Efficient Optimal Minimum Error Discrimination of Symmetric Quantum States

This paper deals with the quantum optimal discrimination among mixed quantum states enjoying geometrical uniform symmetry with respect to a reference density operator $\rho_0$. It is well-known that the minimal error probability is given by the positive operator-valued measure (POVM) obtained as a solution of a convex optimization problem, namely a set of operators satisfying geometrical symmetry, with respect to a reference operator $\Pi_0$, and maximizing $\textrm{Tr}(\rho_0 \Pi_0)$. In this paper, by resolving the dual problem, we show that the same result is obtained by minimizing the trace of a semidefinite positive operator $X$ commuting with the symmetry operator and such that $X >= \rho_0$. The new formulation gives a deeper insight into the optimization problem and allows to obtain closed-form analytical solutions, as shown by a simple but not trivial explanatory example. Besides the theoretical interest, the result leads to semidefinite programming solutions of reduced complexity, allowing to extend the numerical performance evaluation to quantum communication systems modeled in Hilbert spaces of large dimension.Comment: 5 pages, 1 Table, no figure

Improved Nyquist Pulses

In this letter, we propose two new Nyquist (intersymbol interference free) pulses that exhibit better error probability performance in the presence of sampling errors than the popular raised-cosine and a recently proposed pulse by Beaulieu, Tan, and Damen. The new pulses are also robust to the root and truncation operations

Doppler Spread Estimation and Channel Update Period Tuning inOFDM-based Vehicular Communication Systems

Decision directed channel estimation (DD-CE) techniques turn useful for transmissions in time-varying wireless vehicular channels. CE has to be updated several times during the transmission of long data frames. Related works assume that, for IEEE802.11p-compliant physical layer systems, DDCE is performed for every input OFDM symbol, hence independently of the experienced Doppler effect. The purpose of this paper is twofold. First, it is shown how the estimation of the Doppler spread can be reliably performed in vehicular scenarios, and, moreover, an improved yet simplied version of the hybrid autocorrelation-based estimator is proposed. Second, it is discussed how the resulting vehicle relative speed estimate can be used to tune the CE update refresh period accordingly (and thus reduce the power consumption and processing time at the receiver for low to medium speed ranges). In order to reach this goal, it is introduced a novel method that relates the CE update rate to a maximum pre-established threshold value of the signal-to-noise ratio degradation due to CE update delay

Analysis of the Effects of Phase Noise in Filtered Multitone (FMT) Modulated Systems

In this paper, we study the effects of phase noise in a multicarrier system. We show that the phase noise introduces interference components, and we evaluate their second order statistics. The analysis is then applied to two particular multicarrier architectures: discrete multitone (DMT) modulation, and filtered multitone (FMT) modulation. For the DMT case, our results are in agreement with other related work that considers DMT only. For FMT modulation, we demonstrate that the phase noise power spectral density as well as the frequency response of the prototype filters play a key role on the resulting interference power value. Finally, we show that the analytical performance results are close to the simulation results