A New Detection and Decoding Technique for (2×N_r ) MIMO Communication Systems

International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 6 Issue: 7 109 - 113
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109
IJRITCC | July 2018, Available @ http://www.ijritcc.org
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A New Detection and Decoding Technique for 𝟐 × 𝑵 𝒓 MIMO Communication
Systems
Karim Hamidian
Electrical Engineering Department, California State University
Fullerton, CA, USA
Email: khamidian@fullerton.edu
Wurod Qasim
Department of Electronic Engineering, Universityof Diyala
Diyala, Iraq
Email: Wurod89@csu.fullerton.edu
Abstract—The requirements of fifth generation new radio (5G- NR) access networks are very high capacity and ultra-reliability. In this paper,
we proposed a V-BLAST2 × 𝑁𝑟 MIMO system that is analyzed, improved, and expected to achieve both very high throughput and ultra-
reliability simultaneously.A new detection technique called parallel detection algorithm is proposed. The performance of the proposed algorithm
compared with existing linear detection algorithms. It was seen that the proposed technique increases the speed of signal transmission and
prevents error propagation which may be present in serial decoding techniques. The new algorithm reduces the bit error probability and increases
the capacity simultaneouslywithout using a standard STC technique. However, it was seen that the BER of systems using the proposed
algorithm is slightly higher than a similar system using only STC technique. Simulation results show the advantages of using the proposed
technique.
Keywords – component; MIMO, Parallel Detection and Decoding, V-BLAST.
__________________________________________________*****_________________________________________________
I. INTRODUCTION
The major challenge of for 4G- LTE and 5G New Radio (NR)
is to maximize both the reliability and data rate of Multiple
Input Multiple Output (MIMO) techniques simultaneously
[19] [21]. The goal of any MIMO systems is either to combat
or exploit the multipath propagations between multiple
transmit and receive antennas through two separate techniques,
which are called spatial diversity and spatial multiplexing.
Table 1 summarizes the MIMO categories [4].
Table 1 . MIMO Categories
MIMO
technique
Purpose Approach Method
Spatial
diversity
Improve
reliability
Combat
multipath
Space time
coding
Spatial
multiplexing
Increase
capacity
Exploit
multipath
Spatial
de-multiplexing
Spatial diversity is a technique thatcombats fading in the
multipath channel and improves the reliability of the
transmission through transmitting multiple replicas of the
same signal by using space time coding (STC) [3].
There are two common metrics that characterize the amount of
spatial diversity, which are diversity order and diversity gain
[4]. Diversity order represents the number of independent
replicas of the same transmitted signal that are available at the
receiver. In an 𝑁𝑡 × 𝑁𝑟 MIMO system, there are 𝑁𝑡 𝑁𝑟
multipath propagation paths between the 𝑁𝑡 transmit antennas
and the 𝑁𝑟 receive antennas. The general property of the
MIMO communications system that holds for many
modulation types in Rayleigh fading channel is that the
diversity order (𝑁𝑑 ) equals to the diversity gain (𝐺 𝑑 ), and we
say the system achieves full diversity if 𝑁𝑑 = 𝐺 𝑑 =
𝑁𝑡 𝑁𝑟expression is true.
However; spatial multiplexing (SM) technique exploits
multipath propagation to transmit the information at a rate up
to channel capacity (channel capacity improvements) without
increasing the required bandwidth by using the spatial de-
multiplexing method.
In this paper, we propose a novel parallel detection and
decoding algorithm for MIMO communication systems. Our
algorithmoptimizes the capacity, improves the reliability of
transmission without employing a standard STC technique,
and prevents any possible error propagation that may be
presented in other serial detection and decoding algorithms.
The proposed method is compared with current methods that
use STC and SM techniques. In this article, it is assumed the
channel is Rayleigh flat fading and that channel state
information is available at the receiver.For the purpose of
presenting the benefits offered bythe proposed model, we
consider MIMO systems having two transmitting antennas and
different number ofreceiving antenna, withan 𝑁𝑟 ≥ 2 .
The rest of this paper is organized as follows. Section II
provides the transmitter model and its related expressions.
Section III shows the proposed detection and decoding
algorithm. Simulation results are provided and discussed in
section IV. Finally, we conclude in section V.
II. TRANSMITTER MODEL
To enhance the performance of MIMO communications in
Rayleigh fading environment, a new detection technique is
proposed that will exploit the multipath propagation to detect
and decode 𝑁𝑡 received symbols simultaneously and
independently.In this paper, it is assumed,𝑁𝑡 = 2, and a large
number ofantenna elements (antenna array) are used at the
receiver.

