Ofdm Problems 4a4d24

c c c As seen above the fact to have several carriers is actually advantageous whenever they are mathematically orthogonal. So carriers orthogonality is a constrain that can leads to a wrong operation of OFDM systems if not respected. The orthogonality is provided by IFFT that a numerical manipulation, an error of computation could change lightly spacing between to consecutive carriers and break the orthogonality of the whole system. In this case OFDM loses all its efficiency, because the notion of orthogonality is an absolute one.

One of the crucial problems in the receiver is to sample the incoming signal correctly. If the wrong sequence of samples is processed, the Fast Fourier Transform shall not correctly recover the received data on the carriers. The problem is more embarrassing when the receiver is switched on. There is therefore a need for acquiring timing lock. If the signal transmitted is really time domain periodic, as required for the FFT to be correctly applied, then the effect of the time displacement is to modify the phase of all carriers by a known amount. This is due to the time shift theorem in convolutional transform theory.

Symbols Time Sampling

Good synchronization Bad synchronization

However, the signal is not really repetitive, we have cheated and performed the mathematical transform as if it were repetitive, but then chosen different symbols and transmitted them one after the other. The effect of the time shift would then be not only to add the phase shift referred to above, but also to add some intersymbol interference with adjacent symbols. This interference could hardly degrade reception. To avoid these problems, we decide to transmit more than one complete sequence of time samples in order to increase the tolerance in timing. It¶s an additional data guard interval. It is built by repeating a set as long as channel memory of last samples taken in the original sequence. The longer the guard interval, the more rugged the system, but guard interval does not carry any useful information and its transmission leads to a penalty of power. One technique used to obtain good synchronization is to add between each OFDM symbol a null (zero samples) symbol. This technique is used in DAB for time synchronization.

ÿ hen the phase of different subcarriers add up to form large peaks, an important complication comes in OFDM systems. This problem is called Peak Average Power Ratio (PAPR) and it is defined for each OFDM signal on a time interval [n, n+Ts] by the following formula:

For continuous signals max ( )

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For sampled signals è

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In OFDM systems PAPR can have very high values for certain input sets of sample ‰ and overload non-linear characteristics of systems, causing intermodulations among different carriers and undesired out-of-band radiation. Another main drawback of PAPR can be seen as quantization noise domination towards the performance of system. This domination can be excited by avoiding the clipping effect of the maximum level of the Digital to Analog Converter (DAC) that is set too high. Various techniques are proposed to reduce PAPR in OFDM signals, but that reduction is not obvious because PAPR and SNR are closely linked. e will not expound those techniques in this paper, they can be found in reference [14].

â !!!""c ## hen transmitted signals have high PAPRs, amplifiers may produce ³clipping´. In some way, clipping can be regarded as peaks of the input signal being simply cut-off by amplifiers. Consequences of clipping are out-of-band radiation and inter symbol interference between subcarriers. In order to avoid these undesired effects that reduce OFDM performances, one has either to use amplifiers with dynamic range, or try to reduce PAPR. The first alternative is expensive, the second one is more often used.

## At the receiver, a local oscillator can add phase noise to an OFDM signal, for example. The phase noise could so have two effects those are: Common Phase

Vrror (V) due to a rotation of the signal constellation and, Inter Carrier Interference (ICI), similar to additive Gaussian noise. The BBC R&D have made analysis of the effects of phase noise on an OFDM signal, this analysis shows that V arises simultaneously on all carriers. Indeed, the signal constellation within a given symbol is subject to the same rotation for all carriers and this effect can be corrected by using reference information within the same symbol. Unfortunately, ICI is more difficult to overcome, due to the additive noise, which is different for all carriers. This difference can be interpreted as a loss of orthogonality. U $%

An OFDM system can be subject to two types of frequency error. They are Frequency offset (as might be caused by the tolerance of the local oscillator frequency) and, Vrror in the receiver master clock frequency (which will cause the spacing of the demodulating carriers to be different from those transmitted). Before to find solutions to those problems, the system designer needs to determine how much residual frequency error is permissible, and understand exactly how errors affect the received signal.

Both of these error situations have been analyzed so, a frequency offset affects most carriers equally, with the very edge carrier less affected. ICI resulting from a fixed absolute frequency offset increases with the number of carriers, if the system bandwidth is kept constant. About error in the receiver clock frequency, in absence of frequency offset, it affects carriers unequally (the center carrier suffers a little while the worst affected carrier lies close to, but not at, the edge).