ABSTRACT This paper focuses on the channel estimation in OFDM system and it implemented by using pilot type channel estimation by hybrid LS-LMMSE. A LTE system is basically MIMO-OFDM system, where a cyclic prefix is inserted at the beginning of each OFDM symbol in order to suppress both inter-carrier interference (ICI) and inter symbol interference (ISI). The inserted CP is usually longer or equal to the channel length but in some cases, the CP can be shorter. In case of LS and LMMSE channel estimation technique, simulation results shows that LMMSE performs better than LS estimator where cyclic prefix is equal to or longer than the channel length. In other case, LMMSE gives better performance than LS only for low SNR values and for high SNR value, LS gives better performance. Therefore, a hybrid LS-LMMSE channel estimation technique is to reduce the effect of the channel length on system. Simulation results for hybrid system shows its true efficiency and specially for the case where the channel length exceeds the cyclic prefix length

Dr D J Shah

Shraddha Patel

Vijay K Patel

CiteSeerX

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 94-101 © IAEME 
94 
 
 
 
 
 
 
 
 
 
 
PERFORMANCE ANALYSIS OF PILOT-AIDED MIMO-OFDM LTE 
DOWNLINK SYSTEM USING HYBRID LS-LMMSE TECHNIQUE 
 
 
Shraddha Patel
1
,   Vijay K.Patel
2
,   Dr. D.J.Shah
3
 
 
1&2
Department of EC Engineering, Ganpat University, Mehsana 
3
Director, Shruj LED Technologies, Ahmedabad 
 
 
 
ABSTRACT   
 
This paper focuses on the channel estimation in OFDM system and it implemented by using 
pilot type channel estimation by hybrid LS-LMMSE. A LTE system is basically MIMO-OFDM 
system, where a cyclic prefix is inserted at the beginning of each OFDM symbol in order to suppress 
both inter-carrier interference (ICI) and inter symbol interference (ISI). The inserted CP is usually 
longer or equal to the channel length but in some cases, the CP can be shorter. In case of LS and 
LMMSE channel estimation technique, simulation results shows that LMMSE performs better than 
LS estimator where cyclic prefix is equal to or longer than the channel length. In other case, LMMSE 
gives better performance than LS only for low SNR values and for high SNR value, LS gives better 
performance. Therefore, a hybrid LS-LMMSE channel estimation technique is to reduce the effect of 
the channel length on system.  Simulation results for hybrid system shows its true efficiency and 
specially for the case where the channel length exceeds the cyclic prefix length. 
 
Keywords: MIMO, OFDM, Channel Estimation, Channel Length, Cyclic Prefix, Hybrid                    
LS-LMMSE.  
 
1. INTRODUCTION  
 
Over the last few decades, due to the increasing demand for high speed data and widespread 
network access in mobile communications, there has been tremendous ongoing research in the field 
of cellular communications which has resulted in achieving significant developments. Orthogonal 
Frequency Division Multiplexing (OFDM) is most commonly employed in wireless communication 
systems because of the high rate of data transmission potential with efficiency for high bandwidth 
and its ability to combat against multi-path delay. To combat the effect of frequency selective fading, 
MIMO is associated with orthogonal frequency-division multiplexing.  
(OFDM) technique. OFDM is modulation technique which transform frequency selective 
channel into a set of parallel flat fading channels. A cyclic prefix CP is added at the beginning of 
each OFDM symbol to eliminate ICI and ISI. [1] 
INTERNATIONAL JOURNAL OF ELECTRONICS AND 
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) 
 
 
ISSN 0976 – 6464(Print) 
ISSN 0976 – 6472(Online)  
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© IAEME: www.iaeme.com/ijecet.asp 
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IJECET 
© I A E M E 
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 94-101 © IAEME 
95 
 