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The data stream after channel encoder[6] splits into two
data streams, each of which is separately modulated and
transmitted by its respective antenna using V-BLAST
encoding architecture as shown in fig. 1[4].
Figure 1. MIMO Communication Transmitter Using V-BLAST.
As fig. 1 shows, the system transmit two modulated
symbols at one symbol period. Therefore, the transmitted
signal matrix 𝑆 is
𝑆 =
𝑆1
𝑆2
1
We assume the Rayleigh fading channel state informationis
known at the receiver. Therefore the channel matrix is
𝐻 =
𝑕1,1 𝑕1,2
𝑕2,1 𝑕2,2
⋮ ⋮
𝑕Nr ,1 𝑕Nr ,2
(2)
In vector and matrix form, the received signal matrix in the
Rayleigh flat fading environments is expressed as [2] and [4].
𝑅 = 𝜌
𝑕1,1 𝑕1,2
𝑕2,1 𝑕2,2
⋮ ⋮
𝑕Nr,1 𝑕Nr,2
𝑆1
𝑆2
+
𝑍1
𝑍2
⋮
𝑍Nr
3
Where 𝑍𝑖 is the noise term that is received with the 𝑖 − 𝑡𝑕
receive antenna.
III. PROPOSED DETECTION AND DECODING
TECHNIQUE
Figure 2 shows the receiver model of the proposed novel
parallel detection and decoding technique [16] [17], where the
two received symbols will be detected and decoded
independently and simultaneously. In addition, with the new
model, replicas for each transmitted symbol are extracted as
the following procedure shows. First, we decompose the
channel matrix into two components as follows [4]
𝐻 = 𝐻1 𝐻2 , 𝑤𝑕𝑒𝑟𝑒 𝐻j =
𝑕1,j
𝑕2,j
⋮
𝑕Nrj
(4)
Where in the expression of 𝑕𝑖,𝑗 the first index represents
the receiving antenna number and the second index represents
the transmit antenna number.
From figure 2, the received signal components are
𝑟1 = 𝜌 𝑕1,1 𝑆1 + 𝑕1,2 𝑆2 + 𝑍1,
𝑟2 = 𝜌 𝑕2,1 𝑆1 + 𝑕2,2 𝑆2 + 𝑍2, and
𝑟Nr
= 𝜌 𝑕Nr,1 𝑆1 + 𝑕Nr,2 𝑆2 + 𝑍Nr
5
The Front End Receiver combines all these received signal
components and produce the received signal R in vectorial
formas shown in (3).
Figure 2. Proposed Detector and Decoder for MIMO Communication.
Using the proposed algorithm, we can simultaneously and
independently extract the two transmitted symbols 𝑆1 and 𝑆2
bypre-multiplying the received signal matrix 𝑅 by 𝐴1 and 𝐴2
vectors, respectively.Decoding of the 𝑆j transmitted symbol is
obtained by first generating the estimated received signals 𝑅jis
as follows, j =1,2
𝑅j ≜ 𝐴j 𝑅 6
Where 𝐴j(1×Nr)
is the null space vector for the channel
component that constitutes the interference for the jth
transmitter. Thus, as shown in (7),𝐴1 is the null space of
H2..Similarly, 𝐴2 is the null space of H1
A1 = 𝑛𝑢𝑙𝑙𝑠𝑝𝑎𝑐𝑒 𝐻2 7
Thus, each of these estimated received signals can be rewritten
as follows
𝑅j = 𝜌𝐻j
(𝑒𝑓𝑓 )
𝑆j + 𝑍j (8)
Where the effective channel matrix represents
𝐻j
𝑒𝑓𝑓
= Aj 𝐻j 9
The noise term is
𝑍j = 𝐴j 𝑍i (10)
It is interested to note (8) indicates that the energy of 𝑅𝑗 is only
from the 𝑆𝑗 symbol. This demonstrates that the interferences
from the remaining transmitted symbolis suppressed. In
addition, there are 𝑁𝑟 replicas of 𝑆𝑗 symbol available at the
receiver. This implies the receiver achieves a spatial diversity
without using standard STC. We can decode 𝑆𝑗 symbol by
applyingMLD to (8),which is computed as follows, where
𝑆𝑗 refers to the estimate of𝑆𝑗 .
𝑆𝑗 = arg min 𝑆 𝑗
𝑅𝑗 − 𝜌𝐻𝑗
𝑒𝑓𝑓
𝑆𝑗 𝐹
2
(11)
In summary, the transmitter sends two modulated
symbols at one symbol period using spatial multiplexing
technique, and the receiver is enabled to detect and decode
these symbols simultaneously and independently by using the
proposedparallel processing algorithm as outlined above. This
implies that the speed of signal processing and thus the

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throughput will be increased. In addition, at any given symbol
period, this algorithm enables the receiver to have accessto
twice of (𝑁𝑟 − 𝑁𝑡 + 1) replicas of each transmitted symbol.
