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A Proficient Pilot-Designing Pattern for Channel 1

Estimation in MIMO-OFDM Systems 2

3 The channel estimation for high data transmission rates in the communication channel is a 4 recent developing demand because of their exceptional properties. The research focused the 5 multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) 6 systems for channel estimation that adopt the cyclic-delay diversity (CDD) scheme which 7 provides a low-complexity and require just a single inverse discrete Fourier transform (IDFT) 8 operation at the transmitter side. Moreover, the optimal pilot sequences, which limit the mean 9 square error (MSE) of the channel gauge in traditional MIMO-OFDM systems are 10 inapplicable to CDD-OFDM systems. Therefore, this paper utilizes the grey wolf optimization 11 technique for optimal determination of the pilot with the criteria which yield the base MSE of 12 both the least square (LS) channel assess and the MMSE channel appraise in CDD-OFDM 13 systems. The inferred criteria are then used to build up a general strategy for deciding the 14 optimal pilot sequence. Significantly, the proposed design philosophy empowers the status of 15 the channel to be evaluated utilizing single OFDM image. We have compared the 16 performances of channel estimation algorithm by measuring bit error rate versus SNR with 17 BPSK, QPSK 16-PSK and 256-PSK modulation schemes. 18 19

Keywords: channel estimation, cyclic delay diversity, Inter carrier Interference (ICI), 20 multiple input-multiple output technologies, orthogonal frequency-division multiplexing, 21 optimal pilot design. 22 23 24

Introduction 25 26

Orthogonal frequency division multiplexing (OFDM) communication 27 systems is a sort of frequency division multiplexing system which requires 28 accurate estimation of timing balance and channel motivation reaction in order 29 to achieve alluring performance. Channel estimation is one of the critical issues 30 in designing multiple-input multiple-output (MIMO) OFDM systems for 31 coherent detection and decoding. Recently compressive detecting assumes an 32 imperative part in the connected mathematics and signal processing 33 communities which are commonly used in different areas such as imaging, 34 radar, speech recognition, and data acquisition. Consequently, in 35 communication system compressive detecting is for the most part adapted for 36 sparse channel estimation and its variations. 37

In parametric channel model, the channel frequency reaction is evaluated 38 utilizing way channel model. The ESPRIT (estimation of signal parameters by 39 rotational invariance techniques) strategy is used to decide the underlying 40 multipath time delays acquisition and furthermore proposed a bury way 41 interference cancelation delay locked circle to track the channel multipath time 42 delays [1]. A channel estimation scheme in light of time of landings (TOAs) 43 estimation decided utilizing a variant of probabilistic data association (PDA) 44 and utilizing the base description length principle. In order to refine the TOA 45 estimation PDA is expanded by cooperative choice feedbacks [2]. 46

The time assorted variety in the Doppler-induced bury carrier interference 47 (ICI) and its relationship to the carrier frequency counterbalance (CFO) 48

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induced ICI are illustrated utilizing the premise expansion model [3].In pilot 1 supported channel estimation the similarly spaced pilot images are utilized for 2 the reconstruction of channel reaction by means of interpolation. The optimal 3 least mean squared error (MMSE) estimation performs smoothing and 4 interpolation commonly [4]. Innumerous modern wireless communication 5 systems, the assumption of a locally time-invariant (block-fading) channel 6 separates because of increased client versatility, data rates, and carrier 7 frequencies. Quick time-changing channels feature significant Doppler spread 8 in addition to delay spread [5]. 9

The transmission of ultra-short heartbeat through a multipath ultra-10 wideband channel gives ultra-wideband signal which can be approximated 11 utilizing linear combination of a couple of iot as from a pre-characterized 12 dictionary. Along these lines the outcome becomes the sparse representation of 13 the received ultra-wideband signal [6].In comparison with other guided media; 14 the radio channel is highly dynamic subsequently the channel estimation is a 15 challenging issue in wireless systems. During transmission of signal over a 16 communication channel which frequently undergoes various adverse effects 17 that corrupt the signal and regularly place limitations on the performance of the 18 system [7]. 19

Inter- Carrier interference (ICI) is limited by utilizing a delicate non-20 coherent equalizer that influences the sparsely in the delay-control profile to 21 generate close optimal piece gauges with low complexity [8]. The rising 22 hypothesis of compressed detecting gives the key plan to propose sparse 23 channel learning strategies for both single-carrier and multicarrier examining 24 waveforms that utilize reconstruction algorithms in light of convex/linear 25 programming [9]. In inadequate MIMO channel, the nature of the signal is 26 utilized at the transmitter and the algorithms utilized at the receiver to appraise 27 quantification of the mean squared-error in the resulting channel [10]. The 28 physical multipath in point delay-Doppler at a resolution corresponding to the 29 signal space parameters and the dominant non-vanishing virtual channel 30 coefficients characterize the statistically autonomous degrees of flexibility 31 (DoF) in the channel [11]. 32

Channels with Doppler spread, adopted a compressed detecting approach 33 in type of Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) 34 algorithms, and use over complete dictionaries with an increased way delay 35 resolution [12].A prevalent assumption that multipath channels are inadequate 36 in their equal baseband representation has drawbacks. The complete 37 dictionaries that lead to better sparser channel representations and estimation 38 performance [13]. Estimation of time-fluctuating and inadequate channels 39 gives considerable intrigue especially on underwater acoustic communication 40 [15]. The optimal pilot distribution is regularly very different, with more pilot 41 energy distributed to the edges of the signal bandwidth [16]. Recent results 42 indicate that full (all tones carrying pilot images) introductions with rise to 43 pilot images are almost optimal, as in the yield a local least of the mean square 44 error (MSE) performance metric of the assessed channel frequency reaction 45 (CFR), subject to add up to preparing energy constraint [17]. In general, if the 46

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pilots are distributed and properly estimated in the receiver end, then the 1 spacing of the bits not required. 2

Typically, multi-TX/RX-antenna techniques like space-time coding 3 require signal processing in both the transmitter and the receiver. However, 4 CDD as well as DD can be implemented solely at the transmitter, the receiver 5 or both sides. The fact that the counterpart—e.g., the RX in case of a TX-sided 6 implementation—needs not to be aware of the implementation makes these 7 techniques standard compatible [18]. That is, they can be implemented as an 8 extension for already existing systems without changing the standard of space 9 coding schemes.CDD has extensively been investigated for Rayleigh fading 10 channels. It can be shown that CDD transforms the multiple-input/single-11 output (MISO) channel into an equivalent SISO channel. This transformation 12 increases the number of propagation paths and the frequency selectivity of the 13 channel, which improves the system performance in multipath Rayleigh fading 14 scenarios. 15

