**Performance Analysis Of Wireless Communication Link Using Orthogonal Fdm (Ofdm) Over Faded Channel And Space Time Block Code**

**1.1 Introduction: **

With the rapid growth of digital wireless communication in recent years, the need for high-speed mobile data transmission has increased. New modulation techniques are being implemented to keep up with the desire more communication capacity. The main limiting factors in high data rate transmission are noise, inter-symbol-interference (ISI), and multipath effect. In the wireless environment signals are usually impaired by fading and multipath delay spread phenomenon.Traditional single carrier mobile communication systems do not perform well. In such channels, extreme fading of the signal amplitude occurs and Inter symbol Interference (ISI) due to the frequency selectivity of the channel appears at the receiver side. The effect of ISI on the transmission are negligible as long as the delay spread is significantly shorter than the duration of one transmitted symbol. AT higher data rate this problem becomes very obvious.In order to mitigate the effects of ISI many techniques are suggested like equalization which can be used to suppress the echoes caused by the channel. Recently a new and more robust technique is suggested known as OFDM.OFDM stands for Orthogonal Frequency Division Multiplexing.[11]-[12] At present time Orthogonal Frequency Division Multiplexing is widely used for its bandwidth efficiency property. High performance transceiver designs have been proposed for Orthogonal Frequency Division Multiplexing (OFDM) systems to develop high data rate wireless communication systems due to the compelling advantages over competing technologies. In this paper analysis of the non-STBC OFDM system has shown in the first part. Second part shows the analysis of STBC-OFDM. At the end of the paper equations for Signal to Noise Ratio (SNR) and Bit Error Rate (BER) have been derived analytically using four transmitting antennas and one receiving antenna and 6 transmitting antennas and one receiving antenna. For this purpose , here the Rayleigh fading channel has been considered after impaired by AWGN.

**1.2** **Objective of thesis:**

1. The aim of this thesis is to investigate the achievement of high data rates with low bandwidth for the next generation wireless communication.

2. To transmit more data by using OFDM.Because of the orthogonal characteristics of OFDM more data can be transmitted at a certain amount of bandwidth compare to the other systems.

3. Increasing the diversity gain is another way to achieve good performance. By using Space Time Block Code the antenna diversity gain can be increased. Here STBC-OFDM has been used for this purpose.

4. On the whole the aim of this thesis is to analysis of wireless communication link using orthogonal FDM (OFDM) over faded channel and space time block code.

**1.3 Scope of this work:**

The target of next generation wireless communication is to achieve high data rates with low bandwidth. It should be power efficient. This work will cover the performance analysis of the OFDM over faded channel and space time block code for wireless communication systems and the simulation has been done using MATLAB software. Also Signal to Noise Ratio (SNR) and Bit Error Rate (BER) have been evaluated using transmitting and receiving antennas.

**1.4 Thesis outline: **

Chapter 1 consists of introduction of the thesis. This chapter has been divided into

several parts.The objectives of this work has ben clearly discussed and also the scope of this

work has been informed in this chapter.

Chapter 2 includes about the basic OFDM system. Here the system model has been

shown. This chaper also introduce with the CFO, phase noise and the timing jitter by which

the SNR, BER varience has been shown later.

Chapter 3 includes about the STBC-OFDM. This chapter has been divided in some sub-capter. And here the system model for STBC-OFDM, channel, phase noise, received signal, detection with imperfection channel estimation, variance, variance of noise, variance of channel estimator error,varience of inter carrier interference have ben discussed.

Chapter 4 is about the calculation and simulation parameter.

Chapter 5 is about the simulated result and its discussion using the MATLAB software.

Chapter 6 concludes the thesis The conclusion has been given based on the analysis of results from the previous chapter. Recommendations for future works are also presented.

**BACKGROUND OF OFDM**

**2.1 NON-STBC-OFDM**

High performance transceiver designs have been proposed for Orthogonal Frequency Division Multiplexing (OFDM) systems to develop high data rate wireless communication

systems due to the compelling advantages over competing technologies. Orthogonal frequency division multiplexing (OFDM) has been widely adopted and implemented in wire and wireless communication. Orthogonal frequency division multiplexing (OFDM) is being considered the most promising multiplexing techniques to support the future wireless multimedia communication system. It is because of its bandwidth efficiency performance.

a) a regular FDM single carrier –A whole bunch of water coming all in one stream.

b) orthogonal FDM- same amount of water coming from a lot of small stream .