This implies that the reliability of this system will be improved
also. Thus, it is important to note that this system achieves
both spatial diversity and spatial multiplexing simultaneously
without employing a standard STC. However; MGSTCs
method also achieves both spatial diversity and spatial
multiplexing simultaneously, but there are three major
differences between two methods. First, MGSTCs method
requires that number of transmit antenna to satisfy 𝑁𝑡 ≥
4,while the new algorithm requires that 𝑁𝑡 ≥ 2. The second
improvement is the speed of signal processing at the receiver.
In standard MGSTCs method, the decoding of the component
codes are performed iteratively and in a serial way. While,
using the new algorithm, the decoding of component codes are
performed simultaneously and in a parallel way. Also, the
proposed parallel processing technique improves the
probability of bit error by preventing possible error
propagation. In standard MGSTCs method, the decoding of
current component code symbol depends on the values of all
previously decoded component codes. This implies that if an
error occurs in decoding of a component code symbol, such
error will propagate to all remaining component codes. This
problem does not exist in the proposed decoding algorithm
since the receiver decodes the symbols independently and
simultaneously.
In general, the diversity order a MIMO system depends on the
difference between the numbers of receive and transmit
antennas. This difference also affects the gain of the replicas of
each symbol at the receiver. Thus, the diversity order depends
on the number of the rows of the pre-multiplying matrix𝐴j,
which is equal to 𝑁𝑟 − 𝑁𝑡 + 1 . Thus, the diversity order (𝑁𝑑 )
of a MIMO communication system using the proposed parallel
decoding technique is:
𝑁𝑑 = 2 ∗ 𝑁𝑟 − 𝑁𝑡 + 1 (12)
Also, for (2 × Nr ) MIMO communication systems, the
channel capacity is given by the expression shown in (13)
when rank of channel matrix is𝑟 = 2 [2] , [3] and[4].
𝐶 2 × Nr 𝑀𝐼𝑀𝑂 = log2 1 +
𝜌
2
𝜆𝑖
2
𝑖=1
13
Where 𝜆𝑖 is the eigenvalue of the channel matrix.
IV. SIMULATION RESULTS [16]
In this section, we assume that 𝑁𝑡 = 2 and 𝑁𝑟 = 2, 3,
and 4 respectively, and that the transmitter employs spatial
multiplexing technique. The receiver can extract two
transmitted symbols independently and simultaneously by
using the new detection algorithm. Figure 3 shows the
performance results of the proposed method for a (2 ×
2)MIMO communicationsystem compared with two separate
systems, one is a 2 × 2 MIMO usingAlamouti code that can
achieve only spatial diversity, and another is a 2 × 2 MIMO
with SM that uses serial decoding and it can achieve only
spatial multiplexing. In figure 3 the bit error probability is
plotted versus 𝐸𝑏 /𝑁0 in dB in Rayleigh fadingchannel and
using BPSK modulation for all three different systems. Our
proposed decoding method is unique, because currently there
is no a 2 × 2 MIMOsystem that can achieve both spatial
diversity and spatial multiplexing simultaneously.
Figure 3. BER of different types of 2 × 2 MIMO systems.
The bit error probability expression of a parallel
decoding system is
𝑃 𝑏 2×2 𝑀𝐼𝑀𝑂−𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑑𝑒𝑐𝑜𝑑𝑖𝑛𝑔 =
1
2
1 − 𝜇
2
2 + 𝜇 (14)
Where 𝜇 =
𝜌
1+𝜌
.
Where 𝜌 refers to the time averaged signal to noise ratio.
It known that the diversity order is equal to the slope of the bit
error probability curve in the linear region [4]. Thus, the
diversity order of this system approaches to𝑁𝑑 = 2.
The above results show the system that uses thenew decoding
algorithm achieves significantly lower bit errors rate (BER)
than the system that uses spatial multiplexing technique only,
but the new model has higher bit errors rate than the system
that uses Alamouti code technique only.
On the other hand, the proposed parallel processing algorithm
improves the channel capacity as shown in Fig.4. The figure
shows that the channel capacity of the proposed system is
equal to the channel capacity of the 2 × 2 MIMO systemthat
uses spatial multiplexing technique, and it is twice of the
channel capacity of the2 × 2 MIMO systemthat usesAlamouti
code.
