In this paper, we investigate the capacity of the Gaussian two-hop full-duplex (FD) relay channel with residual self-interference. This channel is comprised of a source, an FD relay, and a destination, where a direct source-destination link does not exist and the FD relay is impaired by residual self-interference. We adopt the worst-case linear self-interference model with respect to the channel capacity, and model the residual selfinterference as a Gaussian random variable whose variance depends on the amplitude of the transmit symbol of the relay. For this channel, we derive the capacity and propose an explicit capacity-achieving coding scheme.Thereby, we show that the optimal input distribution at the source is Gaussian and its variance depends on the amplitude of the transmit symbol of the relay. On the other hand, the optimal input distribution at the relay is discrete or Gaussian, where the latter case occurs only when the relay-destination link is the bottleneck link.The derived capacity converges to the capacity of the two-hop ideal FD relay channel without self-interference and to the capacity of the two-hop half-duplex (HD) relay channel in the limiting cases when the residual selfinterference is zero and infinite, respectively. Our numerical results show that significant performance gains are achieved with the proposed capacity-achieving coding scheme compared to the achievable rates of conventional HD relaying and/or conventional FD relaying.
Radio-based indoor localization is currently a very vibrant scientific research field with many potential use cases. It offers high value for customers, for example, in the fields of robotics, logistics, and automation, or in context-aware IT services. Especially for autonomous systems, dynamic human-machine interaction, or augmented reality applications, precise localization coupled with a high update rate is a key. In this paper, we present a completely novel localization concept whereby received radio signal phase values that are fed into an extended Kalman filter (EKF) without any preprocessing are evaluated. Standard preprocessing steps, such as angle-of-arrival estimation, beamforming, and time-of-flight or time-differenceof-arrival estimations are not required with this approach. The innovative localization concept benefits from the high sensitivity of radio signals' phase to distance changes and the fast and straightforward recursive computation offered by the EKF. It completely forgoes the computational burden of other phase-based high-precision localization techniques, such as synthetic aperture methods. To verify the proposed method, we use an exemplary setup employing a 24 GHz frequency-modulated continuous-wave (CW) single-input multiple-output secondary radar with 250 MHz bandwidth. A high-precision six-axis robotic arm serves as a 3D positioning reference. The test setup emulates a realistic industrial indoor environment with significant multipath reflections. Despite the challenging conditions and the rather low bandwidth, the results show an outstanding localization 3D RMSE of around 1.7 cm. The proposed method can easily be applied to nearly any type of radio signal with CW carrier and is an attractive alternative to common multilateration and multiangulation localization approaches. We think it is a quantum leap in wireless locating, as it has the potential for precise, simple, and low-cost wireless localization even with standard narrowband communication signals. INDEX TERMS FMCW, radar, localization, extended Kalman filter, near field, indoor.
Magnetic local positioning systems are a well-suited candidate for reliable indoor positioning systems, as they are robust against blocking by dielectric materials like walls or people. The system presented in this paper is implemented with a one-axis magnetic transmitter and several three-axis field sensors connected to a complete sensor network. Unfortunately, the performance of the system is severely impaired by field sensor nonidealities such as magnetic coupling of the sensor coils, coil misalignment, field sensor rotation, and unsynchronized sampling. In this paper, the overall field sensor impairments and an additive Gaussian noise model superposing the magnetic field are mathematically described. Then, a novel calibration scheme for the overall field sensor nonidealities is presented. Furthermore, a statistically optimal localization procedure coping with the field sensor nonidealities is developed. The proposed novel localization and calibration algorithms are demonstrated in a common office environment with a size of 7 m × 5 m × 3 m. Thereby, the calibration impressively reduces the position rootmean-square error (RMSE) from 46.8 to 10.6 cm and the angle RMSE from 24.8 • to 6.1 • .
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