**2.1.1 Orthogonal Frequency Division Multiplexing:**

Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier transmission

technique, which divides the available spectrum into many carriers, each one being

modulated by a low rate data stream. OFDM is similar to FDMA in that the multiple

user access is achieved by subdividing the available bandwidth into multiple

channels, which are then allocated to users.

**2.1.2 Advantages of OFDM **

The OFDM transmission scheme has the following key advantages

· Makes efficient use of the spectrum by allowing overlap

· By dividing the channel into narrowband flat fading subchannels, OFDM is more resistant to frequency selective fading than single carrier systems are.

· Eliminates ISI and IFI through use of a cyclic prefix.

· Using adequate channel coding and interleaving one can recover symbols lost due to

the frequency selectivity of the channel.

· Channel equalization becomes simpler than by using adaptive equalization

techniques with single carrier systems.

· In conjunction with differential modulation there is no need to implement a channel estimator.

· Is less sensitive to sample timing offsets than single carrier systems are.

· Provides good protection against cochannel interference and impulsive parasitic noise.

**2.1.3 Drawbacks of OFDM: **

· Unfortunately OFDM is very sensitive to the synchronization errors such as Carrier frequency offset (CFO), timing jitter and phase noise.

· The CFO arise mainly due to the Doppler shift. The effect is caused by the CFO reduce the signal amplitude and makes interference between the carriers.

· Phase noise resulted from the imperfection of the local oscillator (LO).

· Timing error would occur either when the clock signal is not correctly recovered or when sampling circuit is not perfect. Propagation delay of the IC also causes the timing error.

· Another term is AWGN. It is introduced in the channel through which data is transmitted.

The purpose of this paper is analysis the Signal To Noise Ratio (SNR) by changing the CFO, timing jitter, phase noise. Analysis has been done from the graphs that have been plotted with the help of MATLAB Program. Another graph also shows the Bit Error Rate according to different SNR.

**2.2 System Model and Description:**

Consider the mth symbol of an N- sub carrier OFDM system in presence of normalized CFO (?), phase noise ?m(n) and timing jitter (?), as shown in figure1.

**2.2.1 CFO:**

Carrier frequency offset is used in order to reduce the interference from the fringe area transmitters transmitting in the same channels Carrier frequency offset (CFO) exist between user terminals and the base station.

The absolute [13]value of CFO is f?, is either an integer multiple or a fraction of ?f. Now if the f? is normalized to the sub carrier spacing ?f then normalized CFO of the channel is expressed as

Where ? is an integer and |?|=<0.5

If the CFO occurs then the symbol transmitted on a certain sub carrier k, will shift to another sub carrier ks = k+?.

**2.2.2 Phase Noise:**

Phase noise is the frequency domain representation of rapid, short-term, random fluctuations in the phase of a waveform, caused by time domain instabilities.

Phase noise ?m(n) can be generated at both transmitter and receiver side[8]. It can be modeled as

Where Cm and Tm are defined by and

respectively. Ng is the length of cyclic prefix an u(i) denotes gaussian random

respectively. Ng is the length of cyclic prefix and u(i) denotes gaussian random

u |

variables having zero mean and variance of ? 2

u |

There is another noise that is introduced by the channel. It is Additive White Gaussian Noise (AWGN). It is added to the message signal and its PDF follows gaussian’s distribution function.

**2.2.3 Timing Jitter:**

Timing Jitter is the undesired deviation from true periodicity of an assumed periodic signal in electronics and telecommunications. Jitte is observed in phase of periodic signals. In the sampling circuit at the receiver additional error may occur in the determination of the best sampling phase[9]. This means that the sampling instants are non-ideal and is given by-

tn = nT + ?n

Where ?n is the timing jitter of the nth sampling instant normalized

by the symbol period T.