The following figures show that increasing the number of the
receiving antennas leads to more performanceimprovements in
MIMO communications. Fig.5 shows the performance results
of a (2 × 3) MIMO communication system using the proposed
model compared with a 2 × 3 MIMO using Alamouti code
and a 2 × 3 MIMO using spatial multiplexing and serial
decoding. The theoretical expression of the bit error
probability for these methods is
𝑃 𝑏 2×3 𝑀𝐼𝑀𝑂−𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑑𝑒𝑐𝑜𝑑𝑖𝑛𝑔 =
1
2
1 − 𝜇
4
3 + 𝑘
𝑘
1
2
1 + 𝜇
𝑘3
𝑘=0
15
The bit error probability curvein figure 5 showsthat
the diversity order of this system approaches to𝑁𝑑 = 4.

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Figure 4. Channel capacity comparison ofdifferent 2 × 2 MIMO systems.
The performance Comparison of different types of 2 ×
3MIMO systems shows that the system that uses the parallel
detection algorithm achieves significantly lower BER than the
system that uses spatial multiplexing technique only, but it is
very close to BER of the system that uses Alamouti codeonly.
On the other hand, the proposed algorithm improves the
channel capacity as displayed in Fig.6. The figure shows that
the channel capacity of our model is equal to the channel
capacity of a similar system that uses spatial multiplexing
technique, and it is more than twice the channel capacity of a
similar system which usesAlamouti code technique.
Figure 6. Channel capacity comparison ofdifferent 2 × 3 MIMO systems.
Finally, fig. 7 shows the performance results of a 2 × 4 MIMO
communication system using the new decoding model
compared with a 2 × 4 MIMO using Alamouti code, and
a 2 × 4 MIMO usingspatial multiplexingunder the
assumption that the channel is Rayleigh fading and BPSK
modulation is used. The theoretical expressionof the bit error
probability is as follows.
𝑃 𝑏, 2×4 𝑀𝐼𝑀𝑂 −𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑑𝑒𝑐𝑜𝑑𝑖𝑛𝑔 =
1
2
1 − 𝜇
6
5 + 𝑘
𝑘
1
2
1 + 𝜇
𝑘5
𝑘=0
16
The results show the diversity order of this system
approaches to 𝑁𝑑 = 6.
The above analysis shows that increasing the number of
receiving antenna elementssignificantly improves the
reliability of 2 × 𝑁𝑟 MIMO communication systems. More
precisely, increasing the difference between the number of
receiving and transmitting antennas improves the BER and
thus the reliability of the system. Fig.8 shows these
improvements.
Figure 8. BER of2 × Nr MIMO systems using the proposed model

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The results in figure 8 show that the probability of bit error of
a 2 × 4 MIMO communication system is significantly
smaller than BER of the 2×2 MIMO and 2×3 MIMO systems
that use the proposed parallel decoding technique.
The above analysis shows the system that employs spatial
multiplexing technique at the transmitter and applies the
parallel detection and decoding algorithm at the receiver,
improves both throughput and transmission reliability
simultaneously, which cannot be achieved by other serial
detection algorithms having similar dimensions.
Future research may investigate the performance of the
proposed algorithm using large number antenna elements at
both end and when the decoding is performed on symbols in
parallel manner by applying a variety types of MIMO
decoding techniques.
V. CONCLUSION
The 5G- NR access networks are expected to provide very
high capacity and ultra-reliability.To achieve these
requirements, we focused on the study and investigation of
MIMO communication techniques that uselarge number
ofantenna elements at the receiver end of communication
system and developed novels ways to enhance the overall
performance of (2 × 𝑁𝑟 ) MIMO systems. We proposed a new
parallel detection and decoding algorithm. The performance
results show that the proposed parallel detection method
improves both throughput and transmission reliability
simultaneously, provided that spatial multiplexing technique is
used at the transmitter. In addition, it was observed that the
proposed method prevents error propagation by extracting all
received symbols independently and simultaneously. Also, it
was shown that parallel decoding technique reduces the bit
error probability and increases the speed of signal transmission
and detection without using a standard STC technique.
However, it was seen that the BER of the proposed algorithm
is slightly higher than a similar system using STC technique.
The BER performance of these two techniques become closer
as 𝑁𝑟 increases and assumes value of 4 or higher in the
2 × 𝑁𝑟 MIMO system.
Finally, it was seen that with new decoding method the bit
error probability, BER, decreases dramatically with increasing
the difference between the number of receiving and
transmitting antennas.
We willgeneralize and investigate the performance of the
proposed parallel signal processing techniquewhen using large
number ofantenna elements (antenna array) at both end of
MIMO communication systems.
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