Minimum Number Of Antennas Research Articles

Joint linear array structure and waveform design for MIMO radar under practical constraints

<abstract> <p>Optimizing the array structure or emission waveform of a multiple-input multiple-output (MIMO) radar system is an effective method to improve the performance in practical applications. In this study, the joint optimization of array structure and the corresponding emission waveform under interference and noise conditions was investigated. When compared with the waveform or array structure optimization alone, this method allowed the MIMO radar system to obtain a higher degree of freedom. By considering the practical limitations of the MIMO radar system, a waveform with good properties, such as orthogonality or pulse compression performance, was selected as the reference waveform. Subsequently, based on the similarity constraint and constant modulus constraint, a bivariate joint optimization problem of array structure and waveform was formulated, and an iterative optimization algorithm was proposed to solve it. The array composition was determined using a combinatorial search algorithm while the emission waveform was obtained by solving the similarity model. Eventually, it effectively converged to form quasi-optimal match variables after limited iterations. The proposed method can be expanded to the optimal launch of a specific target and an environment with a proper or minimum number of antennas, as well as implement array optimization with the desired waveform. The simulation results prove the effectiveness of the proposed method. This method provides an ideal choice for real-time construction, flexible launch, and signal processing of MIMO radar systems.</p> </abstract>

Fast 3D microwave imaging inside cavity with minimum number of antennas and modified inverse algorithm

AbstractThis article proposes an optimized method for 3D microwave imaging of various unknown objects inside a perfect electric conductor cavity. The total field scattered field technique uses the finite difference time domain method to obtain scattered fields inside a cavity in the forward scattering problem. However, the conjugate gradient method is optimized and used alongside a combined regularization term in the inverse scattering problem, which is essential for the reconstruction process. A dipole antenna is located as an incident wave from the transmitting antenna. Besides, one antenna acts as the receiver. Identifying the unknown objects with different shapes, sizes, materials, and locations using the minimum number of transmitting and receiving antennas, and the newly developed algorithm with less computation time, are the main advantages of this article. Also, the implemented method can be used in the 3D microwave imaging of multi‐scattering problems.

Efficient Closed-Form Solution for 3-D Hybrid Localization in Multistatic Radars

In this article, an algebraic solution for localizing a moving target using a nonstationary multistatic radar system is proposed. By utilizing the quadruple hybrid measurement set, which consists of time delay, Doppler shift, angle of arrival, and angle rate measurements, the proposed method can estimate the target position and velocity vectors via a simple one-stage weighted least squares estimator without the need for introduction of the nuisance parameters, which enables us to locate the target with the minimum number of antennas. The proposed estimator takes the uncertainty concerned with the position and velocity of the antennas in its design. The proposed estimator is shown to be approximately unbiased and efficient under small Gaussian noise level assumption, that is, the estimator achieves the smallest possible variance (the Cramér–Rao lower bound) among all other unbiased estimators. Numerical simulations demonstrate substantial performance improvement of the proposed estimator over the state-of-the-art methods presented for moving target localization.

Features of application of ESPRIT method for different configurations of antenna arrays

The paper discusses the features of the application of the ESPRIT method, which provides direction finding of a variety of radio sources with minimal computational costs, including in real time. To be able to use ESPRIT, antenna arrays are required that have the property of shift invariance, and for practical implementation, antenna arrays are required that allow you to form estimates of the directions of arrival of the largest number of signals that overlap in the spectrum, with a minimum number of antennas and reception channels. The aim of the work is to analyze the influence of the antenna array configuration on the features of ESPRIT application for different antenna array with the same number of antennas. A comparative qualitative analysis of the properties and features compared to the MUSIC method is presented. The algorithms developed by the authors for processing multichannel data received by angle and square antenna arrays are presented. It is shown analytically that when using a corner antenna array, it is necessary to take into account the possible presence of signals from indistinguishable-mirror directions of arrival. With a square antenna array, there are no mirror directions of arrival of different signals, which simplifies the implementation of the algorithm. It is shown analytically and by simulation modeling that the configuration of a square antenna array allows to increase the number of simultaneously tracked signals that overlap in the spectrum, compared to a corner antenna array with the same number of antennas.

