The impact and benefits of channel state information (CSI) are analyzed in terms of degrees-of-freedom (DoFs) in a K-user interference network operating over time-selective channels, where the error variance of CSI estimation is assumed to scale with an exponent of the received signal-to-noise ratio (SNR). The original interference alignment (IA) scheme is used with a slight modification in the network. Then, it is shown that the DoFs promised by the original IA can be fully achieved under the condition that the CSI quality order, represented as a function of the error variance and the SNR, is greater than or equal to 1. Our result is extended to the case where the number of communication pairs, K, scales with the SNR, i.e., infinite K scenario, by introducing the user scaling order. As a result, this letter provides vital information to the system designer in terms of allocating training resources for channel estimation in practical cellular environments using IA.

This paper focuses on the development of Cramer-Rao Bound (CRB) expressions for passive source location estimation in various Gaussian noise environments. The scenarios considered involve an unknown deterministic source signal with a short time duration, and additive general Gaussian noise. The mathematical derivation procedure presented is applicable to non-stationary Gaussian noise problems. Specifically, explicit closed-form CRB expressions are presented using the spectrum representation of the signal and noise for stationary Gaussian noise cases.

The additive noise response of a charge pump phase-locked loop in the synchronous mode of operation has been studied. In order to determine the tracking and noise performances of the loop, mean square values of tracking error and local oscillator phase jitter have been analytically obtained. Analytical results agree well with the simulation results obtained here and elsewhere. The analysis performed can be used in choosing different system parameters for optimum system operation.