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Table Of Integrals Series And Products

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

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

Spatial Modulation

In-band full-duplex (IBFD) operation has emerged as an attractive solution for increasing the throughput of wireless communication systems and networks. With IBFD, a wireless terminal is allowed to transmit and receive simultaneously in the same frequency band. This tutorial paper reviews the main concepts of IBFD wireless. One of the biggest practical impediments to IBFD operation is the presence of self-interference, i.e., the interference that the modem's transmitter causes to its own receiver. This tutorial surveys a wide range of IBFD self-interference mitigation techniques. Also discussed are numerous other research challenges and opportunities in the design and analysis of IBFD wireless systems.

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In-Band Full-Duplex Wireless: Challenges and Opportunities

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In-band full-duplex (IBFD) operation has emerged as an attractive solution for increasing the throughput of wireless communication systems and networks. With IBFD, a wireless terminal is allowed to transmit and receive simultaneously in the same frequency band. This tutorial paper reviews the main concepts of IBFD wireless. Because one the biggest practical impediments to IBFD operation is the presence of self-interference, i.e., the interference caused by an IBFD node's own transmissions to its desired receptions, this tutorial surveys a wide range of IBFD self-interference mitigation techniques. Also discussed are numerous other research challenges and opportunities in the design and analysis of IBFD wireless systems.

Full-duplex relaying is more spectrally efficient than half-duplex relaying as only one channel use is needed per two hops. However, it is crucial to minimize relay self-interference to render full duplex feasible. For this purpose, we analyze a broad range of multiple-input multiple-output (MIMO) mitigation schemes: natural isolation, time-domain cancellation, and spatial suppression. Cancellation subtracts replicated interference signal from the relay input while suppression reserves spatial dimensions for receive and transmit filtering. Spatial suppression can be achieved by antenna subset selection, null-space projection, i.e., receiving and transmitting in orthogonal subspaces, or joint transmit and receive beam selection to support more spatial streams by choosing the minimum eigenmodes for overlapping subspaces. In addition, minimum mean square error (MMSE) filtering can be employed to maintain the desired signal quality, which is inherent for cancellation, and the combination of time- and spatial-domain processing may be better than either alone. Targeting at minimal interference power, we solve optimal filters for each scheme in the cases of joint, separate and independent design. The performance of mitigation schemes is evaluated and compared by simulations. The results confirm that self-interference can be mitigated effectively also in the presence of imperfect side information.

Mitigation of Loopback Self-Interference in Full-Duplex MIMO Relays

Focusing on two-antenna infrastructure relays employed for coverage extension, we develop hybrid techniques that switch opportunistically between full-duplex and half-duplex relaying modes. To rationalize the system design, the classic three-node full-duplex relay link is first amended by explicitly modeling residual relay self-interference, i.e., a loopback signal from the transmit antenna to the receive antenna remaining after cancellation. The motivation for opportunistic mode selection stems then from the fundamental trade-off determining the spectral efficiency: The half-duplex mode avoids inherently the self-interference at the cost of halving the end-to-end symbol rate while the full-duplex mode achieves full symbol rate but, in practice, suffers from residual interference even after cancellation. We propose the combination of opportunistic mode selection and transmit power adaptation for maximizing instantaneous and average spectral efficiency after noting that the trade-off favors alternately the modes during operation. The analysis covers both common relaying protocols (amplify-and-forward and decode-and-forward) as well as reflects the difference of downlink and uplink systems. The results show that opportunistic mode selection offers significant performance gain over system design that is confined to either mode without rationalization.

Hybrid Full-Duplex/Half-Duplex Relaying with Transmit Power Adaptation

The invention relates to a transmit diversity method for a wireless communication system comprising a transmitting element and at least one receiver, wherein a transmission signal is transmitted from the transmitting element to the at least one receiver in accordance with a weight information determined in response to a feedback information. The feedback information is derived from the response at the at least one receiver to the transmission signal, and is fed back using multiplexed feedback signals. Multiple feedback signal quantization constellations and/or constellation specific feedback subchannels can be used for channel probing, such that the total feedback resolution and robustness can be enhanced, while maintaining low signaling capacity of the feedback channel.

Risto Wichman

Papers

In-Band Full-Duplex Wireless: Challenges and Opportunities

In-Band Full-Duplex Wireless: Challenges and Opportunities

Mitigation of Loopback Self-Interference in Full-Duplex MIMO Relays

Hybrid Full-Duplex/Half-Duplex Relaying with Transmit Power Adaptation

Transmit diversity method and system