  For the multiuser multiple-input multiple-output (MIMO) downlink channel, the
users feedback their channel state information (CSI) to help the base station
(BS) schedule users and improve the system sum rate. However, this incurs a
large aggregate feedback bandwidth which grows linearly with the number of
users. In this paper, we propose a novel scheme to reduce the feedback load in
a downlink orthogonal space division multiple access (SDMA) system with
zero-forcing receivers by allowing the users to dynamically determine the
number of feedback bits to use according to multiple decision thresholds.
Through theoretical analysis, we show that, while keeping the aggregate
feedback load of the entire system constant regardless of the number of users,
the proposed scheme almost achieves the optimal asymptotic sum rate scaling
with respect to the number of users (also known as the multiuser diversity).
Specifically, given the number of thresholds, the proposed scheme can achieve a
constant portion of the optimal sum rate achievable only by the system where
all the users always feedback, and the remaining portion (referred to as the
sum rate loss) decreases exponentially to zero as the number of thresholds
increases. By deriving a tight upper bound for the sum rate loss, the minimum
number of thresholds for a given tolerable sum rate loss is determined. In
addition, a fast bit allocation method is discussed for the proposed scheme,
and the simulation results show that the sum rate performances with the complex
optimal bit allocation method and with the fast algorithm are almost the same.
We compare our multi-threshold scheme to some previously proposed feedback
schemes. Through simulation, we demonstrate that the proposed scheme can reduce
the feedback load and utilize the limited feedback bandwidth more effectively
than the existing feedback methods.