**CHAPTER 3**

** STBC-OFDM **

**3.1 Space Time Block Code – Orthogonal Frequency Division Multiplexing:**

Severe attenuation in a multipath wireless environment makes it extremely difficult for the receiver to determine the transmitted signal unless the receiver is provided with some form of diversity i.e. some less-attenuated replica of the transmitted signal is provided to the receiver. In some applications, the only practical means of achieving diversity is deployment of antenna array at the transmitter and/or receiver end. As the current trend of communication systems demands highly power-efficient and bandwidth-efficient schemes, techniques that provide such desirable properties are considered very valuable in next generation wireless systems. Making use of multiple antennas increases the capacity of the system with the associated higher data rates than single antenna systems. Space-Time coding is a power-efficient and bandwidth-efficient method of communication over a fading channels by using multiple transmit antennas systems [5].

In multi-transmitting antennas system, instead of emitting the same symbol by all antennas at the same time, *L *successive symbols (over *L *signaling intervals) are stored and arranged to be transmitted through *Nt *transmitting antennas in permutation manner at each signaling interval and this is the main concept of STBC system [14]-[15] .

Previously in this paper the performances have been shown in non-STBC OFDM system. There the equation of Signal to Noise Ratio (SNR) and Bit Error Rate (BER) for 2:1 transmission system has been derived. This paper extended the work by deriving the equations for 4:1 and 6:1 transmission system. After that performances have been shown by plotting various graphs. Results also show the effect of the Inter Carrier Interference (ICI), Channel Estimator Error, and the Additive White Gaussian Noise (AWGN). Gray code mapping is used to calculate the BER. Equations for the SNR and BER have been derived analytically.

**3.2 System Model for STBC-OFDM: **

OFDM system has been considered with transmit diversity, in which the total system bandwidth is divided into *N *equally spaced and orthogonal sub-carriers. This paper extends the work in to a Multi Input Single Output (MISO) communication system by considering STBC-OFDM over two transmit antennas. The system has been investigated with four transmission antennas and one receiving antenna. During the first time instant, the four symbols [ X0 X1 X2 X3 ] have been transmitted from four antennas simultaneously, with X0, X1, X2 and X3 transmitted from all four antennas. In the second time slot [-X1* X0* -X3* X2], third time slot [-X2* -X3* X0* X*] and fourth time slot [X3 -X2 –X1 X0] are transmitted[12].

In wireless systems changes in the physical environment cause the channel to fade. These changes include both relative movement between transmitter and receiver.

This encoding of the transmitted symbol sequence from the transmit antennas has been given by then encoding matrix

H0 H1 H2 H3

– H1* H0* -H3* H2*

-H2* -H3* H0* H2*

H3 -H2 -H1 H0

For each transmit antenna, a block of *N *complex-valued data symbols **{X (k)} for k=0 to N-1 **are grouped and converted into a parallel set to form the input to the OFDM modulator, where

*k*is the sub carrier index and

*N*is the number of sub carriers. The modulator consists of an Inverse Fast Fourier transform (IFFT) block. The output of the IFFT at each transmitter is the complex baseband modulated OFDM symbol in discrete time domain and is given by

**3.2.1 Channel: **

The channel is modeled by a tapped delay line with channel coefficients that are assumed to be slowly varying such that they are almost constant over the two transmission instants. IN this paper STBC-OFDM has been dealed with real orthogonal design.The channel frequency response for the *kth *subcarrier is

Where *h(p) *is the complex channel gain of the *pth *multipath component[12].

**3.2.2 Phase Noise: **

The phase noise ?(n) is modeled as a zero-mean continuous Brownian motion process with variance ? ? 2. The phase noise increments take the form of a Wiener process, with independent Gaussian increments.

**3.2.3 Received Signal:**

The time-domain received signals at the first and second transmission instances at the input to the FFT block are respectively given by

Where ? represents linear convolution, subscripts indicate antenna index, and superscripts indicate transmission instant. The complex Gaussian random variable *w(n) *represents the Additive White Gaussian Noise (AWGN) term with ? w 2= E[lw(n))|2], and ?(n) is the phase noise[12].