Efficient Closed-Form Solution for Moving Target Localization in MIMO Radars With Minimum Number of Antennas

This paper deals with the moving target localization problem from time delay and Doppler shift measurements in a distributed multiple-input multiple-output radar system. An algebraic closed-form two-stage weighted least squares solution is presented to locate the target position and velocity. In the first stage, a set of pseudo-linear equations is established by introducing and decreasing the nuisance parameters. Then, two quadratic equations are obtained in terms of the nuisance parameters by considering relationships among them and the target position and velocity. By applying the elimination method that gives the nuisance parameters and substituting them into the localization problem, the target position and velocity are determined in the first stage. In the second stage, the error in the initial solution is estimated to improve the localization performance. The proposed estimator is shown to achieve the Cramer-Rao lower bound performance under Gaussian noise conditions, when the measurement error is small. The great advantage of the proposed method is that it can give the solution with fewer sensors (transmitters or receivers) in comparison with the state-of-the-art algorithms. Simulation results show that when there are one transmitter and three receivers or two transmitters and two receivers, the method can find the solution with a good accuracy whereas the state-of-the-art ones cannot determine the target position and velocity.

Wideband two dimensional interferometric direction finding algorithm using base-triangles and a proposed minimum planar array

In wideband interferometric direction finding ambiguity is inevitable due to practical antenna array dimensions. A new algorithm for wideband interferometer direction finding is developed to resolve the ambiguity problem with minimum number of antennas. The method is based on direction finding by three antennas arranged at the three vertices of a triangle named the base-triangle. A two dimensional matrix of ambiguous angles is generated. The ambiguity problem is resolved by an auxiliary base-triangle formed by a fourth antenna in the arrangement. The common angle between the two ambiguous directions derived from the two base-triangles, is the desired angle. As such a four antenna array is optimized with the proposed algorithm to minimize the direction finding error through the 6–18 GHz frequency band for different signal to noise ratios and in the presence of channel phase tracking error. The array performance is evaluated through Monte-Carlo simulations for a coverage of ±45° azimuth and ±45° elevation and a polynomial expression is fitted to the evaluated Root Mean Square errors. Finally, a comparison is made between the proposed method and various correlative interferometer methods. The method has an accuracy better or equal to the cosine function correlative interferometer with much less computation time.

A new scheme of dynamic power allocation in wireless powered communication

In this article, we propose a new generalized selection transmit scheme (GSTS) for wireless powered communication (WPC), where data access point (DAP) is powered by energy access point (EAP) to communicate with wireless device (WD). Theoretically speaking, allocating all harvesting energy to the antenna with the best channel gain will achieve the optimal performance. While the harvesting energy is dynamic and may exceed the power limitation of single antenna, we should allocate the harvesting energy to the best antennas subset with the minimum number of antennas. That is GSTS. For GSTS, we derive the new closed-form probability density function (PDF) of signal to noise ratio (SNR). According to the derived PDF, the approximate outage probability is derived. In order to depict the trend of outage probability at high SNR area, the diversity order is derived. It is determined by the minimum one of the transmit antenna number of EAP and that of DAP. Besides, the influence of line-of-sight (LOS) component in wireless power transfer (WPT) is also discussed.