LTE (Long Term Evolution) is the next generation MIMO-OFDM based system. LTE 
downlink system adopts Orthogonal Frequency Division Multiple Access (OFDMA) as a access 
technique. LTE Downlink system is MIMO-OFDM based which delivers high data rates of up to 
100Mbps for 2x2 MIMO systems.[2] 
Channel estimation is an important part for the design of receivers in mobile communication 
systems. In order to recover the transmitted information correctly, the effect of the channel on the 
transmitted signal must be correctly estimated. In most of research work, the CP is equal or longer 
than the channel length but it is also important to study the performance of MIMO-OFDM system 
where the CP length is shorter than channel length. So that this task becomes more difficult because 
of ICI and ISI. 
There were many articles based on the channel estimation for LTE system. Also the 
performance of LS and LMMSE technique for LTE Downlink system under the effect of channel 
length was studies in [2]. 
In this paper, we propose a hybrid LS-LMMSE channel estimation technique which is robust 
to the channel length effect. 
Organization of paper is like this, an overview of LTE Downlink system is described in 
section II. A LTE MIMO-OFDM system model is given in section III. The LS and LMMSE channel 
estimation techniques are discussed and description of the proposed hybrid technique is given in 
section IV. Section V gives the simulation results of both the systems. The conclusion is given in the 
last section. 
 
2. LTE DOWNLINK PHYSICAL LAYER  
 
LTE physical layer will provide peak data rate in uplink up to 50 Mb/s and in downlink up to 
100 Mb/s with a scalable transmission bandwidth ranging from 1.25 to 20 MHz to accommodate the 
users with different capacities. In order to improve the spectral efficiency in downlink direction, 
Orthogonal Frequency Division Multiple Access (OFDMA), together with multiple antenna 
techniques are exploited. LTE air interface exploit both the time division duplex (TDD) and 
frequency division duplex (FDD). Figure 1 shows the structure of the LTE radio frame. The duration 
of one frame in LTE Downlink system is 10 ms. Each LTE radio frame is divided into 10 sub-frames 
of 1 ms. As described in Figure 1, each sub-frame is divided into two time slots, each with duration 
of 0.5 ms. Each time slot consists of either 7 or 6 OFDM symbols depending on the length of the CP 
(normal or extended). In LTE Downlink physical layer, 12 consecutive subcarriers are grouped into 
one Physical Resource Block (PRB). A PRB has the duration of 1 time slot. 
 
 
Figure 1: LTE radio frame structure [1] 
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 94-101 © IAEME 
96 
 
The subcarrier are spaced by 15 KHz from each other. Therefore, each PRB occupies a 
bandwidth of 180 KHz (12 x 15 KHz).  
The LTE specification define parameters for system bandwidths from 1.25 MHz to 20 MHz 
as shown in Table 1. 
                                                   
Table 1: LTE Downlink Parameters 
Transmission Bandwidth 
(MHz) 
1.25 2.5 5 10 15 20 
Sub-frame duration (ms) 0.5 
Sub-carrier spacing 
(KHz) 
15 
Sampling frequency 
(MHz) 
1.92 3.84 7.68 15.36 23.04 30.72 
FFT size 128 256 512 1024 1536 2048 
Number of occupied sub-
carriers 
76 151 301 601 901 1201 
 
 
3. LTE DOWNLINK SYSTEM MODEL 
 
LTE system is basically MIMO-OFDM based system. The system model is given in figure 2. 
 
 
Figure 2: MIMO-OFDM system [1] 
 
OFDM is employed as multiplexing technique in the LTE system. OFDM consists in dividing 
the transmission bandwidth into several orthogonal sub-carriers. The entire set of subcarrier is shared 
between different users. The N subcarriers are spaced by 15 KHz. To combat the effect of frequency 
selective fading, a cyclic prefix (CP) with the length of LCP is inserted at the beginning of each 
OFDM symbol. 
Each OFDM symbol is transmitted over frequency selective fading MIMO channels assumed 
independents of each other. Each channel is modeled as a Finite Impulse Response (FIR) filter with 
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 94-101 © IAEME 
97 
 
L taps. After moving the CP and performing the DFT, the received OFDM symbol at one receive 
antenna can be written as: 
 
                                               Y = XH + µ                                                                                    (1) 
 
Y represents the received signal vector, X is a matrix which contains the transmitted elements 
on its diagonal. H is a channel frequency response, and µ is the noise vector whose entries have the 
i.i.d. complex Guassian distribution with zero mean and variance σ
2
. 
 
