MIMO Channel Estimation Using the LS and MMSE Algorithm

IOSR Journal of Electronics and Communication Engineering (IOSR-JECE)
e-ISSN: 2278-2834,p- ISSN: 2278-8735.Volume 12, Issue 1, Ver. II (Jan.-Feb. 2017), PP 13-22
www.iosrjournals.org
DOI: 10.9790/2834-1201021322 www.iosrjournals.org 13 | Page
MIMO Channel Estimation Using the LS and MMSE Algorithm
*Mohammed Ali Mohammed MOQBEL1
, Wangdong2
, Al-marhabi Zaid Ali3
1,2
Hunan University, Changsha, Hunan, China
3
Hajjah University, Hajjah, Yemen
Abstract: Wireless Communication Technology has developed over the past few yearsfor other objectives.The
Multiple InputMultiple Output (MIMO) is one of techniques that is used to enhancethe data rates, in which
multiple antennas are employed both the transmitter and receiver. Multiple signals are transmitted from
different antennas at the transmitter using the same frequency and separated space. Various channel estimation
techniques are employed in order to judge the physical effects of the medium present. In this paper, we analyze
and implementvarious estimation techniques for MIMO Systems such as Least Squares (LS), Minimum Mean
Square Error (MMSE),these techniques are therefore compared to effectively estimate the channel in MIMO
System. The results demonstrate that SNR required to support different values of bit error rate varies depending
on different low correlation between the transmitting and the receiving antennas .In addition, it is illustrated
that when the number of transmitter and receiver antennas increases, the performance of TBCE schemes
significantly improves. The Same behavior isalso observed for MIMO system. Performance of both MMSE and
LSestimation are the same for allkinds of modulation at small value of SNR but the more we increase the SNR
value the more performance gap goes on increasing.
Keywords: Channel estimation, Minimum mean square error (MMSE), Least square (LS), Kalman filter,
Orthogonal frequency division multiplexing.
I. Introduction
In recent years, Multi-Input Multi-Output (MIMO) communications are introduced as an emerging
technology to offer significant promise for high data rates and mobility required by the next generation wireless
communication systems. Using multiple transmit as well as receive antennas, a MIMO system exploits spatial
diversity, higher data rate, greater coverage and improved link robustness without increasing total transmission
power or bandwidth. However, MIMO relies upon the knowledge of Channel State Information (CSI) at the
receiver for data detection and decoding [1] [2]. It has been proved that when the channel is flat fading and
perfectly known to the receiver, the performance of a MIMO system grows linearlywith the number of transmit
or receive antennas, whichever less is [3]. Therefore, an accurate and robust channel estimation is of crucial
importance for coherent demodulation in wireless MIMO systems [7].
Use of MIMO channels, when bandwidth is limited, has much higher spectral efficiency versus Single-
Input Single-Output (SISO), Single-Input Multi-Output (SIMO), and Multi Input Single-Output (MISO)
channels [4]. It is shown that the maximum achievable diversity gain of MIMO channels is the product of the
number of transmitter and receiver antennas. Therefore, by employing MIMO channels not only the mobility of
wireless communications can be increased, but also its robustness [6].Mobile communication systems transmit
information by changing the amplitude or phase of radio waves. In the receiving side of mobile system,
amplitude or phase can vary widely [11]. This causes degradation in the quality of system since the performance
of receiver is highly dependent on the accuracy of estimated instantaneous channelHowever; these detectors
require knowledge on the channel impulse response (CIR), which can be provided by a separate channel
estimator to minimize the error probability [5].
In this paper, we analyze aLS and MMSE channel estimators, in MIMO system, that signal detector
needs to know channel impulse response (CIR) characteristics to ensure minimum Mean Square Error of the
Channel Estimation and to minimize the error probability. We present an efficient MIMOchannel estimation
with training sequences.The proposed algorithms has been designed and simulated usingMatlab Program then
tested and evaluated the efficiency of the proposed algorithms.
Outlines ….. The rest of this paper is organized as follows. We present the system description Sect. 2.
Section 3 introduces the basics of a phrase-based SMT system, which is regarded as the basis of our
experiments. Section 4 will illustrate the feature factors (POS and CCG) that parse the tag and supertag of the
corpus. In Sect. 5, we will explain how n-gram LM was included in the translation process. Section 6 will
introduce the basis of factored translation model and show its similarity to phrase-based SMT models. In Sect.
7, we will explore our experiments and results on the four models with BLEU scores in the presence of various
high n-gram language models. Section 8 will comprehensively conclude the work.

