS phase shift matrix and the improved quasi-degradation condition, NOMA always outperforms ZFBF. At the same time, we identify the condition under which ZFBF outperforms NOMA, which motivates the proposed hybrid NOMA transmission. Simulation results show that the proposed IRS-assisted MISO system outperforms the MISO case without IRS, and the hybrid NOMA transmission scheme always achieves better performance than orthogonal multiple access.

Hybrid machine learning detection for orbital angular momentum over turbulent MISO wireless channel

This work proposes a machine learning detection scheme for wireless orbital angular momentum (OAM) communication systems. The new scheme works for single-input–single-output (SISO) and multiple-input–single-output (MISO) wireless communication between the transmitter and the receiver. The transmitter encodes its data in OAM modes which are constructed using Laguerre–Gaussian beam form. The transmitted beams travel through a wireless channel with weak to medium turbulence strength and they arrive at random positions on the same receiver area. The authors proposed detection scheme allows the reception of multiple overlapping beams without prior knowledge of beams centre positions. The proposed scheme uses a novel technique of receiver segmentation and space filtering along with neural network to decode the received beams. Simulations show the detection efficiency and the enhanced performance of their proposed scheme for the SISO case and the MISO case with 2, 4, and 16 beams.

Element-wise Bayesian regularization for fast and adaptive force reconstruction

In time domain force reconstruction problems, regularization techniques are widely adopted to solve the intrinsic ill-posedness or ill-conditioning. Different techniques are selected for forces with different temporal profiles, such as Tikhonov regularization for smooth forces and ℓ1 regularization for sparse forces. However, in lack of prior information on force temporal distribution, choosing the appropriate regularization technique is troublesome. In this paper, we propose a novel regularization technique that can reconstruct forces with different types of temporal profiles at known locations. The proposed method, named Element-wise Bayesian regularization, is formulated under the hierarchical Bayesian framework, with an individual prior distribution assumed for each element in the unknown force history. An appropriate regularization level is automatically and adaptively set for each individual element through conditional maximization of the posterior probability of force history. The proposed method is validated by a cantilever plate simulation, an engineering-scale tank simulation, and a laboratory tank experiment under different noise levels and force types. The results conclude that the proposed method accurately reconstruct force histories without any prior information at a fast computation speed under various conditions. The presented work primarily focuses on the single input multiple output case, but the presented methodology can be easily extended towards the multiple input multiple output case.

Decentralized Precoding for Cache-Enabled Ultra-Dense Radio Access Networks

This letter studies the fully decentralized optimization of the precoding matrices for the downlink of multiple-input-multiple-output cache-enabled ultra-dense radio access network. To avoid signalling exchange between coordinated edge radio access nodes (RANs), we first construct a virtual downlink cache-enabled ultra-dense radio access network. Following, a new concept of signal-to-interference-leakage-plus-noise ratio is defined. Based on this concept, a virtual weighted sum rate maximization problem is formulated to optimize the precoders. We then propose a computationally efficient decentralized optimization algorithm that achieves stationary point to the problem. Numerical results show that the proposed algorithm can achieve more than 96.15% of the performance of the centralized optimization without any signalling exchange between coordinated edge RANs for multiple-input single-output cases.

Highly Accurate and Asymptotic Analysis on the SOP Over SIMO <inline-formula> <tex-math notation="LaTeX">$\alpha$ </tex-math> </inline-formula>–<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math> </inline-formula> Fading Channels

In order to fill the gap of the mathematical analysis's lack for the secrecy outage probability (SOP) over single-input multiple-output (SIMO) α-μ wiretap fading channels, this letter initially provides highly accurate and asymptotic closed-form expressions for the SOP. The novel highly accurate formulations are derived in a simple and general form in terms of the bivariate Fox's H-function, which is extensively used in the literature. In addition, the asymptotic analysis of the SOP is derived at high signal-to-noise ratio regime. The obtained expressions are numerically validated and compared with the Monte-Carlo simulation results. The derived SOP is in highly accurate match with simulation results for the SIMO case, and a perfect match with simulated results for single-input single-output (SISO) case.

Axonal Channel Capacity in Neuro-Spike Communication.

