  In this letter, we consider downlink transmission of a multiuser
multiple-input multiple-output (MU-MIMO) system with zero-forcing (ZF)
precoders in the presence of multiple attackers. We propose a cooperative pilot
spoofing attack (CPSA), where the attackers collaboratively impair the channel
estimations in the uplink channel training phase, aiming at deteriorating the
downlink throughput of the whole cell. We first evaluate the impacts of CPSA on
the channel estimation and the downlink ZF precoding design, and then we derive
an analytical expression for the achievable downlink sum-rate. Furthermore, we
investigate the optimal attack strategy to minimize the achievable downlink
sum-rate. We show that the optimization problem under consideration is a convex
one so the global optimum could be obtained conveniently. Numerical results
show that the CPSA attack results in a severe performance deterioration with
the increase in the attacking power and the number of attackers.
