# Channel Coding And Interleaving Ii Computer Science Essay

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OFDM is always used in conjunction with channel coding i.e. for forward error correction, and uses for time interleaving or frequency.

Frequency selective channel conditions such as fading are based on Frequency (subcarrier) interleaving resistance. For example, If frequency interleaving ensures that the bit errors a part of the channel bandwidth fades, that would result the subcarriers in faded part of bandwidth are spread out in the bit-stream rather than being concentrated. Similarly, time interleaving confirms that bits are originally close together in the bit-stream are transmitted far apart in time, thus mitigating against severe fading as would happen when travelling at high speed.

However, time interleaving is of little benefit in slowly fading channels, such as for frequency interleaving and stationary reception, offers slight to no benefit for narrowband channels that suffer from flat-fading where the whole channel bandwidth fades at the same time.

The reason for using the interleaving on OFDM is to spread out the errors in the bit-stream that are offered to the error correction decoder, because when such decoders are found with a high concentration of errors the decoders are unable to correct all the bit errors, and a burst of uncorrected errors take place. A relative design of audio data encoding makes compact disc playback robust.

OFDM-based systems uses a classical type of error correction coding is convolutional coding, often concatenated with Reed-Solomon coding. Usually, addition of interleaving with frequency and time as mentioned above coding is implemented in between the two layers. Outer error correction code is based on the observation which choices for Reed-Solomon coding and the Viterbi decoder is used for inner convolutional decoding produces short errors bursts when there is a high concentration of errors, and Reed-Solomon codes are inherently well-suited to correcting bursts of errors.

In existing systems however, they adopt near-optimal type of error correction codes that uses the turbo decoding principle, where the decoder iterates towards the desired solution. Examples of such error correction coding types include LDPC codes and turbo codes, which perform close to the Shannon limit for the Additive White Gaussian Noise channel. To improve upon an error floor inherent to these codes at high signal-to-noise ratios, Some systems have implemented these codes have concatenated them with either BCH codes on the DVB-S2 system or Reed-Solomon for example on the MediaFLO system

## Adaptive transmission

The flexibility to severe conditions of channel can be further information enhanced about the channel is sent over a return-channel. Based on this feedback information, adaptive modulation, channel coding and power allocation may be applied individually to each sub-carrier or across all sub-carriers. In the latter case, if a particular range of frequencies suffers from interference or attenuation, the carriers within that range can be disabled or made to run slower by applying more robust modulation or error coding to those sub-carriers.

The term discrete multitone modulation denotes OFDM based communication systems by means of bit-loading that adapt the transmission to the channel conditions individually for each sub-carrier, Examples are ADSL and VDSL.

The variations of upstream and downstream speeds can be allocated for each purpose with more or less carriers. There are different forms of features used in real time like rate-adaptive DSL, so whichever subscriber needs the bitrate is adapted to the co-channel interference and bandwidth is allocated.

## OFDM extended with multiple access

OFDM is used for exchanging the one bit data stream using one sequence of OFDM symbols over a single communication channel. Hence it is considered as a digital modulation technique and not a multi-user channel access method. However, using frequency, time or coding parting of users OFDM can be joined with multiple accesses.

Frequency-division multiple access is achieved by assigning different OFDM sub-channels to different users in Orthogonal Frequency Division Multiple Access (OFDMA). It also supports the differentiated quality of service by allocating to number of subcarriers to different users. The similar type of model is followed by CDMA. By using this model Media Access Control or complex scheduling of packet can be avoided. OFDMA is used in:

Wireless MAN standard(IEEE 802.16) commonly preferred in mobility mode, commonly WiMAX

The IEEE 802.20 mobile Wireless MAN standard, commonly used as MBWA,

It is also used in 3GPP long term evolution in mobile broadband download link for fourth generation.

OFDMA is a method to access for IEEE 802.22 Wireless Regional Area Networks. The main aim of the project is to design the first cognitive radio based standard in operating the VHF low UHF spectrum.

Multi-carrier code division multiple access (MC-CDMA), also known as OFDM-CDMA, OFDM is combined with CDMA is to spread out the spectrum for separation of coding and users. The frequency channel allocation planning of frequency is simplified and complex dynamic channel are avoided.

## Space diversity

The wide range area broadcasting based on OFDM have a benefit of receiving signals from a number of spatially dispersed transmitters since transmitters destructively interfere with each other on limited number of subcarriers, which generally supports the coverage over a wide area. This is very useful in many countries, as it allows to operate the national SFNs, which allows to send many transmitters simultaneously over the same channel frequency. So the utilization of multi frequency broadcast networks where program content is simulated on different carrier frequencies is less conventional then SFNs. As a result SFNs in a diversity gain receivers located in midway between the transmitters. Due to the increase of received signal strength on over all averaged subcarriers, the coverage area is increased and the outage probability decreased in comparison to an MFN.

Even though the guard interval contains redundant data, which reduces the capacity, of some OFDM-based systems, such as the broadcasting systems use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN, and longer guard intervals allow larger SFN cell-sizes. A rule of thumb shows the maximum distance between transmitters in an SFN is equal to the distance a signal travels during the guard interval. For example, a guard interval of 200 microseconds would allow transmitters to be spaced 60Â km apart.