**3.2.4 Detection with Imperfect Channel Estimation: **

In the presence of imperfect channel estimation, we assume a channel estimation model such that the channel estimate *H’ *of the true channel *H *is given by

H0 H1 H2 H3 H0+ ?0 H1+ ?1 H2+?2 H3+?3

-H1* H0* -H3* H2* = -H1*+ ?1 * H0*+?0 * – H3*-?3* H2*+?2*

-H2* -H3* H0* H2* -H2*- ?2 -H3*- ?0 H0*+ ?0 * H2*+ ?0*

H3 -H2 -H1 H0 H3+ ?3 -H2-?2 -H1- ?1 H0+ ?0

Where ?0 , ?1 , ?2 and ?3 are the errors in the channel estimate from the first ,second, third and fourth transmit antennas respectively, and are modeled as independent zero-mean complex Gaussian random variables with variances 2??02 , 2??12 , 2??22 and 2??32 respectively.

**3.3 Variance: **

As the noise signal has both positive and negative amplitude, it is squared, then the mean has been taken, which is variance. We consider the variance of noise for calculation.

**3.3.1 Variance of Noise: **

The variance of the noise *W, *after some mathematical manipulations, has been given by,

**3.3.2 Variance of Channel Estimator Error: **

The variance of ? has been given by

**3.3.3 Variance of Inter Carrier Interference: **Similarly, the variance of the ICI term ?’ is given by

**CHAPTER 4 **

**CALCULATION AND SIMULATION PARAMETER**

**4.1 Calculation of SNR and BER:**

As shown in figure: 1 the transmitted OFDM signal for the mth symbol is given by the N point complex modulation sequence

Where n ranges from 0 to N+Ng-1

After passing through a rayleigh fading channel and LO, the received signal impaired by AWGN and PN can be modeled as-

Where

Where S(k), ?(k) and W(k) are the DFT responses of sm(n), ?m(n) and wm(n)

respectively.

Here Hm(k) is the transfer function of the rayleigh fading channel at the frequency of the kth carrier and wm(n) is the complex envelope of the AWGN with zero mean and variance ?2.

Assuming ?m(n) is very small so,

We can then write,

After DFT we get,

**4.1.1 Equations For SINR and BER:**

Finally SINR equation can be expressed by

This Signal To Interference plus Noise Ratio or SINR is in terms of CFO and the variance of ?2. This is with out timing jitter (?). The equation for SINR is including the timing jitter (?) is shown below-

Now the Bit Error Rate can be determined with the help of E0/N0 the equation below:

BER= 0.5*erfc(?(SINR))

**4.2 Calculation of SNR and BER: **

We present the bit error rate analysis for the case of 16QAM modulation using Gray code mapping for *(b1b2b3b4 ). *It is important to note that although the presentation is only for 16QAM, the following analysis is valid for all square QAM constellations. The conditional BER for bit *b1, *condition on *H0, H1, H2, H3 *is given by

+ ]

and for bit *b3 i*s given by

+

+

+ ]

From which the SNR ? is given by

* ( |*H0|2 + |H1|2 + |H3|2 )

* y = —————————— * 2* Eg/5*

* (6?2 + 6?2 + 6w2)*

It follows a Chi-square distribution with probability density function (PDF) given by

Due to the symmetry of square M-QAM constellations, the BER for the in-phase and quadrature bits are equal such that *Pe (b*1) = *Pe (b2) *and *Pe (b3)= Pe (b4 *). Therefore the average BER is obtained by averaging the conditional BER of b1

and *b3 *over the PDF of the SNR ?*. *The average BER is therefore given by

= * )

Similarly for 6:1 transmission system SNR ? is given by

* ( |*H0|2 + |H1|2 + |H3|2 + |H4|2 + |H5|2 )

* y = —————————————————— * 2* Eg/5*

* (6?2 + 6?2 + 6w2)*

And BER is giver by

=

*

**4.3 Simulation parameter :**

The OFDM system parameters and modulation schemes used for simulation are summarized in Table 1 and 2, respectively. Here the channel as considered for this paper is the Rayleigh fading channel. The bit error rate analysis for the case of 16QAM modulation using Gray code mapping for (b1b2b3b4). The input SNR has been taken as 20 db.

