  This paper studies the design and secrecy performance of linear multihop
networks, in the presence of randomly distributed eavesdroppers in a
large-scale two-dimensional space. Depending on whether there is feedback from
the receiver to the transmitter, we study two transmission schemes: on-off
transmission (OFT) and non-on-off transmission (NOFT). In the OFT scheme,
transmission is suspended if the instantaneous received signal-to-noise ratio
(SNR) falls below a given threshold, whereas there is no suspension of
transmission in the NOFT scheme. We investigate the optimal design of the
linear multiple network in terms of the optimal rate parameters of the wiretap
code as well as the optimal number of hops. These design parameters are highly
interrelated since more hops reduces the distance of per-hop communication
which completely changes the optimal design of the wiretap coding rates.
Despite the analytical difficulty, we are able to characterize the optimal
designs and the resulting secure transmission throughput in mathematically
tractable forms in the high SNR regime. Our numerical results demonstrate that
our analytical results obtained in the high SNR regime are accurate at
practical SNR values. Hence, these results provide useful guidelines for
designing linear multihop networks with targeted physical layer security
performance.