II. System Description
Consider a MIMO system equipped with Nttransmit antennas and Nrreceive antennas. The block diagram of a
typical MIMO 2×2 is shown in Figure. 1.
Figure.1 General Architecture of a MIMO
It is assumed that the channel coherence bandwidth is larger than the transmitted signal bandwidth so
that the channel can be considered as narrowband or flat fading [10]. Furthermore, the channel is assumed to be
stationary during the communication process of a block. Hence, by assuming the block Rayleigh fading model
for flat MIMO channels, the channel response is fixed within one block and changes from one block to another
one randomly. During the training period, the received signal in such a system can be written as (1)
where Y, S and N are the complex NR -vector of received signals on theNR receive antennas, the possibly
complex NTvector of transmitted signals on theNTtransmit antennas, and the complex NR -vector of additive
receiver noise, respectively.
The elements of the noise matrix are independent and identically distributed complex Gaussian random
variables with zero-mean and variance, and the correlation matrix ofN is then given by [8]:
where (.)H
is reserved for the matrix hermitian, E(.) is the mathematical expectation,andINpdenotes the
ܰNpxNpidentity matrix. Np the number of transmitted training symbols by each transmitter antenna. The
matrixHin the model (3.1) is theܰNR x Ntmatrix of complex fading coefficients. The (m,n)-th element of the
matrixH denoted byhm,nrepresents the fading coefficient value between the m-th receiver antenna and the n-th
transmitter antenna. Here, it is assumed that the MIMOsystem has equal transmit and receive antennas. The
elements of H and noise are independent of each other. In order to estimate the channelmatrix, it is required that
ܰ training symbols are transmitted by each transmitter antenna. The function of a channel estimation
algorithm is to recover the channel matrixH based on the knowledge of Y andS. Output (received) signals in
locationsCanare as follow:
2.1 Signal Model:
We consider a flat fading MIMO wireless system with NT transmit and NR receive antennas. The symbol
transmitted by antenna m at time instant k is denoted by Sm(k). The transmitted symbols are arranged in the
vector
of length NT , where (·)T
denotes the transpose operation. Between every transmit antenna m and every receive
antenna n there is a complex single-input single-output (SISO) channel impulse response hn,m(k) of length L+1,
described by the vector
Assuming the same channel order L for all channels, theMIMO channel can be described by L+1complex
channel matrices
of the dimension NR×NT .The symbol received by antenna n at time instant k is denoted

byYn(k). The symbols received by the NR antennas are arranged in a vector
of length NR, which can be expressed with (3.1), (3.3) and n(k)as noise vector of length NR as
We assume additive white Gaussian noise (AWGN) with zero mean and variance
per receive antenna, i.e. the spatial correlation matrix of the noise is given by
where is the identity matrix and (·)H
denotes the complex conjugate(Hermitian) transpose.
The receive vector yNfollows to
2.2 QPSK Modulator/ Demodulator
PSK is a digital modulation technique which is most commonly used modulation technique in present
digital communication systems [12]. In PSK modulation, the phase of the carrier is altered in accordance with
the input binary coded information [9]. The PSK is further subdivided into BPSK,8-PSK, 16-PSK, QPSK,
DPSK. In binary phase shifting keying the transmitted signal is sinusoid of fixed amplitude, has fixed phase as
shown in Figure.2.
Figure.2 Phase Shift Keying
QPSK [4] is a phase modulation scheme, used in constellation mapping. Here the input bits stream is
converted into complex stream using equation 10 and where the I and Q both are in phase with I-out and Q-out
respectively. QPSK modulator accepts the binary bits as inputs taken as a symbol and converts them into
complex value. QPSK takes only 4 symbols and generate its complex value in this fashion.
Where =1/1.414
III. Perfect Channel Estimation
Perfect estimator is the simplest algorithm to estimate the channel matrix. By setting the noise equal to zero in
(1), the perfect approach estimates the channel matrix as
In this way the channel matrix is simply will be obtained by inverse matrix of S/Y.
Least Square Algorithm:
In this case we estimate the free noise MIMO channel perfectly. Perfect estimation will be used as a lower
bound. Consider a Rayleigh flat-fading MIMO channel characterized by H, S as the training sequence, Y as
related received signal. N represents Additive White Gaussian Noise. If we assume that:
Y = SH + N
(12)
LS estimator finds Hˆ that SHˆ ≈ Y .[6],[7]LS Algorithm, minimizes the Euclidian distance of SHˆ −Y .
Table 3.1 Table 3.1 Show the Input and the Output of QPSK modulator
Input
Bits
I-Out Q-Out
00
01
10
-1
-1
+1
-1
+1
-1