The combination of orthogonal frequency-division multiplexing (OFDM) 16 and multiple-input multiple output (MIMO) technologies, referred to as 17 MIMO-OFDM, is currently under study as one of the most promising 18 candidate for next-generation communications systems, ranging from wireless 19 LAN to broadband access. Recent works tackled the performance assessment 20 (both through simulation and measurements) of MIMO-OFDM systems in the 21 presence of practical impairments, such as synchronization and channel-22 estimation errors. In so far work, channel estimation is a critical issue for 23 MIMO OFDM systems, especially if multilevel modulation is employed in 24 order to achieve high spectral efficiencies. In the existing work an efficient 25 pilot patterns and channel estimation for the high-rate MIMO-OFDM have 26 used. But while the selection of the pilot pattern, the whole performance of 27 channel estimation get reduced and produce more complexity. Hence 28 considering the issues, the proposed scheme going for the optimization for the 29 selection of the pilot based channel estimation. 30 31 32

Related Works 33 34

Certain modern research efforts linked to the optimal pilot design 35 technique for sparse channel evaluation is elegantly elaborated as follows. 36

Islam et al. [19] primarily focuses on power-domain NOMA that utilizes 37 superposition coding (SC) at the transmitter and successive interference 38 cancellation (SIC) at the receiver. Various researchers have demonstrated that 39 NOMA can be used effectively to meet both network-level and user-40 experienced data rate requirements of fifth-generation (5G) technologies. From 41 that perspective, this paper comprehensively surveys the recent progress of 42 NOMA in 5G systems, reviewing the state-of-the-art capacity analysis, power 43 allocation strategies, user fairness, and user-pairing schemes in NOMA. In 44 addition, this paper discusses how NOMA performs when it is integrated with 45 various proven wireless communications techniques, such as cooperative 46

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communications, multiple-input multiple-output (MIMO), beam forming, 1 space–time coding, and network coding, among others. 2

Ma et al. [20] explained a practical OFDM modulated SC scheme for 3 downlink UWA communications, where the transmitter splits the power 4 between two users based on statistical CSI. The expressions to characterize the 5 boundary of the ergodic rate region achievable by the proposed scheme over 6 long code words are presented first, followed by the analysis of outage 7 probability when coding is applied within one OFDM block. Then we examine 8 the performance of SC in an OFDM-modulated system with practical coding 9 and modulation pairs. Simulation results show that the OFDM-modulated SC 10 scheme outperforms the orthogonal frequency-division multiple access 11 (OFDMA) in performance of both block error rate (BLER) and spectral 12 efficiencies under different data rate pairs. Recorded data from both medium-13 range and short-range sea tests verify that channel statistics are stable over a 14 long period of time and can be used to assist resource allocation. 15

F. Abdelkefi et al. [22] actualized an algorithm for the estimation of sparse 16 channel motivation reaction (CIR) was addressed for OFDM systems. The 17 origination of this algorithm comparably realizes the CIR estimation issue as a 18 decoding one. Hence it achieves the channel sparsity through the modeling of 19 the inadequate CIR as a Bernoulli-Gaussian process. At that point, utilizing the 20 relationship between the Reed-Solomon codes and the OFDM modulator it 21 efficiently appraises the sparse CIR utilizing directly the decoding of the 22 OFDM received signal. 23

Jong-SeobBaek et al. [23] displayed the pilot examples and channel 24 estimations for a high-rate multi-input multi-output orthogonal frequency 25 division multiplexing (MIMO-OFDM) system. This technique concentrated on 26 the basic orthogonal property of the unit grid controlling the scattered pilot 27 (SP), edge pilot (EP), and continuous pilot (CP). From the orthogonal property, 28 the efficient channel frequency reaction (CFR) and channel motivation reaction 29 (CIR) estimations were achieved. 30

Wei-Chieh Huang et al. [24] implemented an optimal pilot sequence 31 design for channel estimation in CDD-OFDM systems, which gives the base 32 MSE of both the least square (LS) channel appraise and the base mean square 33 error (MMSE) channel assess in CDD-OFDM systems. These inferred 34 estimations are then used to build up a general technique for deciding the 35 optimal pilot sequence. Significantly, the designed approach empowers the 36 status of the channel to be assessed utilizing single OFDM image. 37

Peng Cheng et al. [25] introduced a channel estimation scheme in light of 38 distributed compressive detecting (DCS) hypothesis. The advantage of the 39 premise expansion model (BEM) and the channel sparsity in the delay area is 40 utilized to change the first DS channel a novel two-dimensional channel model 41 where a few joint sparse BEM coefficient vectors become the estimation 42 objective. The special decoupling structure beginning from a novel sparse pilot 43 design was designed which results in a without ICI structure and empowers the 44 DCS application to make joint estimation of these vectors accurately. This 45

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smoothing treatment process scheme achieves significantly higher estimation 1 accuracy when compared with existing scheme. 2

Jung-Chieh Chen et al. [26] investigated the pilot placement issue for 3 sparse channel estimation in orthogonal frequency division multiplexing 4 (OFDM) systems. The compressed detecting technique is utilized to recover 5 the inadequate signal from under tested estimations and these signals are then 6 connected for pilot-helped sparse channel estimation in OFDM systems to 7 reduce the transmission overhead. The selection of pilot tones significantly 8 affected channel estimation performance. Hence optimal pilot placement for 9 sparse channel estimation regarding least mean-square error of the channel 10 estimation, through a thorough search of all conceivable pilot placements was 11 to a great degree computationally concentrated. In order to limit the 12 computational complexity and all the while expand the accuracy of sparse 13 channel estimation, cross-entropy optimization was introduced to decide the 14 optimal pilot placement. 15 16 17 Proposed Pilot Pattern Design for Mimo-Ofdm with Ccd 18 19

The usage of MIMO-OFDM systems in modern wireless communication 20 systems provides increased system capacity and coverage with robustness 21 against multipath fading. Hence multiple antennas are used at both ends of the 22 transmitter and the receiver. Because of the unique properties of the MIMO 23 and OFDM systems, these systems are used in high-speed wireless 24 communication systems but the channel estimation in a high-rate MIMO-25 OFDM without reducing the estimation performance is becomes a complex 26 task. So this work intended to improve the performance of the channel 27 estimation in MIMO-OFDM. For that, a novel optimal pilot pattern design for 28 the channel estimation in the cyclic-delay diversity (CDD) OFDM system to 29 maximize either the transmit diversity depending on the channel environment 30 is proposed. 31 The process flow of the proposed system is as follows: 32

33 Modeling of MIMO-OFDM system with cyclic-delay diversity 34 Optimal pilot design for Channel estimation 35 Performance analysis based on bit error rate 36

37 The CDD will provide a low-complexity means of increasing the 38

transmission diversity in MIMO-OFDM systems. Hence the overall 39 performance of the channel estimation in MIMO-OFDM system gets improve 40 by using our proposed optimal pilot pattern design. 41

42

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Mathematical formulation of MIMO-OFDM System 1 2

