Full-duplex (FD) technology holds the potential for twice the spectral efficiency compared to half-duplex (HD) communication. However, simultaneous transmission and reception in the same frequency band may be subject to severe self-interference (SI). Therefore, mitigating the impact of SI becomes a key issue in realizing FD wireless communications. In this paper, we propose a hybrid beamforming design that effectively suppresses SI while maintaining superior communication quality for FD millimeter wave (mmWave) communication systems. Simulation results demonstrate that the designed hybrid transceivers exhibit exceptional resistance to the SI, leading to a significant improvement in spectral efficiency compared to conventional HD communications.

This paper introduces the partial-inverse problem for linearized polynomials and develops its application to decoding Gabidulin codes and lifted Gabidulin codes in linear random network coding. The proposed approach is a natural generalization of its counterpart for ordinary polynomials, thus providing a unified perspective on Reed–Solomon codes for the Hamming metric and for the rank metric. The basic algorithm for solving the partial-inverse problem is a common parent algorithm of a Berlekamp–Massey algorithm, a Euclidean algorithm, and yet another algorithm, all of which are obtained as easy variations of the basic algorithm. Decoding Gabidulin codes can be reduced to the partial-inverse problem via a key equation with a new converse. This paper also develops new algorithms for interpolating crisscross erasures and for joint decoding of errors, erasures, and deviations in random network coding.

For a millimeter wave (mmWave) system consisting of a basestation (BS) and a mobile user-equipment (UE), the problem of signal-and-data detection is investigated, and a low complexity ML-MMSE receiver for mmWave beamforming, beamtracking, and data-symbols detection is proposed. Specifically, with a (practical) hybrid beamforming transceiver architecture at both the BS and UE, a multistage angle-of-arrival (AoA) estimation based beamtraining algorithm that provides fast acquisition of the best beam pairs for the BS-UE link is developed. In addition, a novel joint beamtracking and data-symbols detection algorithm, equipped with an adaptive equalizer, is also developed. The algorithm can simultaneously track the best receiving beams, and produce the data estimates that are easy to extract soft bit information for soft decoding; also, it can tackle the dynamic changes of the baseband effective channel. Analytical and simulation results show that the proposed receiver performs well over a broad range of SNR-it can rapidly acquire the most dominant AoAs for beamforming and constantly track the best moving beams due to UE's mobility or device rotation-and in particular, it achieves near-optimal spectral efficiency for a mobile UE with a single RF chain or very few RF chains.

We study Gabidulin codes from a partial-inverse perspective and obtain a key equation with a new converse, as well as a new interpolation formula. The resulting new algorithm is efficient and conceptually simple.

This paper introduces the simultaneous partial-inverse problem (SPI) for polynomials and develops its application to decoding interleaved Reed-Solomon codes beyond half the minimum distance. While closely related both to standard key equations and to well-known Padé approximation problems, the SPI problem stands out in several respects. First, the SPI problem has a unique solution (up to a scale factor), which satisfies a natural degree bound. Second, the SPI problem can be transformed (monomialized) into an equivalent SPI problem where all moduli are monomials. Third, the SPI problem can be solved by an efficient algorithm of the Berlekamp-Massey type. Fourth, decoding interleaved Reed-Solomon codes (or subfield-evaluation codes) beyond half the minimum distance can be analyzed in terms of a partial-inverse condition for the error pattern: if that condition is satisfied, then the (true) error locator polynomial is the unique solution of a standard key equation and can be computed in many different ways, including the well-known multi-sequence Berlekamp-Massey algorithm and the SPI algorithm of this paper. Two of the best performance bounds from the literature (the Schmidt-Sidorenko-Bossert bound and the Roth-Vontobel bound) are generalized to hold for the partial-inverse condition and thus to apply to several different decoding algorithms.

This semi-tutorial paper introduces the partial-inverse problem for polynomials and develops its application to decoding Reed-Solomon codes and some related codes. The most natural algorithm to solve the partial-inverse problem is very similar to, but more general than, the Berlekamp-Massey algorithm. Two additional algorithms are obtained as easy variations of the basic algorithm: the first variation is entirely new, while the second variation may be viewed as a version of the Euclidean algorithm. Decoding Reed-Solomon codes (and some related codes) can be reduced to the partial-inverse problem, both via the standard key equation and, more naturally, via an alternative key equation with a new converse. Shortened and singly-extended Reed-Solomon codes are automatically included. Using the properties of the partial-inverse problem, two further key equations with attractive properties are obtained. The paper also points out a variety of options for interpolation.

The partial-inverse approach is further developed to decoding interleaved Reed-Solomon codes and subfield-evaluation codes beyond half the minimum distance. The resulting decoding algorithm is new, and its decoding capability is shown to be state-of-the-art.

We propose a new algorithm for decoding Reed-Solomon codes (up to half the minimum distance) and for computing inverses in F[x]/m(x). The proposed algorithm is similar in spirit and structure to the Berlekamp-Massey algorithm, but it works naturally for general m(x).

A general class of polynomial remainder codes is considered. These codes are very flexible in rate and length and include Reed-Solomon codes as a special case. In general, the code symbols of such codes are polynomials of different degree, which leads to two different notions of weights and of distances. The notion of an error locator polynomial is generalized to such codes. A key equation is proposed, from which the error locator polynomial can be computed by means of a gcd algorithm. From the error locator polynomial, the transmitted message can be recovered in two different ways, which may be new even when specialized to Reed-Solomon codes.

For orthogonal frequency-division multiplexing (OFDM) signals that suffer from frequency-selective fading, we derive the maximum-likelihood (ML) pilot-assisted carrier frequency offset (CFO) estimate and show that most proposals based on repetitive pilot symbols did not use the complete set of sufficient statistics. We convert the problem of obtaining the ML solution from searching exhaustively over the entire uncertainty range to that of solving a spectrum polynomial, thereby greatly reducing the computational load. By properly truncating the polynomial, we obtain a closed-form expression for the corresponding zeros so that the root-searching procedure is greatly simplified. The complexity of locating the desired root is further reduced at almost no expense of performance degradation by an alternate algorithm that uses the fact that the solution is related to the root of a special factor of the polynomial. This alternate method is very attractive for its simplicity and excellent performance that, even at low signal-to-noise ratios (SNRs), is very close to the corresponding Crame/spl acute/r-Rao lower bound. A detailed analysis of the mean-squared error performance is presented and the analysis is validated by simulations.