Novel nano-scale communication techniques are inspired by biological systems. Neuro-spike communication is an example of this communication paradigm which transfers vital information about external and internal conditions of the body through the nervous system. The analysis of this communication paradigm is beneficial to exploit in the artificial neural systems where nano-machines are linked to neurons to treat the neurodegenerative diseases. In these networks, nano-machines are used to replace the damaged segments of the nervous system and they exactly behave like biological entities. In neuro-spike communication, neurons / nano-machines exploit the electro-chemical spikes and molecular communication to transfer information. This communication paradigm can be divided into three main parts, namely the axonal pathway, the synaptic transmission, and the spike generation. In this paper, we focus on the axonal transmission part as a separate channel since the capacity of the axonal pathway has a significant effect on the capacity of neuro-spike communication channel. In thinner axons, the capacity of this part is the bottleneck of the neuro-spike communication channel capacity. Hence, we investigate the restricting factors of the axonal transmission which limit its capacity. We derive the capacity of single-input single-output and multiple-input single-output (MISO) axonal channels. In the MISO case, we investigate the effect of the correlation among inputs on the channel capacity. Moreover, we derive a closed form description for the optimum value of the input spike rate to maximize the capacity of the axonal channel when the information is encoded by firing rate of neurons / nano-machines.

The Capacity of Gaussian MIMO Channels Under Total and Per-Antenna Power Constraints

The capacity of a fixed Gaussian multiple-input multiple-output (MIMO) channel and the optimal transmission strategy under the total power (TP) constraint and full channel state information are well known. This problem remains open in the general case under individual per-antenna (PA) power constraints, while some special cases have been solved. These include a full-rank solution for the MIMO channel and a general solution for the multiple-input single-output (MISO) channel. In this paper, the fixed Gaussian MISO channel is considered and its capacity and optimal transmission strategies are determined in a closed form under the joint total and PA power constraints in the general case. In particular, the optimal strategy is hybrid and includes two parts: first is equal-gain transmission and second is maximum-ratio transmission, which are responsible for the PA and TP constraints, respectively. The optimal beamforming vector is given in a closed form and an accurate yet simple approximation to the capacity is proposed. Finally, the above results are extended to the MIMO case by establishing the ergodic capacity of fading MIMO channels under the joint power constraints when the fading distribution is right unitary-invariant (of which i.i.d. and semi-correlated Rayleigh fading are special cases). Unlike the fixed MISO case, the optimal signaling is shown to be isotropic in this case.

Interpolativity of at-least and at-most models of monotone fuzzy rule bases with multiple antecedent variables

Of the many desirable properties of fuzzy inference systems, not all are known to co-exist. For instance, a fuzzy inference system should be interpolative, i.e., if a fuzzy set equivalent to one of the antecedent fuzzy sets appears on the input of such a system, the inferred output should be equivalent to the respective consequent fuzzy set. Similarly, the defuzzified output obtained from a system based on a monotone fuzzy rule base should be monotone, i.e., if x,x′ are crisp inputs to the system that are ordered x≤x′, then, the corresponding defuzzified outputs from the system y,y′ should also be ordered accordingly, i.e., y≤y′. However, the particular setting that ensures monotonicity need not simultaneously ensure interpolativity. Recently, Štěpnička and De Baets have investigated and demonstrated the co-existence of the above two properties in the case of fuzzy relational inference systems and single-input-single-output (SISO) rule bases. An extension of these results to the multiple-input-single-output (MISO) case is not straightforward due to the lack of a natural ordering in higher dimensions. In this work, we study the MISO case and show that similar results can be obtained when the monotone rule base is modeled based on at-most and at-least modifiers.

Capacity of SIMO and MISO Phase-Noise Channels With Common/Separate Oscillators

In multiple antenna systems, phase noise due to instabilities of the radio-frequency (RF) oscillators, acts differently depending on whether the RF circuitries connected to each antenna are driven by separate (independent) local oscillators (SLO) or by a common local oscillator (CLO). In this paper, we investigate the high-SNR capacity of single-input multiple-output (SIMO) and multiple-output single-input (MISO) phase-noise channels for both the CLO and the SLO configurations. Our results show that the first-order term in the high-SNR capacity expansion is the same for all scenarios (SIMO/MISO and SLO/CLO), and equal to $0.5\ln (\rho)$, where $\rho$ stands for the SNR. On the contrary, the second-order term, which we refer to as phase-noise number, turns out to be scenario-dependent. For the SIMO case, the SLO configuration provides a diversity gain, resulting in a larger phase-noise number than for the CLO configuration. For the case of Wiener phase noise, a diversity gain of at least $0.5 \ln(M)$ can be achieved, where $M$ is the number of receive antennas. For the MISO, the CLO configuration yields a higher phase-noise number than the SLO configuration. This is because with the CLO configuration one can obtain a coherent-combining gain through maximum ratio transmission (a.k.a. conjugate beamforming). This gain is unattainable with the SLO configuration.