If symbols to be transmitted are 1,......,1,0, MkX k . The OFDM 3

symbols are placed at a frequency spacing of sf , to keep orthogonality among 4

the subcarriers. Where )/(1 ss MTf , sT is the sampling interval 5

The OFDM signal transmitted through Kth subcarrier is given by 6 7

M

mkiM

k km eXx

2

1

0 (1) 8

9 The block diagram of MIMO-OFDM system with Mt transmit antennas, Mr 10 receive antennas, and M subcarriers shown in Figure 1. Generated OFDM 11 signals are transmitted through a number of antennas in order to achieve 12 diversity. 13

14 Figure 1. Block Diagram of MIMO-OFDM System 15

Mapping

Pilot tones

insertion

Pilot tones

insertion

IFF

TIF

FT

FF

TF

FT

Demapping

Channel

estimation

Output

Data

SymbolsInput

Data

Symbols pTx

1Tx 1Rx

qRx

16 17

In MIMO OFDM system shown in Figure 1 (for SISO-OFDM systems, 18 consider Mt =1), Assume that the duration of the cyclic prefix is long enough 19 to avoid inter-symbols interferences (ISI). 20

A received symbol vector at a discrete time index n transmitted over a flat 21 and time-variant MIMO channel can be written as 22

23

)()(.)(.)(1 1 1

,,mUmXHmXHmY

pk

M

p

M

p

ICI

M

kii

pi

pik

pk

pkk

qk

t t

(2) 24

25

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Where )(mX p

k is the transmitted symbol over the k

th subcarrier from the 1

pth

antenna at time index m , )(mY q

k is the received symbol over the k

th 2

subcarrier from the qth

antenna at time index m . p

ikH , , denotes a frequency 3

channel response between the k th and i th subcarrier. Inter-carrier interference 4 (ICI) can be neglected for time invariant channels and time varying channels 5 with moderate mobility. 6

7 Figure 2. MIMO-OFDM System with 2 Transmitting Antenna and two 8 Receiving Antenna 9

10

11 12

MIMO–OFDM systems with two transmit antennas and two receive 13 antenna as shown in figure 2.The total number of subcarriers is M. 14

Basically, the MIMO-OFDM transmitter has Mt parallel transmission 15 paths which are very similar to the single antenna OFDM system. In OFDM 16 system the binary data is first grouped and mapped according to the 17 modulation in "signal mapper". After modulation the symbol rate reduced to R 18 = (R /log2N), where N is constellation size. Then this serial data is fed to serial 19 to parallel convertor. This reduces data rate by M times, where M is number of 20 parallel streams. Each of parallel streams constitutes tiny bandwidth in the 21 spectrum. 22

So these streams almost undergo flat fading in the channel. After inserting 23 pilots either to all subcarriers with a specific period of blocks or within a 24 uniform period of frequency bins in all blocks, IDFT block is used to transform 25 the data sequence of length into time domain signal. 26

27 x(m)=IDFT{X(k)}, m=0,1,2,………M-1 (3) 28

M

mkiMk

ekXmx

21

0)()( (4) 29

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At the receiver end, discrete domain through A/D and low pass filter, 1

guard time is removed and the signal 1)( MmMformmY ggg will 2

become as y(m) for m=0,1,2,……M-1. Then y (m) is sent to DFT block for the 3 following operation: 4

5

1,.......,2,1,0,)()( MkmyDFTkY (5) 6

As a matter of convenience we can write the entire operation as 7

)()()()( kUkHkXkY (6) 8

9 where X(k)=DFT{x(m)} and U(k)=DFT{u(n)}. Then the binary 10

information data is obtained back in "signal Dapper" block, where M is DFT 11 length. Following IDFT block, guard time, which is chosen to be larger than 12 the expected delay spread, is inserted to prevent inter-symbol interference. This 13 guard time is a copy of the last part which acts as aOFDM symbol. This makes 14 the transmitted symbol periodic, which plays a key role in identifying frames 15 correctly, so as to avoid ISI and inter-carrier interference (ICI). The resultant 16 OFDM symbol is given as follows: 17

18

1.........,,)()( 1 ggggg MMmmmxmX , m=0,1,2 19

….M-1(7) 20 21

Where gM is the length of the guard interval. The transmitted signal will 22

pass through the frequency selective time varying fading channel with additive 23 noise. Then the received signal is 24

25

)()().()( mumhmxmY g (8) 26

27 The channel response h(m) can be represented by 28 29

))(/sin(/)sin(/1)( )1( KMeMmh nnnMkMj

n (9) 30

31 As a MIMO signaling technique, Mt different signals are transmitted 32

simultaneously over Mt X Mr transmission paths and each of those Mr 33 received signals is a combination of all the Mt transmitted signals and the 34 distorting noise. It provides the diversity gain to enhance system capacity. The 35 data stream from each antenna undergoes OFDM Modulation with the 36 encoding matrix represented as, 37

38

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1

12

21

XX

XXX (10) 2

]]1[.].........3[]2[]1[]0[[1 MXXXXXX (11) 3

])2[].......2[]3[]0[]1[(2 MXXXXXX 4

5 The vectors X1 and X2 are modulated using the Inverse Fast Fourier 6

transform (IFFT) and after adding a cyclic prefix as a guard time interval, two 7 modulated blocks Xg1 and Xg2 are generated and then transmitted through 8 first and second Transmit antennas respectively. Assuming the guard time 9 interval is more than the expected largest delay spread of a multipath channel. 10 The received signal will be the convolution of the channel and the transmitted 11 signal. Assuming that the channel is static during an OFDM block, at the 12 receiver side after removing the cyclic prefix, the FFT output as the 13 demodulated received signal can be expressed as 14

15

MMMrMkMkMk

Mr

Mr

Mk U

U

U

X

X

X

HHH

HHH

HHH

Y

Y

Y

.

.

.

.

.

.

.............

.

.

.

...................

...................

.

.

.

2

1

2

1

,2,1,

,22,21,2

,12,11,1

2

1

(12) 16

17 In the equation (13), [U1,U2.. NTU ] denotes AWGN and Hn, m is the 18

(single-input single-output) channel gain between the nth receive and m-th 19 transmit antenna pair. The m-th column of H is often referred to as the spatial 20 signature of the m

th transmit antenna across the receive antenna array. The 21

channel information at the receiver, (ML) detection can be used for decoding 22 of received signals for two antenna transmission system, which can be written 23 as 24

25

]12[]2[]2[]2[]2[ 2,

1

1,

kYkHkYkHkW iii

Mk

i

i

(13) 26

]12[]12[]2[]12[]12[ *1,

*2, kYkHkYKHkW iiiI

(14) 27

28 Where k=0,1,2…(M/2)-1. Assuming that the channel gains between two 29

adjacent sub channels are approximately equal. 30 i.e. ]12[]2[ 1,1, kHkH ii and ]12[]2[ 2,2, kHkH ii At the end, the 31

elements of block w[k]are demodulated to take out the information data. 32 33

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Cyclic Delay Diversity 1 2

As a conventional single antenna OFDM transmitter, the signal stream is 3

divided intoCM , parallel sub streams, termed subcarriers. The

thi subcarrier, of 4

the thl symbol block, named OFDM symbol, is denoted by ilX , . An inverse 5

DFT (IDFT) [27] with CFFT MM , points is performed on each block. 6

Then the data streams split into TM parallel streams, and an antenna dependent 7

cyclic delay, cyc , is inserted, resulting in the following CDD signal of 8

transmit antenna 9

10

FFTcyclmlMmxx mod)(

, (15) 11

12 Usually, the cyclic delay between adjacent transmit antennas are set as 13 equidistant delays 14

15

Tcyccyc M 1,).1( (16) 16

17 Where cyc , is the delay parameter which can be chosen within the 18

range ]/,0[ TFFT MM .It is instructive to consider the signal before OFDM 19

modulation, ilX , which is related to mlx , , by an IDFT. Correspondingly, the 20