Compact cross form antenna arrays intended for wideband two dimensional interferometric direction finding including the channel phase tracking error

The interferometer method as one of the most accurate schemes for wideband direction finding (DF) is used. The interferometer method has various algorithms which can be implemented depending on the required specifications. The advantages and disadvantages of these algorithms have been evaluated and the appropriate algorithm for a general practical case in view of the ambiguity resolution is proposed. The receivers’ channel phase tracking error is of significant concern in practice in interferometric DF systems. The induced error due to channels phase tracking error is estimated. Furthermore the use of physically realizable antennas, achievement of high accuracy, minimum number of antennas and consequently receivers and wideband DF is considered. The interferometric algorithms including Common Angle Search (CAS), Second Order Difference Array (SODA) and SODA-Based Inference (SBI) methods are compared for a linear array and the CAS method is selected as the appropriate algorithm. An optimized two dimensional cross form antenna array is devised by two orthogonal linear arrays. A cubic set for full coverage, has been proposed as the implementation of two dimensional wideband direction finding system with 360° azimuth and ±45° elevation coverage, and its resolution in presence of additive noise and the channel phase tracking error is evaluated.

Uplink Spectral Efficiency Analysis for a Massive MIMO Primary Network

Faster development of smart electronic devices in recent years along with significant increase in demanding higher data rates has made cognitive radio networks (CRNs) to be taken into consideration as a promising technology. A CRN has the ability to increase spectral efficiency (SE) of communication systems by opportunistically using unused spectrums. Furthermore, Massive multiple-input multiple-output is a major candidate to be used in next generation cellular systems in light of its great capabilities to improve system performance from spectral as well as energy efficiency standpoint. In this paper, we propose a CRN whose base station, as well as the primary base station (PBS) are equipped with large numbers of antennas. We derive closed-form expressions for SE in the uplink of primary users for three different scenarios. In these scenarios perfect and imperfect channel state information are considered separately. In addition, the impact of pilot contamination due to the correlation among users’ pilot signals on sum SE of primary network is examined. For the first two scenarios, minimum number of antennas (MNA) at the PBS to achieve a specified SE is derived in a closed-form expression. MNA is analyzed numerically for the third scenario.

Generalised selection at multi‐antenna sources in two‐way relay networks

A generalised selection transmission (GST) and generalised selection combining (GSC) scheme is proposed for two-way relay networks where two multi-antenna sources exchange information via a single-antenna relay. New exact and asymptotic expressions are derived for the outage probability and symbol error rate (SER) in Rayleigh fading. Moreover, a tight upper bound on the ergodic sum-rate is presented. These results are used to demonstrate that the proposed GST/GSC scheme preserves the full diversity order, which equals the minimum number of antennas at the two sources. It is also shown that the impact of the number of selected antennas lies in the array gain only. Furthermore, the GST/GSC scheme significantly improves the performance relative to single-antenna selection, and only incurs a negligible reduction in performance relative to all-antenna beamforming. Finally, the optimal relay location that minimises the SER is determined analytically. It is observed that the optimal relay location shifts towards one source when the number of selected or available antennas at the other source increases.

Electromagnetic Time-Reversal Imaging of Pinholes in Pipes

We have designed and implemented a structural health monitoring (SHM) system to detect and localize multidefects in semi-infinite cylindrical metal pipelines simultaneously. The system utilizes electromagnetic decomposition of the time-reversal operator (known under French acronym DORT) signal processing method. The magnificent performance of the DORT detector against signal-to-noise ratio (SNR), and its ability to detect and localize multidefects simultaneously, are the main advantages of the DORT time-reversal method. In the DORT time-reversal method, the reversed wave would precisely retrace back the exact intricate received path to converge coherently at the original source location by using the proper Green’s function. We have utilized the operating frequencies which are far enough from the (highly dispersive) band near the waveguide $TE_{11}$ cut-off frequency. The radius of the pipe is assumed to be ${\text{a}}=10{\text{cm}}$ . Hence, in order to excite the first two modes, frequency bandwidth is considered to be 300 MHz at the center frequency of 1.15 GHz. This system is tested to localize two rectangular holes of the area $(0.13\, \lambda_{0})^{2}$ , where $\lambda_{0}$ is the free-space wavelength at the central frequency. In addition, required parameters such as the minimum number of antennas for detection, the DORT detector performance analysis, the equivalent reflection coefficients of the holes with different sizes and shapes, and the maximum distance of detection of small holes are calculated.