11 +1 +1
For this minimization we do following steps:
(13)
After derivation in respect to Hˆ and to put the equation equal the zero:
And so we will have:
We use formula (3.15), as the LS channel estimation algorithm.
Minimum Mean Square Error Channel Estimation:
The Minimum Mean Square Error (MMSE) channel estimates given by [5]
Where
and in the case of additive white noise the MMSE channel estimate follows to
Setting the term in (3.18) to zero yields the Least Square channel estimate in the case of additive white noise.
Meansquareerrorofthechannelestimation:
The correlation matrix of the error of the channel estimations given by
For the Minimum Mean Square Error channel estimation itfollows to [5]
(19)
The Mean Square Error (MSE) of a MIMO channel
is the trace of the error correlation matrix Ree. The trace of amatrix denoted bytr (·) is the sum of the diagonal
elements.For additive white noise theMean Square Error follows to
(21)
For the Least Square channel estimation the term hasto be set to zero.
IV. Simulation Results
In this work the Simulation Results of the channel estimation are presented. The chosen network simulate or, c
Matlab. The simulation results that are collected from the implementation of both the LS and MMSE using the
Matlab simulation are presented.
4.1 Simulation Model And Results
It will be useful to provide a simple Matlab example simulating a QPSK transmission and reception in
Flat MIMO channel. The script performs the following
1- Generate random binary sequence of 1′s and 0′s.
2- Mapping the binary sequence using QPSK.
3- Multiply the symbols with the channel and then add white Gaussian noise.
4- At the receiver, equalize (divide) the received symbols with the known channel.
5- Perform hard decision demapping and count the bit errors.
6- Repeat for multiple values of SNR and plot the simulation
Here, simulation results and derived performance metrics of before mentioned algorithms will be
explained. flat fading MIMO channel used for training-based estimating channel After , random data is
generated in the transmitter and modulated signal will be sent through the channel. By counting number of
errors, BER will be extracted. In the perfect channel estimation, we haven’t used the AWGN in estimating
process, but it is used in calculating the error. 8 bits training sequence for a MIMO 2×2 system has been
considered. We also used a QPSk modulator for modulation data in transmitter. In addition, 100 iterations for
calculating BER and MSE which each contains 400 bits have been used. In this section, we evaluate the BER to
estimate the channel conditions. Figure 3shows BER comparison of MMSE and LS with respect perfect
channel. Here we consider MIMO based system for high multimedia communication system. The parameter

consider for simulation is (number of transmitter) Tx=2 , (number of receiver) Rx = 2 , .5 correlation coefficient
and 8 bits training sequence . Fig 3shows the BER comparison between LS and MMSE from which it is clear
that MMSE is better technique than LS which does not utilize the channel statistics. At high SNR values, the
performance gap is more than at low SNR. But for improved performance in MMSE we have to pay for more
complexity which results in increased computational time and high implementation cost of hardware to have a
priori knowledge of channel behavior.
Figure 3 comparison of MMSE with LS with respect to perfect channel
Fig. 4 illustrates the MSE comparison of MMSE with LS estimators versus different SNR for flat fading MIMO
2×2 channel. It is obvious that, increasing SNR is the reason for decreasing MSE.
Figure 4 MSE comparison of MMSE with LS
The parameter consider for simulation is ( number of transmitter ) Tx=2 and (number of receiver)
Rx=2,3,4 ,.5 correlation coefficient , 8 bits training sequence and QPSK modulation technique for data
transmission. Figure 5 and 6 show comparison of MMSE and LS with different antennas values, increasing the
number of transmit antennas leads to increase the performance estimators, but it is highlighted in LS. For
low SNRs, this approximation effect is small compared to the channel noise, while it becomes dominant for
large SNRs. The curves level out to a value determined in the energy of the taps. MMSE estimator reduces the
0 5 10 15 20 25 30
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR in DB
BER
perfect
MMSE
Ls
0 5 10 15 20 25 30
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR in DB
mse
LS
MMSE

mean square error for a range of SNRs compared to LS estimator.As before, increasing the SNR is the reason
for decreasing BER of all estimators but it is more effective for LS one.
Figure 5 BER comparison LS with respect to different antennas
Figure 6 BER comparison MMSE with respect to different antennas
The parameter consider for simulation is (number of transmitter) Tx=2 and (number of receiver)
Rx=2, correlation coefficients of .4 , .5 and .6 , 8 bits training sequence and QPSK modulation technique for
data transmission.
0 5 10 15 20 25 30
10
-4
10
-3
10
-2
10
-1
10
0
SNR in DB
BER
MMSE:BER vs SNR
mmse TX=2,RX=2
mmse TX=2,RX=3
mmse TX=2,RX=4