Symbol Error Rate for Nonblind Adaptive Equalizers Applicable for the SIMO and FGn Case

A nonzero residual intersymbol interference (ISI) causes the symbol error rate (SER) to increase where the achievable SER may not answer any more on the system’s requirements. Recently, a closed-form approximated expression was derived by the same author for the residual ISI obtained by nonblind adaptive equalizers for the single-input single-output (SISO) case. Up to now, there does not exist a closed-form expression for the residual ISI obtained by nonblind adaptive equalizers for the single-input multiple-output (SIMO) case. Furthermore, there does not exist a closed-form expression for the SER valid for the SISO or SIMO case that takes into account the residual ISI obtained by nonblind adaptive equalizers and is valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of0.5≤H<1. In this paper, we derive a closed-form approximated expression for the residual ISI obtained by nonblind adaptive equalizers for the SIMO case (where SISO is a special case of SIMO), valid for fGn input where the Hurst exponent is in the region of0.5≤H<1. Based on this new expression for the residual ISI, a closed-form approximated expression is obtained for the SER valid for the SIMO and fGn case.

On the Number of Independent Channels in Multi-Antenna Systems

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.

Coordinated Beamforming With Relaxed Zero Forcing: The Sequential Orthogonal Projection Combining Method and Rate Control

In this paper, coordinated beamforming based on relaxed zero forcing (RZF) for K transmitter-receiver pair multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) interference channels is considered. In the RZF coordinated beamforming, conventional zero-forcing interference leakage constraints are relaxed so that some predetermined interference leakage to undesired receivers is allowed in order to increase the beam design space for larger rates than those of the zero-forcing (ZF) scheme or to make beam design feasible when ZF is impossible. In the MISO case, it is shown that the rate-maximizing beam vector under the RZF framework for a given set of interference leakage levels can be obtained by sequential orthogonal projection combining (SOPC). Based on this, exact and approximate closed-form solutions are provided in two-user and three-user cases, respectively, and an efficient beam design algorithm for RZF coordinated beamforming is provided in general cases. Furthermore, the rate control problem under the RZF framework is considered. A centralized approach and a distributed heuristic approach are proposed to control the position of the designed rate-tuple in the achievable rate region. Finally, the RZF framework is extended to MIMO interference channels by deriving a new lower bound on the rate of each user.

Symbol Error Rate as a Function of the Residual ISI Obtained by Blind Adaptive Equalizers for the SIMO and Fractional Gaussian Noise Case

A nonzero residual intersymbol interference (ISI) causes the symbol error rate (SER) to increase where the achievable SER may not answer any more on the system&#x2019;s requirements. In the literature, we may find for the single-input-single-output (SISO) case a closed-form approximated expression for the SER that takes into account the achievable performance of the chosen blind adaptive equalizer from the residual ISI point of view and a closed-form approximated expression for the residual ISI valid for the single-input-multiple-output (SIMO) case. Both expressions were obtained by assuming that the input noise is a white Gaussian process where the Hurst exponent (<i>H</i>) is equal to 0.5. In this paper, we derive a closed-form approximated expression for the residual ISI obtained by blind adaptive equalizers for the SIMO case, valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of <svg style="vertical-align:-0.546pt;width:82.224998px;" id="M1" height="11.85" version="1.1" viewBox="0 0 82.224998 11.85" width="82.224998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g><g transform="matrix(.017,-0,0,-.017,8.222,11.113)"><path id="x2E" d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" /></g><g transform="matrix(.017,-0,0,-.017,12.098,11.113)"><path id="x35" d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8&#xA;l-26 -65h-233z" /></g><g transform="matrix(.017,-0,0,-.017,24.966,11.113)"><path id="x2264" d="M531 71l-474 214v50l474 215v-56l-416 -184l416 -183v-56zM531 -40h-474v50h474v-50z" /></g><g transform="matrix(.017,-0,0,-.017,39.67,11.113)"><path id="x1D43B" d="M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28&#xA;h263l-6 -28q-58 -5 -75.5 -21t-30.5 -81l-26 -153h377l29 153q12 67 2 81t-74 21l5 28h268z" /></g><g transform="matrix(.017,-0,0,-.017,59.303,11.113)"><path id="x3C" d="M512 -3l-437 233v51l437 233v-58l-378 -200v-2l378 -199v-58z" /></g><g transform="matrix(.017,-0,0,-.017,74.007,11.113)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g> </svg>. Based on this new expression for the residual ISI, a closed-form approximated expression is obtained for the SER valid for the SIMO and fGn case. In this paper, we show via simulation results that the SER might get improved for increasing values of <i >H</i>.

