Structure theorem of square complex orthogonal design

Square COD (complex orthogonal design) with size $[n, n, k]$ is an $n \times n$ matrix $\mathcal{O}_z$, where each entry is a complex linear combination of $z_i$ and their conjugations $z_i^*$, $i=1,\ldots, k$, such that $\mathcal{O}_z^H \mathcal{O}_z = (|z_1|^2 + \ldots + |z_k|^2)I_n$. Closely following the work of Hottinen and Tirkkonen, which proved an upper bound of $k/n$ by making a crucial observation between square COD and group representation, we prove the structure theorem of square COD

Coding on Flag Manifolds for Limited Feedback MIMO Systems

The efficiency of the physical layer in modern communication systems using multi-input multi-output (MIMO) techniques is largely based on the availability of channel state information (CSI) at the transmitter. In many practical systems, CSI needs to be quantized at the receiver side before transmission through a limited rate feedback channel. This is typically done using a codebook-based precoding transmission, where the receiver transmits the index of a codeword from a pre-designed codebook shared with the transmitter. To construct such codes one has to discretize complex flag manifolds. For single-user MIMO with a maximum likelihood receiver, the spaces of interest are Grassmann manifolds. With a linear receiver and network MIMO, the codebook design is related to discretization of Stiefel manifolds and more general flag manifolds. In this thesis, coding in flag manifolds is studied. In a first part, flag manifolds are defined as metric spaces corresponding to subsurfaces of hyperspheres. The choice of distance defines the geometry of the space and impacts clustering and averaging (centroid computation) in vector quantization, as well as coding theoretical packing bounds and optimum constructions. For two transmitter antenna systems, the problem reduces to designing spherical codes. A simple isomorphism enables to analytically derive closed-form codebooks with inherent low-implementation complexity. For more antennas, the concept of orbits of symmetry groups is investigated. Optimum codebooks, having desirable implementation properties as described in industry standardization, can be obtained using orbits of specific groups. For large antenna systems and base station cooperation, a product codebook strategy is also considered. Such a design requires to jointly discretize the Grassmann and Stiefel manifolds. A vector quantization algorithm for joint Grassmann-Stiefel quantization is proposed. Finally, the pertinence of flag codebook design is illustrated for a MIMO system with linear receiver

Design of Radio-Frequency Arrays for Ultra-High Field MRI

Magnetic Resonance Imaging (MRI) is an indispensable, non-invasive diagnostic tool for the assessment of disease and function. As an investigational device, MRI has found routine use in both basic science research and medicine for both human and non-human subjects. Due to the potential increase in spatial resolution, signal-to-noise ratio (SNR), and the ability to exploit novel tissue contrasts, the main magnetic field strength of human MRI scanners has steadily increased since inception. Beginning in the early 1980’s, 0.15 T human MRI scanners have steadily risen in main magnetic field strength with ultra-high field (UHF) 8 T MRI systems deemed to be insignificant risk by the FDA (as of 2016). However, at UHF the electromagnetic fields describing the collective behaviour of spin dynamics in human tissue assume ‘wave-like’ behaviour due to an increase in the processional frequency of nuclei at UHF. At these frequencies, the electromagnetic interactions transition from purely near-field interactions to a mixture of near- and far-field mechanisms. Due to this, the transmission field at UHF can produce areas of localized power deposition – leading to tissue heating – as well as tissue-independent contrast in the reconstructed images. Correcting for these difficulties is typically achieved via multi-channel radio-frequency (RF) arrays. This technology allows multiple transmitting elements to synthesize a more uniform field that can selectively minimize areas of local power deposition and remove transmission field weighting from the final reconstructed image. This thesis provides several advancements in the design and construction of these arrays. First, in Chapter 2 a general framework for modeling the electromagnetic interactions occurring inside an RF array is adopted from multiply-coupled waveguide filters and applied to a subset of decoupling problems encountered when constructing RF arrays. It is demonstrated that using classic filter synthesis, RF arrays of arbitrary size and geometry can be decoupled via coupling matrix synthesis. Secondly, in Chapters 3 and 4 this framework is extended for designing distributed filters for simple decoupling of RF arrays and removing the iterative tuning portion of utilizing decoupling circuits when constructing RF arrays. Lastly, in Chapter 5 the coupling matrix synthesis framework is applied to the construction of a conformal transmit/receive RF array that is shape optimized to minimize power deposition in the human head during any routine MRI examination

Order-Theoretic Methods for Space-Time Coding: Symmetric and Asymmetric Designs

Siirretty Doriast

Analog least mean square loop for self-interference cancellation: A practical perspective

©2020 by the authors. Licensee MDPI, Basel, Switzerland. Self-interference (SI) is the key issue that prevents in-band full-duplex (IBFD) communications from being practical. Analog multi-tap adaptive filter is an efficient structure to cancel SI since it can capture the nonlinear components and noise in the transmitted signal. Analog least mean square (ALMS) loop is a simple adaptive filter that can be implemented by purely analog means to sufficiently mitigate SI. Comprehensive analyses on the behaviors of the ALMS loop have been published in the literature. This paper proposes a practical structure and presents an implementation of the ALMS loop. By employing off-the-shelf components, a prototype of the ALMS loop including two taps is implemented for an IBFD system operating at the carrier frequency of 2.4 GHz. The prototype is firstly evaluated in a single carrier signaling IBFD system with 20 MHz and 50 MHz bandwidths, respectively. Measured results show that the ALMS loop can provide 39 dB and 33 dB of SI cancellation in the radio frequency domain for the two bandwidths, respectively. Furthermore, the impact of the roll-off factor of the pulse shaping filter on the SI cancellation level provided by the prototype is presented. Finally, the experiment with multicarrier signaling shows that the performance of the ALMS loop is the same as that in the single carrier system. These experimental results validate the theoretical analyses presented in our previous publications on the ALMS loop behaviors

Analog Least Mean Square Loop for Self-Interference Cancellation: A Practical Perspective

Self-interference (SI) is the key issue that prevents in-band full-duplex (IBFD) communications from being practical. Analog multi-tap adaptive filter is an efficient structure to cancel SI since it can capture the nonlinear components and noise in the transmitted signal. Analog least mean square (ALMS) loop is a simple adaptive filter that can be implemented by purely analog means to sufficiently mitigate SI. Comprehensive analyses on the behaviors of the ALMS loop have been published in the literature. This paper proposes a practical structure and presents an implementation of the ALMS loop. By employing off-the-shelf components, a prototype of the ALMS loop including two taps is implemented for an IBFD system operating at the carrier frequency of 2.4 GHz. The prototype is firstly evaluated in a single carrier signaling IBFD system with 20 MHz and 50 MHz bandwidths, respectively. Measured results show that the ALMS loop can provide 39 dB and 33 dB of SI cancellation in the radio frequency domain for the two bandwidths, respectively. Furthermore, the impact of the roll-off factor of the pulse shaping filter on the SI cancellation level provided by the prototype is presented. Finally, the experiment with multicarrier signaling shows that the performance of the ALMS loop is the same as that in the single carrier system. These experimental results validate the theoretical analyses presented in our previous publications on the ALMS loop behaviors