depends on the distribution of the data. Thus, we define the average symbol interval as follows.

![Comparison of a pulse sequence with static symbol intervals and dynamic symbol intervals.[]{data-label="fig:system:plot_comparison_spacing"}](plot_comparison_spacing)

\[def:avg\_duration\] The average symbol interval is $$\begin{aligned}
\bar{T}(X) &\triangleq \sum_{k=1}^{M} p_X (\lambda_k) {T{\mathopen{}\mathclose\bgroup\originalleft}(\lambda_k{\aftergroup\egroup\originalright})} = {\mathbb{E}_{X}\!{\mathopen{}\mathclose\bgroup\originalleft}\{{{T{\mathopen{}\mathclose\bgroup\originalleft}(\lambda{\aftergroup\egroup\originalright})}}{\aftergroup\egroup\originalright}\}
}.\end{aligned}$$

In [@shevchenko2018tcom], only eigenvalues with an imaginary part larger than zero are used. We extend this by allowing ${\mathfrak{I}\{\lambda\}}=0$. In the time domain, this results in a pulse with amplitude zero, i.e., we do not transmit anything. We define its corresponding duration as the same as the duration of the shortest pulse, ${T{\mathopen{}\mathclose\bgroup\originalleft}(\lambda=0{\aftergroup\egroup\originalright})} \triangleq {T{\mathopen{}\mathclose\bgroup\originalleft}(\lambda_M{\aftergroup\egroup\originalright})}$.

As any practical system can handle only a maximum peak power and a maximum bandwidth, we enforce a peak power constraint which relates to a maximum eigenvalue constraint. Especially in systems with lumped amplification and , such a constraint is required as eigenvalues fluctuate depending on their amplitude, which decreases the performance [@zafrulla2003].

We note that the varying symbol interval introduces additional challenges on detection. In particular, an erroneously detected symbol may lead to error propagation, insertion errors (detection of symbols when none was transmitted), deletion errors (not detecting a transmitted symbol), or the loss of synchronization. To calculate the 