4. CHANNEL ESTIMATION 
 
To estimate the channel, LTE systems use pilot signals called reference signals. When short 
CP is used, they are being transmitted during the first and fifth OFDM symbols of every slot. When 
long CP is used, they are transmitted during the first and the fourth OFDM symbols. 
 
 
Figure 3: Downlink reference signal structure on one antenna [2] 
 
From (1), the received pilot signals can be written as: 
 
                                        YP = XP HP + µP                                                                                        (2) 
  
(.)P denotes positions where reference signals are transmitted. 
In this paper, we study the performance of LS and LMMSE channel estimation techniques. 
 
4.1 Least Square LS 
The main purpose of the channel least square estimator is to minimize the square distance 
between the received signals and the original signal. 
The least square estimate (LS) of the channel at the pilot subcarrier given in (2) can be 
obtained by the following equation [3]. 
 
                                       Hp
LS
 = (XP)
-1
YP                                                                                          (3)                                                                             
 
4.2 Linear Minimum Mean Square Error LMMSE 
The LMMSE channel estimator is designed to minimize the estimation MSE. The LMMSE 
estimate of the channel responses given in (2) is: 
 
                           Hp
LMMSE 
= RHHP (RHPHP + σ
2
(XX
H
)
-1
) Hp
LS
                                               (4) 
 
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3,
RHHP represents the cross correlation matrix 
reference signals. RHPHP represents the autocorrelation matrix of the subcarrier with reference 
signals. The high complexity of LMMSE estimator (4) is due to the inversion matrix. Every time 
data changes, inversion is needed. The complexity of this estimator can be reduced by averaging the 
transmitted data. Therefore, we replace the term (XX
 
The simplified LMMSE estimator becomes:
 
                                     Hp
LMMSE
 = RHHP
 
Where β is scaling factor which depend on the signal constellation. SNR is the average signal 
to noise ratio, and IP  is identity matrix.
 
4.3 Hybrid LS-LMMSE Channel estimation technique
For LTE Downlink systems, the performance of LS and LMMSE channel estimation 
techniques under the channel length effect was studied in [
shows that, in the case where CP is longer than the channel length, the LMMSE gives better 
performance than LS but at cost of complexity. In the other case, where CP is shorter than the 
channel length, LMMSE shows also better performance but only at low SNR
values, LS gives better performance than LMMSE.
So that we propose hybrid LS
channel length effect. In this hybrid system, when CP is equal to or longer than the channel lengt
the hybrid LS-LMMSE algorithm will apply directly the LMMSE channel estimation technique. In 
other hand, when CP is shorter than channel length, the hybrid algorithm will act depending on 
received SNR value. When received SNR value is low, this algorith
estimation technique and when SNR value is high, hybrid algorithm will switch to LS estimation.
 
Figure 4: Hybrid LS
 March (2014), pp. 94-101 © IAEME
98 
between all subcarrier and the subcarrier with 
H
)
-1 
in (4) with its expectation E[(XX
[3] 
 [RHPHP + (β/SNR)IP]
-1
 Hp
LS
                                            
[3] 
 
2][3]. In that paper, the simulation results 
 value. For higher SNR 
 
-LMMSE channel estimation technique which is robust to the 
m will apply LMMSE channel 
-LMMSE channel estimation algorithm [3] 
– 
 
H
)
-1
]. 
   (5) 
h, 
 
 
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 94-101 © IAEME 
99 
 
5. SIMULATION RESULTS 
 
In this section, we investigates the performance of hybrid LS -LMMSE estimation techniques 
for 2x2 LTE Downlink system under the effect of the channel length. The transmitted signals are 
quadrature phase-shift keying (QPSK) modulated. The number of subcarrier in each OFDM symbol 
is N = 300, and the length of CP is LCP = 36. 100 LTE radio frames are sent through a frequency- 
selective channel. The frequency selective fading channel responses are randomly generated with a 
Rayleigh probability distribution. Table 2 gives a summary of simulation parameters. 
 
