  In the $K$-user single-input single-output (SISO) frequency-selective fading
interference channel, it is shown that the maximal achievable multiplexing gain
is almost surely $K/2$ by using interference alignment (IA). However, when the
signaling dimensions are limited, allocating all the resources to all users
simultaneously is not optimal. So, a group based interference alignment (GIA)
scheme is proposed, and it is formulated as an unbounded knapsack problem.
Optimal and greedy search algorithms are proposed to obtain group patterns.
Analysis and numerical results show that the GIA scheme can obtain a higher
multiplexing gain when the resources are limited.
