The capacity region of the Gaussian multiple-input multiple-output broadcast channel：（高斯多输入多输出能力地区的广播频道）.pdfVIP

3936 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 9, SEPTEMBER 2006 The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel Hanan Weingarten, Student Member, IEEE, Yossef Steinberg, Member, IEEE, and Shlomo Shamai (Shitz), Fellow, IEEE Abstract— The Gaussian multiple-input multiple-output matrices where means that is a positive (MIMO) broadcast channel (BC) is considered. The dirty-paper semidefinite matrix). coding (DPC) rate region is shown to coincide with the capacity re- • is a real output vector, received by user gion. To that end, a new notion of an enhanced broadcast channel . This is a vector of size (the vec- is introduced and is used jointly with the entropy power inequality, to show that a superposition of Gaussian codes is optimal for the tors are not necessarily of the same size). degraded vector broadcast channel and that DPC is optimal • is a fixed, real gain matrix imposed on user . This is a for the nondegraded case. Furthermore, the capacity region is matrix of size . The gain matrices are fixed and are characterized under a wide range of input constraints, accounting, perfectly known at the transmitter and at all receivers. as special cases, for the total power and the per-antenna power • is a real Gaussian random vector with zero mean and constraints.