DFT of a cyclically delayed signal ml

x, translates to a phase shifted version 21

of ilX , . Cyclic delays by cyc )1( samples in the time domain correspond 22

to the following phase shift between adjacent subcarriers. 23 24

FFTcyc M/)1.(2)( (17) 25

26 The time domain signal of transmit antenna is related to the frequency 27

domain transmitted signal by 28 29

il

jiilml

XIDFTeXIDFTx,,,

(18) 30

31 Where

ilX , represents the transmitted frequency domain signal of transmit 32

antenna . Note that ilX , does exist only virtually but it is the equivalent 33

signal which would be obtained by inducing phase shifts before OFDM 34 modulation rather than time delays after OFDM modulation. 35

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Consequently a guard interval (GI) having GIN samples is inserted, in the 1

form of a cyclic prefix. The signal stream is transmitted over a multipath 2 fading channel. At the receiver the guard interval is removed and a DFT on the 3 received block of signal samples is performed, to obtain the output of the 4

OFDM demodulation ilY , . Assume the cyclic prefix to yield perfect 5

orthogonal. Generally, the received signal of a MISO system after OFDM 6 demodulation is

ililN

ilil MHXY T

,,1 ,,

. 7

Taking into account the properties of CDD the received signal can be 8 expressed as 9

10

il

jiM

ililil MeHXYT

,1

,,,

(19) 11

12 where ilM , denotes additive white Gaussian noise (AWGN) with zero mean 13

and variance 0M . 14

The channel transfer function (CTF), ilH ,

is obtained by sampling the 15

analog CTF, ),,( ftH at time and frequency instants 16

symlTt and Tif / , where splGIFFTsym TMMT )( and 17

splFFTTMT represent the OFDM symbol duration with and without the 18

guard interval, and splT is the sample duration. The CTF, ),( ftH is the 19

Fourier transform of the channel impulse response (CIR). 20 Considering a frequency selective, Rayleigh fading channel, modeled by a 21

taped delay line with 0Q non-zero taps,

0

1

()(),(Q

qqq thth

,the 22

CTF can be described by 23 24

TijQq qlil

qehH/2

1 ,,0

(20) 25

26

where ql

h,

is the thq tap of the CIR, impinging with time delay qT The 27

channel is assumed to be constant during one OFDM symbol, 28

so

).(, symqql

lThh It is assumed that all channel taps and all antennas are 29

mutually uncorrelated, and all tap delays are within the range ],0[ max 30

31 Channel Estimation in CDD-OFDM Systems 32 33

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In developing the proposed pilot design scheme, it is assumed that the 1 channels remain static for V consecutive OFDM symbols and the receiver 2 collects a total of S pilot symbols from these V OFDM symbols. Therefore, the 3 bandwidth efficiency (i.e., the ratio of the number of data symbols to the total 4 number of data symbols plus pilot symbols) is given by (M・V − S) / (M・V) 5 = 1 − S/ (M・V). In other words, the bandwidth efficiency depends upon the 6 channel coherence time. 7 8 Figure 3. Block Diagram of the Transmitter of an OFDM Based System 9 Utilizing Cyclic Delay Diversity (CDD) 10 11

gen

pilot

MUX

PilotIFFT P/S

+GI

+GI

+GI

. . . . . . . . . . . .. . . . . .

. . . . . . . .

12 13

Figure 4. Receiver of an OFDM Based System 14 15

-GI S/P FFTDMUX

Pilot

det

Channel

estimation

. .. . .

. . . .

16 17

It is further assumed that the sth pilot symbol is located on the sm th sub-18

carrier of the sv th OFDM symbol, where sm ∈{0,1...M−1} and sv ∈{0,1... V − 19

1}. The sth received pilot is given by 20 21

)()(....1

)(1

0, sv

M

mmsLmsv

Tsv mUhmGMX

MmY

s

T

T

TTss

(21) 22

)(.. svS mUhMs

(22) 23

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WheresvX ,

svY and svU denote the sv th transmitted OFDM symbol, the 1

sv th received OFDM symbol, and AWGN noise, respectively. In 2

addition, )/2exp( ,, MdmjTsT mvtms , where

Tsmvd is the cyclic-delay of 3

the sv th OFDM symbol of the Tm th transmit antenna, and )( sLmG denotes 4

the sm th row of matrixGL. Furthermore,

S

is a

L1 row vector 5

LML T

defined as )(.1.....,),........(.1,),(.0,).( sLssLssLssvSmMmmmX GGG

s

. 6

Finally,

h is a 1

L column vector with the 7

form TM

TT

TT

hhhM

h ],,.........,.[1

110

.Assuming that the MIMO channels 8

are independent and identically distributed (i.i.d.), then

1,....,2,1,0, Lllh

, are 9

independent complex Gaussian random variables with zero mean and a 10 variance of 2

)(

lh . The S received pilot symbols can be written in the form of 11

anS×1 column vector Tsvvv mYmYmYYs

)1(),....,(),( 11010

. 12

Moreover,Y

can be re-written as UY hM

13

14

Where

is a

LS matrix defined as 15

16

LTMLL

S

GGG 110

1

1

0

........,,,

.

.

.

(23) 17

Tm

is a SS matrix with the form 18

19

TS

T

T

T

mSSv

mv

mv

m

m

m

m

,

,11

,00

)(

.

.

.

