  We investigate the relay selection problem for a decode and forward
collaborative network. Users are able to collaborate; decode messages of each
other, re-encode and forward along with their own messages. We study the
performance obtained from collaboration in terms of 1) increasing the
achievable rate, 2) saving the transmit energy and 3) reducing the resource
requirement (resource means time-bandwidth). To ensure fairness, we fix the
transmit-energy-to-rate ratio among all users. We allocate resource optimally
for the collaborative protocol (CP), and compare the result with the
non-collaborative protocol (NCP) where users transmits their messages directly.
The collaboration gain is a function of the channel gain and available energies
and allows us 1) to decide to collaborate or not, 2) to select one relay among
the possible relay users, and 3) to determine the involved gain and loss of
possible collaboration. A considerable gain can be obtained if the direct
source-destination channel gain is significantly smaller than those of
alternative involved links. We demonstrate that a rate and energy improvement
of up to $(1+\sqrt[\eta]{\frac{k}{k+1}})^\eta$ can be obtained, where $\eta$ is
the environment path loss exponent and $k$ is the ratio of the rates of
involved users. The gain is maximum for low
transmit-energy-to-received-noise-ratio (TERN) and in a high TERN environment
the NCP is preferred.