** Table 1: System and Channel Parameters (OFDM)**

No. of Sub carriers(N) | 64 |

Channel type | Rayleigh fading |

Input SNR | 20dB |

Channel attenuation/gain(?) | ? Ideal (1) |

** Table 2: System and Channel Parameters (STBC-OFDM)**

Parameters | Values |

??2 | 0.1 0.2 0.02 0.4 |

??2 | 0.1 0.04 0.06 |

Subcarriers (N) | 64 |

Channel Path Gains | -9.7 -0.9 -8.5 -0.5 |

Here, ??2 denotes variance of phase noise. And ??2 denotes imperfect channel estimation.

**CHAPTER 5**

**SIMULATION AND RESULT **

Figure 2: Graph shows SNR Vs Normalized form of CFO

As shown in the graph, X- axis denotes normalized CFO i.e. carrier frequency offset. And Y-axis denotes SNR. 3 plotting shows in figure for different variance of noise, as v=0.5, 0.7 and 0.9

Figure 3: Graph shows SNR Vs variance of Phase Noise

Above figure shows SNR Vs variance of Phase Noise. Here X-axis denotes variance of phase noise. And Y-axis denotes for SNR. 3 plotting shows for the different value of CFO, as e = 0.07, 0.1, and 0.2.

Figure 4: Graph shows SNR Vs Timing Jitter

Figure shows above is SNR Vs Timing Jitter, in which X-axis denotes for timing jitter, and Y-axis denotes SNR. 3 plotting shows for different values of variance of phase noise and carrier frequency offset , where v= 0.5 e = 0.07, when v= 0.7, then e=0.1 , and when v= 0.9, e= 0.2

Figure 5: Graph shows the BER Vs SNR (dB)

Figure shows above is the BER vs SNR. Here , X- axis denotes for SNR, and Y-axis denotes for BER.

Figure 6: Graph shows different plotting of BER Vs SNR of different

values of variance of Phase Noise

Figure shows above is the different plotting of BER Vs SNR of different values of variance of Phase Noise. Here X-axis denotes for SNR, Y-axis denotes for BER. And different values used for variance are v= 0.5, 0.7, 0.9. And for these values 3 plots have been got.

Figure 7: SNR Vs BER graph for 2:1 transmission system

Figure shows above is the SNR Vs BER graph for 2:1 transmission system. Here , transmitting antenna Tx = 2, and receiving antenna used Rx =1. X-axis used to denotes SNR, and Y –axis denotes BER.

Figure 8: SNR Vs BER graph for different value of noises (Tx=2 ; Rx=1)

Figure shows above is the SNR Vs BER graph for different values of noises. Here transmitting antenna Tx= 2, and receiving antenna Rx= 1. Different values of noise are ve0 = 0.3, 0.2, 0.1 and ve1 =0.04 for 3 plots.

Figure 9: SNR Vs BER for 4:1, 2:1, 1:1 transmission system

Figure shows above is the SNR Vs BER for 4:1, 2:1, 1:1 transmission system. Here X-axis denotes for SNR, And Y-axis denotes for BER. 3 curves have been shown. Red curve shows for 4:1, in which transmitting antenna =4, receiving antenna =1. Green curve shows for 2:1 system, i.e transmitting antenna =2, and receiving antenna = 1. And blue curve shows for 1:1 system, i.e transmitting antenna = 1, and receiving antenna = 1

Figure 10: SNR Vs BER graph for different values of noises (Tx=4 ; Rx=1)

Figure shows above is the SNR Vs BER graph for different values of noises. Here transmitting antenna Tx= 4, and receiving antenna = 1. X-axis denotes for SNR, and Y-axis denotes for BER. 3 plots have been shown for different values of noise, in which variance of phase noise are accordance with vh= 0.18, 0.22, 0.25, and emprfect channel estimation is ve = 0.06 for 3 plots.

