This paper proposes a joint transmitter-receiver design to minimize the weighted sum power under the post-processing signal-to-interference-and-noise ratio (post-SINR) constraints for all subchannels. Simulation results demonstrate that the algorithm can not only satisfy the post-SINR constraints but also easily adjust the power distribution among the users by changing the weights accordingly. Hence the algorithm can be used to alleviates the adjacent cell interference by reducing the transmitting power to the edge users without performance penalty.
Deep Dive into Joint Transmitter-Receiver Design for the Downlink Multiuser Spatial Multiplexing MIMO System.
This paper proposes a joint transmitter-receiver design to minimize the weighted sum power under the post-processing signal-to-interference-and-noise ratio (post-SINR) constraints for all subchannels. Simulation results demonstrate that the algorithm can not only satisfy the post-SINR constraints but also easily adjust the power distribution among the users by changing the weights accordingly. Hence the algorithm can be used to alleviates the adjacent cell interference by reducing the transmitting power to the edge users without performance penalty.
arXiv:0811.0241v2 [cs.IT] 4 Nov 2008
Joint Transmitter-Receiver Design for the Downlink
Multiuser Spatial Multiplexing MIMO System
Pengfei Ma, Wenbo Wang, Xiaochuan Zhao and Kan Zheng
Wireless Signal Processing and Network Lab,
Key Laboratory of Universal Wireless Communication Ministry of Education,
Beijing University of Posts and Telecommunications, Beijing, China
Abstract—In the multiuser spatial multiplexing multiple-input
multiple-output (MIMO) system, the joint transmitter-receiver
(Tx-Rx) design is investigated to minimize the weighted sum
power under the post-processing signal-to-interference-and-noise
ratio (post-SINR) constraints for all subchannels. Firstly, we show
that the uplink-downlink duality is equivalent to the Lagrangian
duality in the optimization problems. Then, an iterative algorithm
for the joint Tx-Rx design is proposed according to the above
result. Simulation results show that the algorithm can not only
satisfy the post-SINR constraints, but also easily adjust the
power distribution among the users by changing the weights
accordingly. So that the transmitting power to the edge users in
a cell can be decreased effectively to alleviate the adjacent cell
interference without performance penalty.
Index Terms—spatial multiplexing, MIMO, power allocation,
Lagrangian duality.
I. INTRODUCTION
Spatial multiplexing for the multiple-input multiple-output
(MIMO) systems, employing multiple transmit and receive
antennas, has been recognized as an effective way to improve
the spectral efficiency of the wireless link [1]. More recently,
the multiuser schemes have been investigated for the spatial
multiplexing MIMO systems. This paper focuses on the down-
link multiuser schemes in which each user can not cooperate
with the others thus suffers from the interference from them.
Mainly, there are two kinds of multiuser schemes. One is the
precoder or the transmit beamforming, such as the dirty-paper
coding (DPC) [2] and the zero-forcing (ZF) [3], etc., which
mitigates the multiuser interference only by processing at the
transmitter. The other is the joint transmitter-receiver (Tx-Rx)
design, such as the nullspace-directed SVD (Nu-SVD) [4] and
the minimum total mean squared error (TMMSE) [5], etc.
In general, the former possesses lower complexity but more
performance penalty. With the great development of signal
processors, the latter gradually draws more attention.
For the joint Tx-Rx design, the schemes proposed in
[4][5] minimize mean squared error (MMSE), or maximize
the capacity under the transmit power constraint. Whereas
on some occasions, such as the multimedia communication,
it is required to minimize the total transmit power while
guarantee the quality of service (QoS). [6][7] investigate the
beamforming and the power allocation policy when all users
are subjected to a set of post-processing signal-to-interference-
and-noise ratio (post-SINR) constrains in the uplink SIMO
and the downlink MISO. [8][9] extend this work to the
downlink MIMO and the MIMO network, however the MIMO
systems discussed in [8][9] are assumed that there is only
one substream between each pair of the transmitter and re-
ceiver. In other words, only the multiuser interference appears
in the so-called diversity MIMO system in [8][9]. For the
multiuser spatial multiplexing MIMO system, however, both
the multiuser interference between individual users and self-
interference between individual substreams of a user should
be mitigated.
For the downlink, the transmit beamforming affects the
interference signature of all receivers, whereas the receive
beamforming only affects that of the corresponding user. [7][8]
construct a dual system, called the virtual uplink, and indicate
that the virtual uplink can obtain the same post-SINR as the
primary downlink. Moreover, the receive beamforming matrix
of the virtual uplink is identical with the transmit beamforming
matrix of the primary downlink. The design of the downlink,
therefore, can resort to the virtual uplink.
In this paper, we extend the duality derived for MIMO
network in [9] to the multiuser spatial multiplexing MIMO
system. According to the uplink-downlink duality, we propose
a joint Tx-Rx scheme to minimize the weighted sum power
under the post-SINR constraints of all the subchannels.
Notation: Boldface upper-case letters denote matrices, and
boldface lower-case letters denote column vectors. tr(·), (·)∗,
(·)H, ||·||2 and ||·||F denote trace, conjugate, conjugate trans-
position, Euclidian norm and Frobenius norm, respectively.
diag(x) denotes a diagonal matrix with diagonal elements
drawn from the vector x. [·]i,j, [·]:,j denote the (i,j)-th element
and j-th column of a matrix, respectively.
II. SYSTEM MODEL
We consider a base station (BS) with M antennas and
K mobile stations (MS’s) each having Ni(i = 1, . . . , K)
antennas. There are Li(i = 1, . . . , K) substreams between
BS and MSi(i = 1, . . . , K), that is to say, BS transmits Li
symbols to MSi simultaneously. T
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