density $N_0/2$ [@kahn2002wireless; @audeh2002performance; @lapidoth2009capacity; @proakis2001digital]. Although the input signal to the channel $x(t)$ must be nonnegative, there is no such constraint on the received signal $y(t)$ [@farid2010capacity].

The received signal passes through a filter with impulse response $g(t)$, resulting in $$r(t)=y(t)\otimes g(t),\label{eq:FilteredSignal}$$ which is then sampled at the symbol rate. In this paper, two scenarios are considered for the receiver filter:

\(i) Similarly to [@1577875; @4132995], $y(t)$ can enter a sampling receiver, which in this paper is assumed to have a rectangular frequency response to limit the power of the noise in the receiver, and is given by $$G(\omega)=\begin{cases}
\begin{array}{cc}
G(0) & |\omega|<2\pi B\\
0 & |\omega|\geq 2 \pi B\end{array}.\end{cases}\label{eq:G(f)}$$ (ii) According to our proposed method, $y(t)$ can enter a matched filter receiver with frequency response $G(\omega)=\zeta Q^{*}(\omega)$ where [$\left( \cdot \right)^*$]{} is the complex conjugate and $\zeta$ is an arbitrary scaling factor. This type of filter will limit the power of the noise, and can also result in ISI-free transmission if the pulses are root-Nyquist (see Sec. \[sec:RootPulse-shaping\]).

The system model introduced in this section is a generalization of the one in [@4132995], which is obtained by considering $\mathcal{C}\subset\mathbb{R}^{+}$ and setting $\mu=0$ in (\[eq:TxSignal\]). If $\mu=0$, the pulse 