Figure 7 BER comparison LS with respect to correlation coefficients
Figure 7 and 8 show BER comparison of MMSE and LS with different correlation for 2x2 MIMO
systems using flat fading channel with, that BER decreases with low correlation values. The results demonstrate
that SNR required to support different values of bit error rate varies depending on different low correlation
between the transmitting and the receiving antennas. The parameter consider for simulation is (number of
transmitter) Tx=2 and (number of receiver) Rx=2, .5 correlation coefficients , 8 bits training sequence and
BPSK ,QPSK ,8-PSK and 16-PSK modulation technique for data transmission.
Fig. 9 and 10 demonstrate the performance of MIMO system employing different modulation
techniques for data transmission. As from the general modulation theory we know the performance is
better for less order modulation technique as compared to high order modulation but in high order
modulation we have larger data rate. Same behavior is also observed for MIMO system. Performance is same
for all kinds of modulation at small value of SNR but as we increasethe SNR value the performance gap goes
on increasing.Outperforms all other modulations techniques. At low SNR, the performance is same for all
modulations but the increasing effect in SNR has clear demonstration of the difference of
performance. So for high SNR, we choose modulation according to the system requirement but for low SNR we
can choose any one.
Figure 8 BER comparison MMSE with respect to correlation coefficients
The parameter consider for simulation is (number of transmitter) Tx=2 and (number of receiver)
Rx=2, .5 correlation coefficients, 4 , 8 , 16 and 32 bits training sequence and QPSK modulation technique for
data transmission. Figure 11 and 12 show BER curves for 2x2 MIMO systems using flat fading channel by
MMSE and Ls estimation with respect to different bit training values which show that BER decreases with large
bit training values.
0 5 10 15 20 25 30
10
-4
10
-3
10
-2
10
-1
10
0
SNR in DB
BER
LS:BER vs SNR
r=.6 ls
r=.5 ls
r=.4 ls
0 5 10 15 20 25 30
10
-4
10
-3
10
-2
10
-1
10
0
SNR in DB
BER
MMSE:BER vs SNR
MMSE, r=.6
MMSE, r=.5
MMSE, r=.4
Figure 7 BER comparison LS with respect to correlation coefficients

Figure 9 BER comparison LS with respect to different modulation techniques
Figure 10 BER comparisons MMSE with respect to different modulation techniques
Figure 11 BER comparison LS with respect different bit training values
0 5 10 15 20 25 30
10
-4
10
-3
10
-2
10
-1
10
0
SNR in DB
BER
MMSE : SNR V/S BER
BPSK
4-PSK
8-PSK
16-PSK
0 5 10 15 20 25
10
-4
10
-3
10
-2
10
-1
10
0
SNR in DB
BER
LS:BER vs SNR
LS,4 Training symbols
LS,32Training symbols

Figure 12 BER comparison MMSE with respect different bit training values
V. Conclusion
MIMO systems play a vital role in fourth generation wireless systems to provide advanced data rate. In
order to attain the advantages of MIMO systems, it is necessary that the receiver and/or transmitter have access
CSI. The time-varying nature of the channel typically requires the use of frequent channel retraining, which in
turn increases the data overhead due to training signals, thus reducing the system’s overall spectral efficiency.
Hence, effective channel estimation algorithms are needed to guarantee the performance of communication. In
this project, a number of channel estimation algorithms have been implemented and evaluated. In this chapter,
training based channel estimation schemes in flat fading MIMO systems are investigated. After introducing LS
and MMSE estimators, they are simulated in a flat fading MIMO channel considering AWGN.
Simulation results show that The algorithm of LS estimator is very simple, As LS algorithm does not
require correlation function calculation nor does it require matrix inversion. MMSE estimator is complex; As
MMSE algorithm requires both correlation function calculation and matrix inversion. From the Simulation
results it is clear that MMSE estimator provides better performance than LS estimator in terms of mean square
error (MSE) and Bit error rate (BER) whereas implementation of LS algorithm is much easier than MMSE
algorithm Also Simulation results show that the BER for 2x2 MIMO systems using flat fading channel with
different correlation values decreases with low correlation values. The results demonstrate that SNR required to
support different values of bit error rate varies depending on different low correlation between the transmitting
and the receiving antennas. In addition, it is illustrated that when the number of and receiver antennas increases,
the performance of TBCE schemes significantly improves. Also The results show BER curves for 2x2 MIMO
systems using flat fading channel by MMSE and Ls estimation with different bit training values which show
that BER decreases with large bit training values.As from the general modulation theory weknow the
performance is better for less order modulation technique as compared to high order modulation but in
highorder modulation we have larger data rate. Same behavior isalso observed for MIMO system. Performance
both MMSE and LS estimation are same for allkinds of modulation at small value of SNR but as we increase the
SNR value the performance gap goes on increasing.
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