)(

)(

1

0

(24) 20

21

Where LG

is a S×L matrix defined 22

as TTSL

TL

TLL

mmm GGGG )(,.....,)(,)( 110

. Finally, U is aS×1 column 23

vector describing the AWGN. The matrix incorporates the effects of cyclic 24

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delay and pilot location. Moreover, the channel vector to be estimated,h

, is 1

obtained by concatenating TM channel impulse responses, hT

m. Accordingly, 2

the developed approach does not estimate the equivalent-SISO channel, but the 3

TM channel impulse responses are estimated individually. 4

Analysis of MMSE channel estimate 5 6

The MMSE channel estimate for a given

has the 7

form

1

hMMSEh ,where

H

h hFand8

H

FR. Meanwhile, the MSE of the MMSE channel estimate is 9

given by

1

21

22 1

H

hMMSEMMSE tpF hh

.Note that 10

H

h hhFis diagonal since all the channel taps are assumed 11

sample spaced and mutually independent. For analytical convenience, let the 12

LL matrix

H

h 2

1 1

be introduced, 2

MMSE is lower bounded by 13

14

1

212 1

H

hMMSE tp

(25) 15

][ 1 tp 11

0

),(

llL

l

1

022

22L

llh

lh

(26) 16

17

The equality holds when I L

H

. Note that the values of 18

1

22H

ULS tp

and19

1

212 1

H

hMMSE tp

are both a function 20

of

H

tp

. Moreover, the value of

is influenced by the cyclic 21

delays and pilot locations. 22 23

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Design Criteria for Optimal Pilots in CDD-OFDM Systems 1 2

This division presents an over-all approach for designing the pilot 3

sequence which satisfies, I L

H

and therefore diminishes the MSE 4

of the LS and MMSE channel estimates. In emerging the optimal pilot design, 5 it is noted that

H can be rewritten as 6

1,11,1,1

1,11,1,1

1,1,0,

............

.

.

.

............

............

TTTT

T

T

MMMOM

MO

MOOO

H

(27) 7

Where }1,...,1,0{,,

TikMki , is an L×L matrix defined 8

as FF LiH

Lkik ,.In order to satisfy the 9

condition I L

H

, it is essential that 10

1,....,1,0,,

,

0,

T

LL

Lik Mki

ik

ik here0 LLis an 11

L×L zero matrix. 12 13 A. Case of k=i 14 When k=i, ),(, dcik

has the form 15

1

0

,,2

,

)(2exp

)(2exp)(),(

S

S

kvskvssvkk

dbmjcbmjmdc ss

s

16

17

1

0

2 )(2exp)(

S

S

ssv

dcmjm

s

(28) 18

In examining for the optimal pilot sequence required to estimate 19

TM channels of length L, the S pilot symbols are equally divided into R groups, 20

with each group containing RM pilots, i.e., S=R ・ RM , where RM ≥L and 21

R≥ TM . It is revealed that Lkk ,

if the S pilot symbols have the form 22

),exp()()( ),(),(),(

rrrvsv jmmrs

(29) 23

Where24

1,....,1,0,1,....1,0,,1

0),(

RrTtTtm rr

R

rRrr M

and 25

1,....,1,0 M R . 26

27 B. Case of ik 28 For ik , the matrix

ik ,has the form as shown in (30), 29

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16

Li

H

Lkik FF

,

(30) 1

2 3 4 5 6 7 8

Where

)(2exp

,,

,,

~kvivs

kisss

bbmj

(31)

9

The(c, d)th element of ik ,is given by (30) 10

M

bbdcmjmX

M

dmj

M

bbmj

M

cmjmX

dc

kvivsS

ssv

skvivssS

ssv

ik

ss

s

ss

s

,,1

0

2

,,1

0

2

,

(2exp)(

2exp

)(2exp

2exp)(

),( (32) 11

In order to satisfy the condition,

LLik , it is necessary 12

that. 0),(, dcik Using the pilot structure given in (30), and replacing the 13

index sby the index set (r, τ), ),(, dcik can be expressed as in (33), 14

)(21

exp),( ,,

1

0

1

0,

),(),(kviv

Rr

R

r

M

rikrr

R

bbdcM

Mtj

Mdc

(33) 15

Equation (33) shows that ),(, dcik is a function of the cyclic-16

delay ib rv ,),( . However, (33) cannot be further simplified unless the value of 17

the cyclic delay ib rv ,),( is constrained. To facilitate the analysis, the cyclic-18

delay is therefore specified as 19

RTrmvTv mbmrbTr

,),,( (34) 20

Where rv is the sub-carrier index of the OFDM symbol which carries the rth 21

pilot group and

RTr

1

1,....2,1

is a cyclic-delay 22

coefficient, which guarantees the condition kvivrr

bbL ,, for 23

ik . Equation (34) ensures that all of the pilots in the same group have the 24

same cyclic delay, i.e., ivivrr

bb ,,),(

. As a result, ),(, dcik can be 25

rewritten as, 26

)(

.

.

.

)(

)(

)(

.

.

.

)(

)(

)(

.

.

.

)(

)(

1

1

0

,,1

~2

1

,,1

~2

0

,,0

~2

0

1

1

0

1

0

0

SL

L

L

kiSSV

kiV

kiVH

SL

L

L

m

m

m

mX

mX

mX

m

m

m

F

F

F

F

F

F

S

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1

0

1

0

1

0

1

0,

))((2exp

))((2exp

))((21

exp),(

R

r

M

R

RrRrrr

RrR

r

R

r

M

rik

R

R

M

Mkidcj

M

Mkidctj

MkidcM

Mtj

Mdc

(35) 1

It is observed from (39) that 2

0),(,

dcik

when0

))((2exp1

0

R

RrM kidcjR

. 3

Applying the summation property, it is easily shown 4

that 0)((2

exp1

0

RM

R

Rr

M

Mkidcj

if5

,.....}.2,,0{))(( RRRr MMMkiba 6

Furthermore, it is shown that 7 ,.....}2,,0{))(( RRRr MMMkidc if and only if c=d. 8

Under such conditions, Γk,i(c, d) in (37) can be simplified to (38). 9

1

0

1

0

1

0,,

).(.2exp.

))(.2exp

))(2exp),(),(

R

r

RrrrR

R

r

M

R

RrRrrrikik

M

MkitjM

M

Mkij

M

Mkitjccdc

R

(36) 10

It should be noted in (40) that |i−k|≤MT−1≤R−1 since 0≤i, k<MT and R≥MT. 11 Using the summation property once again, it can be shown that Γk,i(c,c)=0if 12

.))(1(2

exp)(2

exp

R

kirj

SM

Mkitj Rrrr

Thus, 13

to obtain the desired result Γk,i(c,d) = 0, it is necessary that 14

Sr

, 15

RT

rrrrMM

MTtr

S

Mt

)1(

1,....2,1},1,.......,2,1{),1( 16

(37) 17 Equation (37) shows that all of the pilots have the same magnitude even if 18

they belong to different groups. In addition, tr and λr should be jointly 19 determined in accordance with (37). Since tr and λr are both integers, (37) 20 implies that Sand Mare constrained by mod (M, S) =0. 21 22 Proposed pilot design procedure 23 24

This section describes the pilot design methodology proposed in this study 25 based on the criteria derived in above two sections. As described in above 26 design section, the minimum MSE of the channel estimate in CDD-OFDM 27 systems is obtained when

I L

H

, which requires the condition 28

specified in equation(28) to be satisfied. The pilot sequence which satisfies 29 equation (28) can be determined as follows. 30

31 Step 1. Determination of V: 32

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In the proposed pilot design, the S pilot symbols are scattered over V 1 consecutive OFDM symbols. Moreover, it is assumed that the channel remains 2 static for at least V OFDM symbols. The value of V can be as small as 1 and is 3 upper bounded by the channel coherence time. 4