Sum Capacity of MIMO Interference Channels in the Low Interference Regime

Using Gaussian inputs and treating interference as noise at the receivers has recently been shown to be sum capacity achieving for the two-user single-input single-output (SISO) Gaussian interference channel in a low interference regime, where the interference levels are below certain thresholds. In this paper, such a low interference regime is characterized for multiple-input multiple-output (MIMO) Gaussian interference channels. Conditions are provided on the direct and cross channel gain matrices under which using Gaussian inputs and treating interference as noise at the receivers is sum capacity achieving. For the special cases of the symmetric multiple-input single-output (MISO) and single-input multiple-output (SIMO) Gaussian interference channels, more explicit expressions for the low interference regime are derived. In particular, the threshold on the interference levels that characterize low interference regime is related to the input SNR and the angle between the direct and cross channel gain vectors. It is shown that the low interference regime can be quite significant for MIMO interference channels, with the low interference threshold being at least as large as the sine of the angle between the direct and cross channel gain vectors for the MISO and SIMO cases.

Sum Capacity of a Class of Symmetric SIMO Gaussian Interference Channels Within $ {\cal O}(1)$

The N +1 user, 1 ×N single-input multiple-output (SIMO) Gaussian interference channel where each transmitter has a single antenna and each receiver has N antennas is studied. The sum capacity within O(1) is characterized for the symmetric case where all direct links have the same signal-to-noise ratio (SNR) and all undesired links have the same interference-to-noise ratio (INR). The gap to the exact capacity is a constant which is independent of SNR and INR. To get this result, we first generalize the deterministic interference channel introduced by El Gamal and Costa to model interference channels with multiple antennas. We derive the capacity region of this deterministic interference channel. Based on the insights provided by the deterministic channel, we characterize the generalized degrees of freedom (GDOF) of Gaussian case, which directly leads to the O(1) capacity approximation. On the achievability side, an interesting conclusion is that the GDOF regime where treating interference as noise is found to be optimal in the two-user interference channel, does not appear in the N + 1 user, 1 × N SIMO case. On the converse side, new multiuser outer bounds emerge out of this work that do not follow directly from the two-user case. In addition to the GDOF region, the outer bounds identify a strong interference regime where the capacity region is established.

Channel estimation for multicarrier multiple input single output systems using the em algorithm

This paper investigates the problem of blindly and semi-blindly acquiring the channel gains for an underdetermined synchronous multiuser multicarrier system. The special case of a multiple-input single-output (MISO) channel is considered where the different users transmit at the same time and in the same bandwidth. In order to separate the different users blindly, techniques exploiting the finite alphabet are used. For such techniques, and for a general underdetermined MIMO system, we study conditions under which the channel and the data for each user are blindly and semi-blindly identifiable. We consider the stochastic maximum likelihood (SML) criterion in which the unknown input symbols are modeled as discrete random variables. We apply the expectation-maximization (EM) algorithm in the frequency domain to get blind and semi-blind channel estimates for each user in the MISO case. We also present a recursive EM solution that updates the channel and noise estimates at each time instant. Simulations show that users can be separated, even at low SNR. Furthermore, semi-blind estimation allows for a more robust estimation solution since a possible singularity problem is avoided.

Connecting PE identification and robust control theory: the multiple-input single-output case. part I: uncertainty region validation

This paper and its companion paper extend previous results to connect PE identification and robust control theory in the SISO (single-input single output) case to the MISO (multiple-input single-output) case.