A single frequency network is a form of transmitter macro diversity. The concept can be further utilized in dynamic single-frequency networks (DSFN), where the grouping in SFN is changed from timeslot to timeslot. OFDM may be combined with other forms of space diversity, for example antenna arrays and MIMO channels which is done in the IEEE 802.11n Wireless LAN standard.

## Linear transmitter power amplifier

## In OFDM signal the independent phases of subcarriers are often combined constructively because of high peak to average power ratio. While handling of high peak to average power ratio it requires:

## An digital to analogue converter is used in transmitter which is of high resolution.

## An analogue to digital converter is obtained in receiver which is of high resolution.

## A linear signal chain.

Intermodulation distortion occurs due to any non-linearity in the signal chain causes

noise floor

inter-carrier interference

Generates false out-of-band radiation.

The requirement of linearity is demanding because the transmitter RF output circuitry amplifiers are designed to be nonlinear in order to reduce the power consumption. In present system OFDM shows small amount of peak clipping which allows to control PAPR judicious trade off against above significances. Though transmitter output filter requires to reduce out of band levels to legal levels represents an effect of restoring peak levels that are clipped, so clipping cannot be an effective way to reduce PAPR. While the OFDM spectral efficiency is attractive towards both terrestrial and space communications, so high PAPR requirements have limited OFDM applications to terrestrial systems.

## Idealized system model

A simple idealized OFDM system model suitable for describing a time-invariant AWGN channel.

## Transmitter

OFDM transmitter ideal.png

An OFDM carrier signal is the addition of number of orthogonal subcarriers, by which data on each baseband subcarriers being separately modulated using quadrature amplitude modulation or phase shift keying. To modulate a main RF carrier the compound of baseband signal is used. A serial stream of binary digits is denoted as \scriptstyle s[n]. The N parallel streams are first de multiplexed by inverse multiplexing and each symbol in a stream uses a modulation constellation like QAM,PSK etc.. The constellations which are different carry a higher bit rate rather than others.

Each set of symbols in inverse FFT can be calculated by using a set of complex domain samples. Then samples are quadrature mixed in standard way to passband. By this way real and imaginary components are converted first into analogue domain using digital-to-analogue converters. These signals used to modulate as sin or cosine waves at carrier frequency, fc respectively. At the end signals are summed up to give a transmission signal \scriptstyle s(t).

## Receiver

OFDM receiver ideal.png

The receiver takes the signal \scriptstyle r(t), which uses sine and cosine waves as carrier frequency is then quadrature-mixed down to baseband. This makes the signal to center on 2fc, because they reject the low pass filter. The signals using analog to digital converters are sampled and digitized. Finally to convert back to frequency domain forward FFT is utilized. Then we find a return stream as N parallel, in which each binary system is converted using an appropriate symbol detector. Later on streams are streams are recombine into a serial stream called \scriptstyle {\hat s}[n] which is used to estimate the original binary stream at transmitter.

## Mathematical description:

## Using M alternative symbols each subcarrier is modulated with the help of N subcarriers, the alphabet symbol of OFDM contains of \scriptstyle M^N combined symbols.

## The OFDM signal base on low pass equivalent can be determined as:

## \ \nu(t)=\sum_{k=0}^{N-1}X_k e^{j2\pi kt/T}, \quad 0\le t<T,

Where N denotes the number of sub carriers,

T represents as symbol time of OFDM.

are data symbols.

The spacing of a subcarrier\scriptstyle \frac{1}{T} makes orthogonal on each symbol period; this property detemines as:

\begin{align} &\frac{1}{T}\int_0^{T}\left(e^{-j2\pi k_1t/T}\right)^* \left(e^{j2\pi k_2t/T}\right)dt \\ = &\frac{1}{T}\int_0^{T}e^{j2\pi (k_2-k_1)t/T}dt = \delta_{k_1k_2} \end{align}

where \scriptstyle\delta\,is the Kronecker delta.

\scriptstyle (\cdot)^*is denoted as the complex conjugate operator

To reduce the interface of each symbol in multipath fading channels, where Tg is the guard interval inserted in OFDM block. During this interval, the signal in the interval \scriptstyle (T-T_\mathrm{g}) \,\le\, t \,<\, T equals to a cyclic prefix is transmitted such that the signal in the interval \scriptstyle -T_\mathrm{g} \,\le\, t \,<\, 0. The OFDM signal with represents as:

\ \nu(t)=\sum_{k=0}^{N-1}X_ke^{j2\pi kt/T}, \quad -T_\mathrm{g}\le t < T

The value can be either a real or complex in low pass signal. If the value is real in low pass signal typically these are transmitted at baseband like wire line applications such as DSL approach. If the value is complex then the transmitted signal is up converted to carrier frequency fc which is used for wireless applications. In general, the transmitted signal can be represented as:

\begin{align} s(t) & = \Re\left\{\nu(t) e^{j2\pi f_c t}\right\} \\ & = \sum_{k=0}^{N-1}|X_k|\cos\left(2\pi [f_c + k/T]t + \arg[X_k]\right) \end{align}