Transmit Antenna Selection in Cognitive MIMO Relaying With Multiple Primary Transceivers

The authors consider transmit antenna selection (TAS) in cognitive multiple-input–multiple-output (MIMO) relay networks as an interference-aware design for secondary users (SUs) to ensure power and interference constraints of multiple primary users (PUs). In doing so, the authors derive new exact and asymptotic expressions for the outage probability of TAS with maximal ratio combining (TAS/MRC) and with selection combining (TAS/SC) over Rayleigh fading. The proposed analysis and simulations highlight that TAS/MRC and TAS/SC with decode-and-forward relaying achieve the same diversity order in cognitive MIMO networks, which scales with the minimum number of antennas at the SUs. Furthermore, the authors accurately characterize the outage gap between TAS/MRC and TAS/SC relaying as a concise ratio of their array gains.

Performance Evaluation of Decode-and-Forward Satellite Relaying

In this paper, we consider decode-and-forward (DF) relaying of the data of a multiple-antenna-based source Earth station, via a single-antenna-based satellite, to a multiple-antenna-based destination Earth station. The source uses beamforming for transmission of the data, and the destination utilizes the maximal ratio combining for demodulating the transmitted signal. The uplink and downlink satellite channels are assumed to be shadowed-Rician (SR) fading. First, we consider independent and identically distributed SR fading and derive the closed-form expressions of the approximate bit error rate (BER) and probability of outage for the considered scheme. By using the BER expression, the analytical diversity order of the scheme is obtained. It is deduced on the basis of the diversity order analysis that the diversity of the considered DF scheme linearly depends upon the minimum number of antennas at the source and destination nodes. Next, we consider correlated SR fading links and derive power-series-based expression of the approximate BER of the DF satellite relay system. For the correlated SR fading, the diversity order is analytically obtained; it is shown by analysis and simulation that the diversity order of the scheme with correlated channels does not depend upon the antenna correlation matrices of the source and destination nodes.

Minimum number of antennas and degrees of freedom of multiple‐input–multiple‐output multi‐user two‐way relay X channels

In this study, the minimum number of antennas at each user is derived to obtain 2M 2 degrees of freedom (DOF) in the M × 1 × M multiple-input–multiple-output (MIMO) multi-user two-way relay X channels. Based on the design of beamforming vectors for the conventional signal space alignment scheme, it is shown that each user needs at least ⌈M 2 − (M/2)⌉ antennas to obtain DOF 2M 2 with the relay having M 2 antennas. As the number of users increases, the number of antennas also increases, which makes the implementation difficult. In an effort to reduce the number of antennas, the authors propose a new beamforming scheme of MIMO multi-user two-way relay X channels using the time extension. Through the numerical analysis, it is confirmed that the proposed scheme with time extension is a good alternative scheme to replace the conventional scheme.

On the Achievable Degrees of Freedom of a K-User MIMO Interference Channel with a MIMO Relay

This paper investigates the achievable degrees of freedom (DoF) of a fully connected K-user multiple-input-multiple-output (MIMO) interference channel with a MIMO relay, where each transmitter (Tx) has M antennas and each receiver (Rx) has N antennas (K-user M × N channel). For the special case where M = N, previous works showed that even with the presence of relays, the sum DoF is still KM/2 and is achieved by interference alignment, assuming all Txs and Rxs have global channel state information (CSI). While this result showed that relays cannot increase the achievable DoF, we find that relay eliminates the CSI requirement at the Txs if global CSI is available at the relay. We propose a two-time-slot transmission scheme through which interference can be aligned, provided that the relay has enough antennas. We obtain the minimum number of antennas required at the relay for each Tx-Rx pair to achieve the maximum DoF and this number is less than that needed in the decode-and-forward approach and all other reported approaches in existing literature. Moreover, this can be achieved with just linear processing at the relay. Then the interference alignment based scheme is generalized to M ≠ N case, where we focus on the achievable symmetric DoF. A lower bound for the number of antennas required at the relay is derived and is shown to be tight in some cases.