Table 2: Simulation Parameter. 
LTE Bandwidth 5 MHz 
No of used subcarrier 300 
Cyclic prefix length 36 
No of transmitted frames 100 
No of transmitted antenna 2 
No of received antenna 2 
Modulation scheme QPSK 
Channel model Rayleigh 
 
 
5.1 Case with L ≤ LCP  
In this case, the cyclic prefix is longer than the channel length. So that, ISI and ICI are 
completely suppressed. The hybrid LS-LMMSE estimation will apply directly the LMMSE 
estimation technique. Simulation results shows that the LMMSE estimator gives better result than LS 
but at cost of complexity. Figure 5 and Figure 6 show respectively the performance of LS, LMMSE 
and hybrid estimator in terms of BER and MSE for L = 10. 
 
           
           Figure 5: BER versus SNR for L=10                  Figure 6: MSE versus SNR for L=10 
                                   
5.2 Case with L > LCP  
In this case, the cyclic prefix is shorter than the channel length which shows the true 
efficiency for the performance of LTE Downlink system. In this case, some unforeseen behavior of 
the channel can occur. That will cause the introduction of ISI and ICI. Figure 7 and Figure 8 show 
the performance of LMMSE and Hybrid estimator in terms of BER and MSE respectively for L=46.  
0 5 10 15 20 25 30
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR(dB)
B
E
R
BER performance using LS-LMMSE and hybrid techniques
 
 
LS-10
LMMSE-10
Hybrid-10
0 5 10 15 20 25 30 35
10
-4
10
-3
10
-2
10
-1
10
0
SNR(dB)
M
S
E
MSE performance using LS-LMMSE and hybrid techniques
 
 
LS-10
LMMSE-10
Hybrid-10
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 94-101 © IAEME 
100 
 
 
 
              Figure 7: BER versus SNR for L=46                 Figure 8: BER versus SNR for L=46 
 
Simulation results show that the Hybrid LS-LMMSE estimator performs better than LMMSE 
estimator specially for high SNR range. For this range of SNR values, simulation results show large 
difference between two estimators and this proves well the efficiency of the proposed technique.  
 
6. CONCLUSION 
 
Channel estimation is a challenging problem in wireless system. In this paper, we evaluate 
the performance of Hybrid LS-LMMSE estimation techniques for LTE Downlink systems under the 
effect of the channel length. The cyclic prefix inserted at the beginning of each OFDM symbol is 
usually equal to or longer than the channel length in order to suppress ISI and ICI. Simulation results 
for LS and LMMSE techniques show that the LMMSE gives better performance than LS in case 
where CP is longer or equal to the channel length at cost of complexity. In the other case, where CP 
is shorter than the channel length, LMMSE gives better result only for low SNR value. For high SNR 
value, LS performs better than LMMSE estimator. In this paper, we compare the simulation results 
for both the hybrid and Non-hybrid system. Simulation results for the proposed hybrid system have 
shown the efficiency of hybrid technique and specially for the case where the channel length exceed 
the cyclic prefix length. In this paper, the hybrid technique applies LMMSE estimator for low SNR 
value. For high SNR value, the proposed technique applies LS estimator. 
 
REFERENCES  
 
[1]   Hlaing Minn and Vijay K.Bhargava, “An investigation into Time-domain approach for 
OFDM channel estimation”, IEEE Transcations on Broadcasting, Vol. 46, No. 4, December 
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[3]   A. Khlifi and R. Bouallegue, “Performance Analysis of LS and LMMSE Channel estimation 
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[4]  Helmut Bolcskei and Eth Zurich, “MIMO-OFDM Wireless Systems: Basics, Perspective, and 
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0 5 10 15 20 25 30 35
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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 3, March (2014), pp. 94-101 © IAEME 
101 
 
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PERFORMANCE ANALYSIS OF PILOT-AIDED MIMO-OFDM LTE DOWNLINK SYSTEM USING HYBRID LS-LMMSE TECHNIQUE

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PERFORMANCE ANALYSIS OF PILOT-AIDED MIMO-OFDM LTE DOWNLINK SYSTEM USING HYBRID LS-LMMSE TECHNIQUE

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