Optimal System Designs for Cyclostationary Noise Channels

Abstract

The objective of this thesis is the optimal system designs for cyclostationary noise channels.We consider two classes of cyclostationarity, wide-sense cyclostationarity (WSCS) and second-order cyclostationarity (SOCS) for the model of Gaussian interference signal.Although the capacity and capacity-achieving input distribution are both well known for a channel corrupted only by an additive stationary Gaussian noise, no result is available when the Gaussian noise is cyclostationary.First, we derive the capacity of a continuous-time, single-input single-output (SISO), frequency-selective, band-limited, linear time-invariant channel, whose output is corrupted by a WSCS complex Gaussian noise.By using a pair of invertible, linear-conjugate linear time-varying operators called a FREquency SHift (FRESH) vectorizer/scalarizer pair, it is shown that the SISO channel can always be converted to an equivalent multiple-input multiple-output channel whose output is now corrupted by a proper-complex vector wide-sense stationary noise.It is also extended to a case of an SOCS complex Gaussian noise by using properizing FRESH (p-FRESH) vectorizer/scalarizer pair.It turns out that the optimal input obtained through the cyclic water filling (CWF), similar to the water filling, is a WSCS or an SOCS complex Gaussian random process with the same cycle period as the noise.Then, we present the application of the propoded optimal design, such as the design of a selfless overlay cognitive radio.Under the assumptions that the primary signal is a cyclostationary Gaussian random process and the primary receiver employs a linear time-invariant filters followed by uniform samplers, the throughput of the secondary user is maximized, subject to no modification and no performance degradation on the primary side.The optimal solution obtained through the orthogonal CWF (O-CWF) is derived.It is shown that the O-CWF can fully recycle the excess bandwidth spent for the pulse shaping of the primary signal and, consequently, the primary and the secondary systems share the entire spectrum as if they are optimal frequency-division systems.Lastly, the peak-to-average power ratio (PAPR) is evaluated for the uncoded orthogonal frequency division multiplexing (OFDM) signals generated by using the inverse discrete Fourier transform procedure. The power spectral density of the transmitted OFDM signal is derived, taking into account the effects of cyclic prefix, windowing, digital-to-analog converter, null-subcarriers, and analog transmit filter. The PAPR distribution is then analyzed based on the extreme value theory. It is shown that the PAPR distribution is parameterized only by the length of the observation interval and the root mean square bandwidth of thesignal, whose computation requires the PSD of the transmitted signal.