Performance Analysis of MIMO Channel Inversion in Rayleigh Fading

The performance of eigenmode transmission over a multiple-input-multiple-output (MIMO) Rayleigh channel under the channel inversion (CI) power allocation scheme is investigated. The moment-generating function of the reciprocal of the received signal-to-noise ratio (SNR) is derived. For the special case when the minimum number of antennas at the transmitter and the receiver is two, the exact closed-form expressions for the probability density function (pdf) and cumulative distribution function (cdf) are also derived. The average symbol error rate (SER) is derived as an application of the results. The extension to Rician and semicorrelated Rayleigh fading scenarios is also outlined.

Design of Near-Field Circular Antenna Arrays Based on Convex Optimization

In this paper, a convex-optimization based design method is proposed for the near-field beamformer design problem to improve the performance of an MRI system. The aim is to find the minimum number of antennas required for a uniform circular array, and the array antenna is capable of forming a beam with a pre-defined sidelobe attenuation level for an arbitrary focal point within a given circular scanning area. Two sets of design criteria based on convex optimization are studied: minimizing the maximum response over the sidelobe area and minimizing the mean squared response over the sidelobe area. Design examples have shown that the proposed method can solve the problem successfully.

Modulation-Mode Assignment for SVD-assisted Downlink Multiuser MIMO Transmission Schemes with Iterative Detection

Modulation-Mode Assignment for SVD-assisted Downlink Multiuser MIMO Transmission Schemes with Iterative DetectionSince the capacity of multiple-input multiple-output (MIMO) systems increases linearly with the minimum number of antennas at both, the transmitter as well as the receiver side, MIMO systems have attracted a lot of attention for both frequency and non-frequency selective channels and reached a state of maturity. By contrast, MIMO-aided multiple-user systems require substantial further research. In comparison to zero-forcing (ZF) multiuser transmission techniques, where all users are treated jointly, the investigated singular value decomposition (SVD) assisted DL multiuser MIMO solution takes the individual user's channel characteristics into account. In analogy to bit-interleaved coded irregular modulation, we introduce a MIMO-BICM scheme, where different user-specific signal constellations and mapping arrangement were used within a single codeword. Extrinsic information transfer (EXIT) charts are used for analyzing and optimizing the convergence behaviour of the iterative demapping and decoding. Our results show that in order to achieve the best bit-error rate, not necessarily all user-specific MIMO layers have to be activated.

On overloaded vector precoding for single-user MIMO channels

We address the possibility of overloaded vector precoding in single user MIMO channels, i.e. the number of data streams is larger than the minimum of the number of antennas at transmitter and receiver side.We find that the convex vector precoding introduced in [1] allows for overloading while, with a certain probability, keeping the received signal free of interference. We find that the probability that overloading is not possible decays exponentially with the size of the system as long as the number of data streams is less than twice the minimum number of antennas. We give an explicit formula to calculate this probability for any antenna configuration in presence of correlated Rayleigh fading. Although overloading comes with the need for increased transmitted power, we show by means of the replica method that overloading up to 22% yields better spectral and power efficiency than without overload and spatial matched filter processing at the receiver.

Modulation-mode and power assignment in broadband MIMO systems

Since the capacity of multiple-input multiple-output (MIMO) systems increases linearly with the minimum number of antennas at both, the transmitter as well as the receiver side, MIMO schemes have attracted a lot of attention. However, non-frequency selective MIMO links have reached a state of maturity. By contrast, frequency selective MIMO links require substantial further research, leading in this contribution to a joint optimization of the number of activated MIMO layers and the number of bits per symbol along with the appropriate allocation of the transmit power under the constraint of a given fixed data throughput. Our results show that in order to achieve the best possible bit-error rate, not necessarily all MIMO layers have to be activated. .