Hence, they require an infinite amount of DC bias to be nonnegative.

Analysis and Results\[sec:RESULTS\]
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Received Sequence for Sampling Receiver\[subsec:RxSequence\_Nyq\]
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Considering the assumptions mentioned in Sec. \[sec:SYSTEM-MODEL\], the received signal (\[eq:FilteredSignal\]) is $$\begin{aligned}
r(t) &=\left(x(t)+n(t)\right)\otimes g(t) \nonumber\\
 &=A\left(\mu+\sum_{k=-\infty}^{\infty}a_{k}q(t-k{T_\mathrm{s}})\right)\otimes g(t)+z(t) \nonumber\\
 & =AG(0)\left[\mu+\sum_{k=-\infty}^{\infty}a_{k}q(t-k{T_\mathrm{s}})\right]+z(t),\label{eq:receivedSignal}\end{aligned}$$ where (\[eq:receivedSignal\]) holds since $g(t)$ has a flat frequency response given by (\[eq:G(f)\]) over the bandwidth of $q(t)$ given by (\[eq:bandwidthLimitation\]); Therefore, the convolution has no effect on $x(t)$. The noise at the output of the receiver filter, which is given by $z(t)=n(t)\otimes g(t)$, is zero mean additive white Gaussian with variance $\sigma_{z}^2=G(0)^2N_{0}B$.

Applying the Nyquist criterion given in (\[eq:NyquistInTime\]) to the sampled version of (\[eq:receivedSignal\]), we can write the $i$-th filtered sample as $$r(i{T_\mathrm{s}})=AG(0)\left[\mu+a_{i}q(0)\right]+z(i{T_\mathrm{s}}).\label{eq:RecSamplesEQ}$$ for any constellation $\mathcal{C}$. The received waveform $r(t)$, for several Nyquist pulses, is shown in Fig. \[eye-diagrams\], in the form of eye diagrams in a noise-free setting ($z(t) = 0$). As expected, the output samples $r(i {T_\mathrm{s}})$ are ISI-free.

Received Sequence for Matched Filter Receiver\[subsec:RxSequence\_MF\]
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Similar to Sec. \[subsec:RxSequence\_Nyq\], the received signal will be $$\begin{aligned}
 \vspace{-3mm}
r(t) & =\left(x(t)+n(t)\right)\otimes g(t) \nonumber \\
& =A\left(\mu+\sum_{k=-\infty}^{\infty}a_{k}q(t-k{T_\mathrm{s}})\right)\otimes \zeta q(-t)+u(t) \nonumber \\
& =A\zeta \Big(\mu\intop_{-\infty}^{\infty}q(-t)dt+\sum_{k=-\infty}^{\infty}a_{k}\intop_{-\infty}^{\infty}q(\tau-k{T_\mathrm{s}})q(\tau-t)d\tau\Big)+u(t) \nonumber \\
& =A\zeta \left(\mu Q(0)+\sum_{k=-\infty}^{\infty}a_{k}\intop_{-\infty}^{\infty}q(\tau)q(\tau-t+k{T_\mathrm{s}})d\tau\right)+u(t)\label{eq:MF_Output}\end{aligned}$$ where $u(t)$ is 