Joint Power and Bit Allocation Algorithm for
MIMO Systems
Jichao Liu
?
, Yunchao Song
?
, Chen Liu
?
, and Hua-An ZHAO
†
?
School of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications, 210003, China.
†
Department of Computer Science and Electrical Engineering, Kumamoto University, Kumamoto-shi, 860-8555, Japan.
Email: {1015020712,1010020702, lc}@njupt.edu.cn, cho@cs.kumamoto-u.ac.jp
Abstract—In this paper, a joint power and bit allocation
algorithm, subjected to transmit power and transmission rate,
is proposed to improve the reliability of MIMO systems. When
the channel state information (CSI) of a MIMO system is known
by the transmitter, the water-pouring power allocation algorithm
can be used to obtain the maximum channel capacity. However,
this policy takes no account of the influence of modulation and
bit allocation, and it can not obtain the minimum bit error
rate (BER) performance of MIMO systems. Hence, this paper is
devoted to the presentation of a novel strategy which allocates
the bit and power jointly, aiming to approach the minimum
BER for MIMO systems. Compared with the conventional power
allocation algorithm, the simulation results demonstrate that this
proposed scheme can significantly reduce the BER of MIMO
systems.
Index Terms—MIMO, bit error rate, power and bit allocation,
modulation
I. INTRODUCTION
As a vital means to improve the performance of wireless
systems, Multiple-input multiple-output (MIMO) technology
is considered to be one of the key technologies [1]. MIMO
technology provides both spatial multiplexing gain and diver-
sity gain [2] to improve the performance of wireless systems.
It is widely understood that in a system with multiple transmit
and receive antennas, the spectrum efficiency is much higher
than that of the conventional single antenna systems [3]. A
key feature of MIMO systems is the ability to turn multipath
propagation, traditionally a pitfall of wireless transmission,
into a benefit for the users [4]. In fading channels, MIMO
technology can make full use of space resources and elevate
the channel capacity exponentially without additional band-
width and transmit power consumptions [5].
In general, the performance of communication scheme can
be measured by efficiency, reliability and complexity. In the
scenario of which CSI is obtained by transmitter, channel-
dependent processing of data streams in the transmit side can
improve the performance of the MIMO systems by efficiently
allocating resources such as power and bits over multiple
antennas [6]. In the all-important case that the noises impairing
each of the parallel branches are Gaussian and independent,
the capacity of the system under a power constraint is maxi-
mized if the inputs to the channels are mutually independent
and also Gaussian, with their power allocated according to
This work was supported by the Natural Science Foundation of China under
Grants 61372126 and 61302101.
the water-pouring policy [7],[8]. First devised by Shannon and
rigorously formalized in the context of dispersive channel in
[9], the water-pouring policy is a central result in information
theory.
In practice, information should be modulated before trans-
mission, and different sub-channels can be modulated by dif-
ferent modulation types [10]. However, the conventional water-
pouring algorithm does not take the modulation and the bit
allocation into account. Therefore, in this paper, we modulate
the transmit signal adaptively by BPSK and QAM modulation,
aiming at seeking for a joint power and bit allocation method
to approach the minimum BER of MIMO systems. Firstly,
we derive an unified BER formula of the MIMO system in
terms of the power and bits allocated. Then based on the BER
formula derived, a joint power and bit allocation algorithm
is designed so as to obtain the minimum BER of the MIMO
system. Simulation results validate that the proposed algorithm
can substantially reduce the BER of MIMO systems, compared
with the traditional power allocation algorithm.
The rest of this paper is organized as follows. Section II
describes the considered MIMO communication system model
and gives the transmission schemes. Section III proposes the
joint power and bit allocation algorithm. Simulation results,
which compare the BER performance between our proposed
method and conventional power allocation method, are given
in Section IV. Finally, Section V concludes the paper.
Notations: Throughout the paper, we use tr(A) to represent
the trace of matrix A. Scalars are denoted by lowercase
letters, vectors by lowercase boldface letters and matrices by
uppercase boldface letters. The transpose and the Hermitian
operators are denoted by (·)
T
and (·)
H
respectively.
II. SYSTEM MODELS AND TRANSMISSION SCHEMES
Consider a wireless communication system with N
t
transmit
and N
r
receive antennas. Assuming the path gains between
individual antenna pairs are independent and identically dis-
tributed (i.i.d.) Raleigh faded, then the system model can be
written as
y = Hs + n, (1)
where y ∈ C
N
r
×1
is the received vector, s ∈ C
N
t
×1
is the
transmitted vector and n ∈ C
N
r
×1
is the Gaussian noise vector
with zero-mean i.i.d. circularly symmetric complex Gaussian
entries. The channel matrix H ∈ C
N
r
×N
t
is the deterministic