Figure 11: SNR Vs BER for 6:1, 4:1, 2:1, 1:1 transmission system

Figure shows above is the SNR Vs BER for 6:1, 4:1, 2:1, 1:1 transmission system. X –axis denotes SNR, and Y-axis denotes BER. Here transmitting antenna Tx = 6, followed by 4, 2, 1 . And receiving antenna is 1

Figure 12: SNR Vs BER graph for different value of noises (Tx=6 ; Rx=1)

Figure sh X –axis denotes SNR, and Y-axis denotes BER. Here transmitting antenna Tx = 6, ows above is the SNR Vs BER graph for different value of noises (Tx=6 ; Rx=1). In this case variance of phase noise remain same, and imperfect channele estimation are = ve= 0.03, 0.04, 0.05

Figure 13: Rx Sensitivity for BER

In this figure Rx sensitivity for BER has been shown by graph. X-axis denotes no of transmitting antenna, and Y-axis denotes transmission power. Variance of phase noise are v1= 0.48, v2=0.50, v3=0.53

**CHAPTER 6**

** ANALYSIS AND RESULT **

**6.1 Non STBC-OFDM:**

In figure: 2 x-axis denotes the normalized CFO and y-axis denotes the SNR (dB). It is observed that when CFO is zero then SNR is high. And after that SNR is exponentially decreasing with the increasing of CFO.

In figure: 3 x-axis denotes the variance of Phase Noise and y-axis denotes the SNR (dB). It is shown that increasing the phase noise will decrease the SNR. There are three plotting for three different value of CFO (e). The curve is decreasing if the value of CFO is increasing.

Figure: 4 shows the SNR Vs Timinig Jitter curve. It is observed that if the delay or the timing jitter increases then the signal strength decreased. For this the SNR is also decreasing. There are plotting shows different graphs for different values of phase noise and CFO.

Figure: 5 shows the SNR Vs BER graph. With the increase of SNR, the BER is decreased.

And Figure: 6 shows the same graph or different value of noise. From the graph it has been seen that for v=0.5, we get highest SNR curve. And for this highest SNR value the BER is decreasing fast compared to the other value of v and corresponding SNR.

** 6.2 STBC-OFDM **

Figure: 7 shows the SNR Vs BER graph for 2:1 transmission system. With the increased SNR, the BER is decreased.

Figure: 8 shows the same graph for different value of noises.Here SNR is highest when ve =0.3

Then figure: 9 shows the graph of SNR Vs BER for 4:1 transmission system along with 2:1 and 1:1 system. It is seen that 4:1 graph is closer to the two axes than the others. It means that the BER is decreasing fast when the number of antennas increases.

Figure: 10 shows the SNR Vs BER graph of 4:1 for different value of noises. Here , SNR is highest when phase noise is vh0 =0.18, and imperfect channel estimator ve0= 0.06

Then figure: 11 shows the performance of 6:1 along with 4:1, 2:1, 1:1 transmission system.

Figure: 12 shows the SNR Vs BER graph of 6:1 for different value of noise.

It is observed that increasing the diversity gain will improve the performance of the system.

From the figure: 13 receiver sensitivity graphs are plotted for different value of noises. It shows that transmission power decreases when number of antennas increase. The graph is shown in figure: 13. Another analysis can be drawn from the graph shown in figure: 13 is that for a fixed value of transmission power the noise term can be reduced by increasing the number of antennas.

** CHAPTER 7**

**CONCLUSION AND RECOMMENDATION**

In today’s modern world, the interconnection and interfacing of differing technologies are becoming commonplace.. In this paper, performance evaluation of an OFDM wireless

communication system has been studied by using STBC-OFDM taking normalized CFO

and variance of phase noise under consideration in Rayleigh fading channel.The equations for SNR and BER using 4:1 and 6:1 transmission system have been derived. The effects of noise, carrier interference and channel estimator error on the system are analyzed. The SNR Vs BER curve shows that increasing the diversity gain improve the performance of the system. Receiver sensitivity graph shows the power efficiency characteristic of the system.

It is recommended that, we need better performance of the wireless system. And for this SNR should be high and BER should be small. In this paper , this analysis has been done. It also recommended that, with the decreasing of timming jitter, variance of noise, and carrier frequency offset , performance of the system will be better.

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