5 Step 2. Determination of number of pilot symbols: 6 The pilots are equally partitioned into R groups, with each group 7

containing RM pilots. In other words, RMRS , where TR MRandLM 8

9 Step 3. Determination of pilot pattern: 10 The th

pilot of the rth group has the form given in equation (30) and (37), 11 i.e. )exp()/()( ),(),(

),(

rrv

jSmXr

. Note that the phase term ),( r is 12

arbitrarily assigned, and can therefore be adjusted as required to minimize the 13 peak to average power ratio (PAPR). An instinctive option is that the pilot 14 symbols allocated to each OFDM symbol should form a perfect sequence, i.e., 15 a sequence with equal amplitude in both the time domain and the frequency 16 domain. However, the issue of perfect sequences lies beyond the scope of this 17 paper, and thus the value of ),( r is simply set to 0. In other words, all of the 18

pilots in our proposed design have the following pattern: 19

)/()( ),(),(

Sm rvXr

(38) 20

21 Step 4. Determination of pilot locations and cyclic-delays: 22 As shown in (32), the cyclic delay of the rv th OFDM symbol at the Tm th 23

antenna is given by 24

RTrmv MmdTr

, (39) 25

Therefore, to determine the cyclic-delayTr mvd , is equivalent to determine 26

the cyclic-delay coefficient r . In general, the pilot location is described by two 27

parameters, namely the subcarrier index and the OFDM symbol index. The 28 sub-carrier index ),( rm of the th pilot of the rth group has the form 29

,),( Ttm rr ,/ RMMT 1,...,2,1 Ttr (40) 30

It can be seen that the pilots in the same group are equally-spaced in the 31 frequency domain. As noted in the above Section, rr tand are constrained by 32

RT

rrrMM

Mr

S

Mt

)1(

1,...,2,1),1(

(41) 33 34 Although the cyclic-delay may vary from one OFDM symbol to another 35

for a given antenna, an OFDM symbol transmitted by any given antenna 36 cannot have two different cyclic delays. In other words, pilot groups with the 37 same value of r can be allocated to the same OFDM symbol, but pilot groups 38

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with different values of r must be transmitted via different OFDM symbols. 1

As a result, the OFDM symbol index of a given pilot is not fixed, but has 2 certain flexibility. In determining the OFDM symbol index, the following steps 3 are as follows: 4

5 1) Each pilot group is associated with a cyclic-delay coefficient r , where the 6

value of r may be repeated among different pilot groups. 7

2) Pilots with different values of r are transmitted via different OFDM symbols. 8

3) Pilot groups with the same value of r may be allocated to the same OFDM 9 symbol. It is important to emphasize that the pilot sub-carrier indexes, OFDM 10 symbol indexes, and cyclic-delay coefficients should be determined mutually 11 but not individually. In addition, it is noted that the value of V must be larger 12

than the number of distinct values of r . 13 14

Illustration of Pilot Design Procedure 15 16

This section illustrates the proposed pilot design procedure for a CDD-17 OFDM system with 4TM transmit antennas and M=128 sub-carriers. The 18

multi-path channel is assumed to have a length of L=8. As a result, the 19 minimum number of pilot symbols is equal to S=32, which is obtained by 20 setting the number of pilot groups equal to )(4 TMRR and the number of 21

pilots in each group to )(8 LMM RR . From (41), all the pilot symbols have 22

the same pattern 32// S . In designing the pilot sequence, the pilot 23

locations and cyclic delays were mutually determined since the cyclic delay 24 coefficient r and the initial sub-carrier index of the rth pilot group rt . In 25

principle, when the number of total pilot symbols is a constant, the pilot 26 placement is a 2D problem (frequency and time). However, in addition to 27 identifying pilot locations in the frequency-time plane, the optimal pilot design 28 determines the cyclic delays of various antennas. The following discussions 29 present the optimal pilot designs for two different cases, namely V= 1 and 30 V>1.Thus in order to select the Pilot design more optimally the optimization 31 technique of Grey wolf strategy has been utilized which is explained 32 followingly below, 33 34

Grey wolf optimization for optimal pilot design. Step 1: Initialize the 35 GWO parameters such as search agents (Gs), design variable size 36 (Gd), vectors a, A, C and maximum number of iteration (itermax). 37

arandaA

..2 1 (42) 38

2.2 randC

(43) 39

40 The values of a

are linearly decreased from 2 to 0 over the course of 41

iterations. 42 43

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Step 2: Generate wolves randomly based on size of the pack. Mathematically, 1 these 2 wolves can be expressed as, 3 4

GS

Gd

GS

Gd

GsGSGs

GdGd

GdGd

GGGGG

GGGGG

GGGGG

Wolves

11321

2

132

22

12

1321

.........

...........

...........

..............

.........

(44) 5

6 Where, Gj is the initial value of the j

th pack of the i

th wolves. 7

8 Step 3: Estimate the fitness value of each hunt agent using 9 10

)()(. tGtGCD P

(45) 11

DAtGtG P

.)(1 (46) 12

13 Step 4: Identify the best hunt agent (Gα), the second best hunt agent (Gβ) and 14 the third best 15 hunt agent (Gδ) using (47), 16

GGcD

.1 (47) 17

GGcD

.2 (48) 18

GGcD s

.3 (49) 19

).(11 DAGG

(50) 20

DAGG

22 (51) 21

)(32 DAGG

(52) 22

23 Step 5: Renew the location of the current hunt agent using Equation 24

3

1 321 GGGtG

(53) 25

Step 6: Estimate the fitness value of all hunts 26 Step 7: Update the value of Gα ,Gβ and Gδ. 27 Step 8: Check for stopping condition i.e., whether the Itermax reaches Itermax, if 28 yes, print the 29 best value of solution otherwise go to step 5. 30

31

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1 Figure 5. Illustrative Example of the Proposed Pilot Design - all Pilots are 2 Allocated to one OFDM Symbol (V = 1, 4TM ,R= 4, RM = 8). 3

4

CP

CP

CP

CP

Cyclic delay

& Add CP

Cyclic delay

& Add CP

Cyclic delay

& Add CP

Cyclic delay

& Add CP

IDFT

r=0 r=1 r=2 r=3

5 6

A. Optimal pilot design for V = 1 7 If the channel is time-varying, it is desirable to accomplish channel 8

estimation using one OFDM symbol. In other words all the pilot groups should 9 be allocated to a single OFDM symbol and have the same value of r , 10

i.e., 1,....,1,0,))1/(()1(,....2,1 RrMMM RTr . 11 In this scenario, the sub-carrier index of the τth pilot within the rth pilot 12

group is given by Ttrm r ),( , in which rt is given 13

by )/()1( SrMtr . It is noted that λ should be carefully selected such 14

that 1,...2,1 Ttr . Once r has been determined, the cyclic delay can be 15

computed from (45) as RTmv MmdTr

, . Figure 6 illustrates the pilot design 16

for the case of V=1, in which all R=4 pilot groups are allocated to the same 17 OFDM symbol, 0X , and therefore have the same cyclic-delay coefficient, 18

