In general for all integers n and m , sin mx , cos mx , cos nx , sin nx are all orthogonal to each other.

These frequencies are called harmonics. The orthogonality allows simultaneous transmission of many sub-carriers in a tight frequency space without interference from each other. This is similar to CDMA, where codes are used to make data sequences independent also orthogonal which allows many independent users to transmit in same space successfully. Suppose a bandwidth goes from frequency say a to b , then this can be subdivided into a frequency of equal spaces.

In frequency space the modulated carriers would look like this. The frequencies a and bcan be anything, integer or non-integer since no relationship is implied between a and b same is true of the carrier center frequencies which are based on frequencies that do not have any special relationship to each other. If frequency[Abbildung in dieser Leseprobe nicht enthalten]and[Abbildung in dieser Leseprobe nicht enthalten]were such that for any n , an integer, the following holds.

In this case, these carriers are orthogonal to each other. Hence when added together, they do not provide interference with each other. In FDM, frequenciesare not orthogonal to each other, so it suffers interference from neighbor carriers. To provide adjacent channel interference protection, signals are moved further apart.

It is the guard band that keeps interference under control. To do so, it performs the signal processing operations as shown in Figure 1. Signal processing is repetitive in a few different time intervals. Resource assignment takes place in transmit time intervals TTIs. The TTI is further divided into time intervals referred to as blocks. A block is the time used to transmit all of subcarriers once. Next,the transmitter groups the modulation symbols,[Abbildung in dieser Leseprobe nicht enthalten] into blocks, each containing N symbols.

As in OFDMA, a typical value of M is subcarriers and [Abbildung in dieser Leseprobe nicht enthalten]is an integer submultiple of[Abbildung in dieser Leseprobe nicht enthalten]is the bandwidth expansion factor of the symbol sequence. The transmitter performs two other signal processing operations prior to transmission. It inserts a set of symbols referred to as a cyclic prefix CP in order to provide a guard time to prevent inter-block interference IBI due to multipath propagation. The transmitter also performs a linear filtering operation referred to as pulse shaping in order to reduce out-of- band signal energy.

Thus, transmitted data propagating through the channel can be modelled as a circular convolution between the channel impulse response and the transmitted data block, which in the frequency domain is a point wise multiplication of the DFT frequency samples. Then, to remove the channel distortion,the DFT of the received signal can simply be divided by the DFT of the channel impulse response.

Inter-Symbol Interference ISI is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable. It is usually caused by multipath propagation or the inherent non - linear frequency response of a channel causing successive symbols to blur together. The presence of ISI in the system introduces error in the decision device at the receiver output.

Therefore, in the design of the transmitting and receiving filters, the objective is to minimize the effects of ISI and thereby deliver the digital data to its destination with the smallest possibleerror rate. Presence of Doppler shifts and frequency and phase offsets in an OFDM system causes loss in orthogonality of the sub-carriers. As a result, interference is observed between sub-carriers. This phenomenon is known as inter - carrier interference ICI. Cyclic Prefix can be best understood with the following example.

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- PhD Thesis on OFDM?
- Thesis Abstract | Dissertation Abstracts Thesis Library - Papr Reduction Tecniques In Ofdm System.

Suppose you are driving a car in rain, and the car in front of you splashes a bunch of water on you. What do you do? If we compare the reach of splash to delay spread of a splashed signal then we have a better picture of the phenomena and how to avoid it. Increasing the distance avoid splashesfrom front car. The time elapsed to reach the splash is same as the delay spread of a signal. In composite, these splashes are noise and affect the beginning of the next symbol.

To mitigate this noise at the front of the symbol, symbol is further moved away from the region of delay spread as shown below. A little bit of blank space has been added between symbols to catch the delay spread. But signalscannot have blank spaces. This will not work for the hardware which likes to crank out signals continuously. So there should be something here.

### Papr Reduction In Ofdm Thesis

Suppose the symbol run longer as the first choice. Suppose the symbol is extended into the empty space, so that the actual symbol is more than one cycle. But now the start of the symbol falls into the danger zone, and this start is the most important thing about the symbol because the slicer needs it to take a decision about the bit. The start of the symbol is undesired to fall in this region, so the symbol is slided backwards, so that the start of the original symbol lands at the outside of this zone.

The start of the symbol should be out of the delay spread zone so that it will not corrupt. The signal should be started at the new boundary so that the actual symbol falls outside this zone. Therefore symbol is slided to start at the edge of the delay spread time and then the guard space is filled with a copy of tail end of the symbol.

Then, the symbol is extended to 1.

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## Analysis and reduction of PAPR effect using linear coding in OFDM system

To do this, copy the back of the symbol is taken and glued in the front. In reality, the symbol source is continuous, so the starting phase is adjusted ,making the symbol period longer. This procedure is called adding a cyclic prefix. We add the prefix just after doing the IFFT.

When the signal arrives at the receiver, this cyclic prefix is removed, to get back the original periodic signal. After doing FFT the symbols are recovered on each carrier. The Cyclic Prefix or Guard Interval is a periodic extension of the last part of an OFDM symbol that is added to the front of the symbol in the transmitter, and is removed at the receiver before demodulation. The cyclic prefix acts as a guard interval. It eliminates the inter-symbol interference from the previous symbol.

### Pulse shaping approach to PAPR reduction for OFDM communication systems

It acts as a repetition of the end of the symbol thus allowing the linear convolution of a frequency-selective multipath channel to be modeled as circular convolution which in turn maybe transformed to the frequency domain using a discrete fourier transform. This approach allows for simple frequency-domain processing such as channel estimation and equalization.

Consider a data sequence[Abbildung in dieser Leseprobe nicht enthalten] where each[Abbildung in dieser Leseprobe nicht enthalten] is a complex symbol. Suppose we perform an IDFT on the sequence [Abbildung in dieser Leseprobe nicht enthalten] the factor 2 is used purely for scaling purposes , we get a result of [Abbildung in dieser Leseprobe nicht enthalten]complex numbers[Abbildung in dieser Leseprobe nicht enthalten]as:.

Passing the real part of the symbol sequence represented by equation 1. By using adequate channel coding and interleaving, the symbols lost can be recovered, due to the frequency selectivity of the channel. Presence of large number of independently modulated sub-carriers in an OFDM system the peak value of the system, can be very high as compared to the average of the whole system. The application of OFDM to high data rate mobile communication system is being investigated by many researchers.

## Papr ofdm dsplog

Rashedul Islam Lecturer, Dept. Hence it provides better BER performance. Singh, PhD. One major drawback of OFDM systems is the high peak to average power ratio PAPR which leads to power inefficiency and signal distortion with practical power amplifiers used at the transmitter. Its superiority relies on the fact that information can be split in large amount of frequencies. The Architecture of the Viterbi Decoder. Nurul Islam3Md.

OFDM have been extensively applied in wireless communication systems.