30-05-2013, 12:56 PM
FAST SPHERE DECODER FOR MIMO SYSTEMS
FAST SPHERE.pdf (Size: 308.17 KB / Downloads: 19)
ABSTRACT
This work focuses on variants of the conventional sphere decoding technique for Multi
Input Multi Output (MIMO) systems. Space Time Block Codes (STBC) have emerged as a
popular way of transmitting data over multiple antennas achieving the right balance between
diversity and spatial multiplexing. The Maximum Likelihood (ML) technique is a conven-
tional way of decoding the transmitted information from the received data, but at the cost
of increased complexity. The sphere decoder algorithm is a sub-optimal decoding technique
that is computationally e±cient achieving a symbol error rate that is dependent on the initial
radius of the sphere.
In this thesis, the decreasing rate of the radius of the sphere is increased by using a
scaling factor of less than unity. This allows the algorithm to examine less number of vectors
compared to the original algorithm making it much more computationally e±cient. The sphere
decoding algorithm is largely focussed on the Alamouti codes that have two antennas at the
transmitter. This work extends the sphere decoding algorithm to other STBC having more
than 2 transmit and receive antennas.
INTRODUCTION
Multi Input Multi Output (MIMO) systems have replaced the conventional Single Input
Single Output (SISO) systems in the last decade, and has emerged as a major area of research
in the ¯eld of Wireless Communications for major applications. The multiple antennas at the
transmitter and receiver can achieve a data rate that is much higher than that of the SISO
system. The multiple antennas also aim to improve the performance of the system through
various diversity techniques.
A MIMO system can be de¯ned as a wireless communication system consisting of multi-
ple antennas at the transmitter and multiple antennas at the receiver. The number of antennas
at the transmitter and receiver are denoted by M and N respectively. For the case, when the
transmit antennas equal the receive antennas, we denote the number by N.
The demand on higher data rates have always been of prime importance for wireless
subscribers, as a result of which, new techniques in signal processing and coding need to
be developed. There was a need to utilize the existing bandwidth to support a larger data
rate with better quality that would combat the e®ects of multipath fading and Additive
White Gaussian Noise (AWGN) prevalent in the channel. The quality of transmission can be
improved by sending multiple copies of the transmitted signal over various paths to multiple
receivers. This would ensure that, under the worst case circumstances, one received antenna
would carry the desired signal. This technique is called as diversity. There are di®erent types
of diversity - time, frequency, space and polarization. Space diversity would ensure that the
bandwidth utilization remains the same as that of SISO systems, while at the same time
ensuring that the data rate and quality of transmission is increased [1].
SPACE-TIME BLOCK CODES
INTRODUCTION
The space-time block codes provide a new dimension to the transmission of data us-
ing multiple transmit and receive antennas. Data is encoded using a space-time block code,
and the encoded data is split into N streams which are simultaneously transmitted using N
transmit antennas. The received signal at each antenna is a linear superposition of the N
transmitted signals, perturbed by noise [1]. In most situations, the wireless channel su®ers
attenuation and path loss due to destructive addition of multipaths in the propagation media
and to interference from other users. In a Rayleigh fading environment, it is often di±cult
for the receiver to determine the exact message transmitted due to severe attenuation and
multipath fading characteristics, unless some less attenuated component of the signal is pro-
vided to the receiver. In many situations, since the wireless channel is neither signi¯cantly
time-variant nor highly frequency selective, the possibility of deploying multiple antennas at
the transmitter and receiver is considered to achieve spatial diversity.
SPACE-TIME BLOCK CODES GENERATION
The Space-Time Block codes are matrices that are designed to make use of transmit and
receive diversity. The elements in the matrix are symbols taken from any particular constella-
tion. The constellation may be as simple as a Binary Phase Shift Keying (BPSK)constellation
with only real symbols, or the symbols may also be complex as can be seen in a Quadrature
Amplitude Modulation (QAM) or Quadrature Phase Shift Keying (QPSK) constellations.
The constellation decides the real or complex symbols transmitted as a part of the matrix.
ALAMOUTI CODE
Alamouti space-time block codes are a special class of orthogonal block codes achieving
a code rate of 1. Space-time block codes are represented by a m £ l matrix, where m repre-
sents the number of transmit antennas and l represents the number of time slots required for
transmission. Alamouti codes have a special signi¯cance in that the columns of the matrix are
orthogonal achieving a code rate of 1. The code rate is determined by the number of symbols
transmitted in a given number of time slots. For example, for a two transmit two receive
antenna system, two symbols are transmitted in two time slots, thus getting a code rate of 1.
The Alamouti code for a two transmit two receive antenna system is given by (2.12).
MAXIMUM LIKELIHOOD DETECTION
INTRODUCTION
Maximum likelihood decoder achieves the best performance in terms of SER among all
the decoding techniques. The computational complexity of this technique is very high, but
with the advent of orthogonal space-time block codes, the exponential complexity is reduced
to linear processing at the receiver. The space-time block codes along with multiple antennas
achieve signi¯cant performance gain at no extra processing expense. In a maximum likelihood
decoder, the complexity of the decoder increases exponentially as the number of transmit
antennas. The signi¯cance of orthogonal space time block codes arises from the fact that the
exponential complexity is reduced to a linear complexity.
CONCLUSION
Space Time Block Codes have emerged as popular means of transmitting information
over MIMO systems achieving the right balance between diversity and spatial multiplexing.
Alamouti code is a well known space time block code that makes use of two transmit antennas.
There are other space time block codes for multiple transmit antennas. These codes do not
have a code rate of unity, but there is the trade-o® of good performance due to better diversity
and more antennas at the transmitter and receiver. In this paper, space time block codes for
three, four and ¯ve transmit antennas are studied and their performance is compared with
that of the Alamouti code.
In the ¯rst section, we examined the Maximum Likelihood (ML) Detector to decode the
di®erent space time block codes. The following result was observed. Increasing(Decreasing)
SNR increased(decreased) the performance of the system in terms of the Symbol Error Rate
(SER). The FLOPS per symbol is independent of the SNR, since increasing or decreasing the
SNR does not change the number of points visited in the constellation. ML decoding is a
brute force algorithm with large overhead in the computational complexity.