5,...,2,1, r . As noted above, λ must be selected in such a way 19

that 1,...,2,1 Ttr . In other words, for the illustrative example considered 20

here, λ has valid values of only 2 or 4. Arbitrarily selecting a value of λ=2, the 21 cyclic-delay of the Tm th transmit antenna is given 22

by TTRm mmMdT

162,0 . Furthermore, the sub-carrier indexes of the 23

various pilots are given by 16)1(2)/()1(),( rTSrMm r , 24

where r∈ {0,1,2,3} and = {0, 1,...,7}. 25 26

B. Optimal pilot design for V>1 27 When the channel is stationary for V>1 OFDM symbols, the S pilots are 28

scattered over V consecutive OFDM symbols. Consider the illustrative 29

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22

example shown in Figure. 7, in which V=4. In this scenario, one pilot group is 1 assigned to each OFDM symbol and the initial sub-carrier indexes rt of the R= 2

4pilot groups are set equal to one another, i.e 3,2,1,0,15,...,2,1 rttr . The 3

sub-carrier index sets of the R= 4 pilot groups are therefore identical to one 4 another, i.e., 7,.....,1,0,),( Ttm r . 5

Since ])1/[()1(,....,1),/()1( RTrr MMMStrM , it follows that t can 6

only be specified as 4. Therefore, the sub-carrier indexes of the four pilot 7 groups are given by {4, 20, 36, 52, 68, 84, 100, 116}. Meanwhile, the cyclic-8 delay coefficients of the various pilot groups are given as 9

1)/()1( rStrMr and the cyclic-delays of the various transmit 10

antennas are given by TRTrmv mrMmdTr

)1(8, . 11

12 Figure 6. Illustrative Example of the Proposed Pilot Design - Pilot Groups 13 Have Same Sub-Carrier Indexes But Different Cyclic Delays (V = 4,NT = 4,R 14 =4,NQ = 8). 15

CPCyclic delay &

Add CP

Cyclic delay &

Add CP

Cyclic delay &

Add CP

Cyclic delay &

Add CP

r = 0 : r = 1 r = 2 r = 3

IDFT

CP CP CP

CP CP CP CP

CP CP CP CP

CP CP CP CP

16 17 Figure 7. Illustrative Example of the Proposed Pilot Design - Pilot Groups 18 Have Same Sub-Carrier Indexes But Different Cyclic Delays (V = 4,NT = 4,R 19 =4,NQ = 8). 20

Cyclic delay &

Add CP

Cyclic delay &

Add CP

Cyclic delay &

Add CP

Cyclic delay &

Add CP

IDFT

CP CP CP

CP CP CP

CP CP CP

CP CP CP

r = 0 : r = 1 r = 2 r = 3

21

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1 Figure 7 presents an alternative pilot design for the same example. In this 2

case, the initial sub-carrier index is set as for r = 0, 2, and for r = 1, 3. The 3 corresponding sub-carrier indexes are given by (43) as {4, 20, 36, 52, 68, 84, 4 100, 116} for r = 0, 2, and {8, 24, 40, 56, 72, 88, 104, 120} for r = 1, 3. Finally, 5 the cyclic-delay coefficients are specified as and the cyclic-delays are for r 6 =0, 1, 2, 3, respectively. As a result, the first two pilot groups (r = 0, 1) can be 7 allocated to the same OFDM symbol, as depicted in Figure. 8. In other words, 8 the four pilot groups can be allocated to three OFDM symbols and the 9 corresponding cyclic-delays of the various transmit antennas are specified. 10 Such a pilot design is suitable for the case in which the channel remains 11 stationary over only V = 3 OFDM symbols. As demonstrated in Figures. 6-8, 12 the proposed pilot design can be realized using a number of different strategies. 13 Therefore, the proposed scheme is flexible and can be adapted as required by 14 the channel status. 15 16 C. Optimal pilot design for V = 8 17 When the channel is stationary for V=8 OFDM symbols, the S=64 pilots are 18 scattered over V consecutive OFDM symbols. If the pilot design can be 19 extended for more than 4 (For example v=8), then the minimum number of 20 pilots becomes 64, thereby now the subcarrier indices would become {4, 16, 21 32, 48, 64, 80, 96, 112, 128}.Thus way the design produce the flexible results 22

In figure 9 V= 8scenario, one pilot group is assigned to each OFDM symbol 23 and the initial sub-carrier indexes rt of the R=8 pilot groups are set equal to 24

one another, i.e 3,2,1,0,15,...,2,1 rttr . The sub-carrier index sets of the 25

R=4 pilot groups are therefore identical to one another, 26

i.e., 7,.....,1,0,),( Ttm r .Since27

])1/[()1(,....,1),/()1( RTrr MMMStrM , it follows that 28

t can only be specified as 4. Therefore, the sub-carrier indexes of the four pilot 29 groups are given by {44, 16, 32, 48, 64, 80, 96, 112, 128 }. Meanwhile, the 30 cyclic-delay coefficients of the various pilot groups are given as 31

1)/()1( rStrMr and the cyclic-delays of the various transmit 32

antennas are given by TRTrmv mrMmdTr

)1(8,

33

34 35

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Figure 8: Illustrative Example of the Proposed Pilot Design - Pilot Groups 1 Have Same Sub-Carrier Indexes But Different Cyclic Delays (V = 8, NT = 4, R 2 =4, NQ = 16, s=64). 3

4

CPCyclic delay &

Add CP

Cyclic delay &

Add CP

Cyclic delay &

Add CP

Cyclic delay &

Add CP

r = 0 : r = 1 r = 2 r = 3

IDFT

CP CP CP

CP CP CP CP

CP CP CP CP

CP CP CP CP

5 6 7

Considering the case, when the OFDM symbols V>8 the same 8 configuration is carried out as V=4 except the number of pilots selection in 9 each group would become 16 [if this remains 8 then the 2 OFDM symbol 10 needs one pilot group, which is a waste of resources], Thus when Nq>16 the 11 number of pilots becomes also increase correspondingly. i.e. all pilots would 12 have the same pattern ( 64// S ). 13

14 15

Simulation Results 16 17

This section shows the experimental results obtained by our proposed pilot 18 pattern design and the comparison results of our proposed method with the 19 existing methods by means of the parameters obtained from the performance 20 evaluation. 21

System configuration: 22 Operating System: Windows 8 23 Processor: Intel Core i3 24 RAM: 4 GB 25 Platform: Matlab 26

27 Performance Evaluation 28 29

To evaluate the performance of the proposed methodology, the values 30 regarding the bit error rate, signal to noise ratio, maximum mean square error 31 evaluated that has shown in the following figures and tables. 32

33

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1 Table 1. Performance evaluation for SNR vs BER of proposed system 2

SNR BER

0 0.9

1 0.05

2 0.036

3 0.02

4 0.015

5 0.009

6 0.005

7 0.0035

8 0.002

9 0.00012

10 0.00096

11 0.000762

12 0.00054

13 0.000423

14 0.0002

15 0.000192

16 0.00009

17 0.00006

18 0.00005

19 0.000023

20 0.00000156

3 In table 1, evaluating the SNR values ranging from o to 20 implies that 4

increasing the SNR results in the decrease of the BER which shows that the 5 proposed method estimate the accurate value by the pilot sequences in the 6 CDD-OFDM system. The graphical representation for the above table is given 7 in figure 10. 8

9 Figure 9. SNR Vs BER 10

11 12

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26

Figure 9 shows the BER vs SNR graph for our proposed MIMO-OFDM 1 channel, which projects that the BER get reduced due to the pilot design in 2 CDD with increase in SNR. 3 4 Table 2. Performance evaluation for SNR vs MMSE of proposed system 5

SNR MMSE

10 -13.8

11 -15.8

12 -16.3

13 -17.5

14 -21.3

15 -24.4

16 -25

17 -26

18 -29.5

19 -31.28

20 -33

6 In table 2, evaluating the SNR with the MMSE (Minimum Mean Square error) 7 results in the increase of the MMSE vale with inverse proportional of the SNR 8 which reflects the CDD-OFDM system considered the MMSE for the channel 9 estimation. 10 11 Figure 10. SNR Vs MMSE 12

13 14 The following evaluation is done in comparison with the state of arts methods 15 to show the possibilities of the proposed system. 16

17

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1 Figure 11. Basic Comparison of SNR Vs MSE 2 3

4 5 6 The results obtained by our proposed MIMO-OFDM channel shown above. 7 Figure 11 shows the MSE vs SNR graph for our proposed MIMO-OFDM 8 channel in comparison with the SISO-OFDM and MSO-OFDM channel. 9

10 Figure 12. Basic Comparison of BER Vs SNR 11

12 13 Figure 12 shows the BER vs SNR graph for our proposed MIMO-OFDM 14 channel in comparison with the SISO-OFDM and MSO-OFDM channel. 15

16

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Performance Comparison 1 2

To show the performance of the proposed methodology, various methods 3 of MIMO-OFDM [24] system like with only LI, MDF and LI, LF and LI and 4 MISO-OFDM that has been shown below in figure 14 and figure 15. 5 6 Table 3. Comparison for SNR vs SER with the Existing Methods 7

SNR

Symbol error rate

MIMO-

OFDM

MIMO-

OFDM with

PSO

MIMO-

OFDM with

GA

Proposed

(MIMO-OFDM with

CCD with GWO)

0 0.1 0.3 0.29 0.05

2 0.07 0.083 0.092 0.02

4 0.054 0.0568 0.068 0.009

6 0.01 0.025 0.035 0.005

8 0.0069 0.0072 0.008 0.002

10 0.003 0.0042 0.0056 0.001

12 0.0019 0.0012 0.0023 0.0005

14 0.0009 0.0009 0.0009 0.0002

16 0.0006 0.0008 0.0008 9E-05

18 0.0005 0.0007 0.0002 5E-05

20 7E-05 3E-05 9E-05 1E-05

8 The table 3 shows the comparison of the proposed methodology with the 9 existing methods like MIMO-OFDM system with the three modes such as only 10 LI, MDF and LI, LF and LI and MISO-OFDM. The SNR values considered for 11 the evaluation is ranging from the 10 to 20. The graphical representation shown 12 in the figure 14 suggested that the proposed method possess the low SER 13 withSNR compared to the other techniques because the high data transmission 14 by the proper pilot arrangements makes the system efficient to get the low BER 15 value by their proper channel estimation. 16

17 Figure 13. Comparison Graph for SER Vs SNR with Various Methods 18

19

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1 Table 4. Comparison for SNR vs MMSE with the Existing Methods 2

SNR

Minimum mean squared error

MISO-OFDM

MIMO-

OFDM

(PSO)

MIMO-

OFDM

(GA)

Proposed

(MIMO-

OFDM-

CCD

with

GWO)

10 -17.5 -15 -14.2 -13.8

11 -18.2 -16.9 -14.09 -15.8

12 -20 -17.5 -15 -16.3

13 -23 -20 -17.5 -17.5

14 -25 -21 -20 -21.3

15 -27.5 -22 -22.5 -24.4

16 -28 -24.5 -23 -25

17 -29 -25 -23 -26

18 -30 -26 -24 -29.5

19 -31 -26.5 -25 -31.28

20 -32 -27 -26 -33

3 The table 4 shows the comparison of the proposed methodology with the 4 existing methods like MIMO-OFDM system with the three modes such as only 5 LI,MDF and LI ,LF and LI .The SNR values considered for the evaluation is 6 ranging about the 10 to 20 db. This results proved that the inapplicability of 7 MMSE in CDD–OFDM system is eliminated and the consideration of MMSE 8 through pilot design provides the lower value as compared to the other existing 9 methods. 10

11 Figure 14. Comparison Graph for MMSE Vs SNR With Various Methods 12

13 14 By comparing the proposed methodology with the existing technologies, due to 15 the proper channel estimation and the interference cancellation by the pilot 16

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pattern design with cyclic delay diversity the SNR get reduced with increase in 1 MMSE and symbol error rate. While compared to the other techniques, the 2 SNR, MMSE and SER varies without steadiness. Thus it is clear that proposed 3 method shows the proper flexible outcomes. 4 5 6

Conclusion 7 8

The paper presented a work based on the Performance Evaluation of 9 Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing 10 (MIMO-OFDM) with pilot pattern design used in Wireless Communication 11 Applications. Our proposed method overcome this frequency selective fading 12 an also improves the performance of transmission quality. To overcome the 13 channel estimation and the synchronization problems in the multilevel 14 modulation schemes pilot pattern design with cyclic delay diversity utilized. 15 The simulation results, comparison and the performance results demonstrates 16 that the pilot pattern design is most optimal and produce better results and 17 enhance the performance of the whole system. 18 19 20

Bibliography 21 22 [1] Yang, B., Letaief, K.B., Cheng, R.S and Cao, Z. 2001. Channel Estimation for 23

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[3] Cui, T., Tellambura, C and Wu, Y. 2005. Low-Complexity Pilot-Aided Channel 29 Estimation for OFDM Systems Over Doubly-Selective Channels. In Proceedings 30 of IEEE International Conference on Communications (ICC 2005), 3. 31

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[8] Hwang, S.J and Schniter, P. 2008. Efficient Multicarrier Communication for 43 Highly Spread Underwater Acoustic Channels. IEEE Journal on Selected Areas in 44 Communications, 26(9),1674-1683. 45

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[10] Bajwa, W.U., Sayeed, A.M and Nowak, R. 2008. Compressed Sensing of 1 Wireless Channels in Time, Frequency, and Space. In Proceedings 42nd Asilomar 2 Conf. Signals, Systems, and Computers, Pacific Grove. 3

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