Ofdm why fft

Figure 1. OFDM system model. So this algorithm can compute N-point FFT in cycles. In case of N-data points expressed as power of 4 v , we can employ radix-4 algorithm instead of radix-2 algorithm for more efficient estimation.

So this algorithm results in log 2 N complex multiplications and log 2 N complex additions. It can be implemented either by various level of approximation or replacing the FFT exactly with floating point accuracy. G-Matrix is a suitable tool in this regard with different quantization level concept.

Fourier matrix F N is normalized by in the G-matrix. Important properties of G-matrix are outlined as follows [8,9]:. Row-gain is unity for the Fourier matrix, whereas is not necessarily unity.

This causes non-uniform power spectral density in the transmitted signal and non-uniform noise power in the received demodulated signal. This is the main disadvantage in this G-matrix design. In order to compare the computational complexities among the different Fourier transforms on OFDM, the calculations based on the OFDM block sizes have been performed which are given in Table 1. In case of multiplication computation for VFFT, the speed improvement factor is as high as That indicates the multiplication complexity is decreased by This is due to the computational savings done by VFFT with complexity reduced to only of the order of N.

This rate of complexity reduction in terms multiplication would be a huge factor for OFDM systems to meet the demand of multi-user high data traffic environment. In Table 2 , the comparison of the different FFT algorithms evolved has been shown. We can see that higher radix FFT algorithms reduces the number of both multiplications and additions and as such can give less complexity for OFDM calculations for larger FFT blocks [10,11].

This less complexity leads to more robust and effective multicarrier system design for OFDM. It also assures optimum performance in terms of high speed data processing for communication systems using OFDM technique.

VFFT algorithm surely can save a lot of computational power but it has been often effected by a slight degradation of 1dB bit error rate BER performance [8,12]. Overall, FFT algorithms provide the different. Table 1. But, suppose we wish to set any particular one of those vectors to zero. That's probably the catch. When it comes time to transmit each vector by means of regular quadrature carrier QM - quadrature modulation technique - where the real part of the vector modulates a carrier, while the imaginary part modulates a 'quadrature' carrier - then we don't want to be transmitting a 'zero' vector - which would mean transmitting no sinusoidal carriers at all ie.

This is where IFFT might help, as the IFFT of a vector sequence where some of those vectors are set to zero results in another sequence, where all the vectors in that new sequence from the IFFT contains no vectors that are zero. Then maybe at least all the vectors are not 'zero' - which may go well with quadrature carrier transmissions. Naturally, the cyclic prefix needs to be added after this, which just needs to be done for dealing with multi-path channels.

So adding the cyclic prefix simply results in a longer time-domain sequence. A sequence of vectors that is ie. We can transmit those vectors by means of quadrature carrier modulation. The time-domain waveform that is actually transmitted has really nothing to do with physical sub-carriers at all. The 'sub-carriers' actually refer to the original virtual frequency-domain vectors which are only 'on paper'.

It is unlike 'classical' OFDM. Then - assuming that the system is designed so that the receiver is able to synchronise with the incoming transmission, and is able to recover the symbols that are embedded in the incoming transmission. And yes synchronisation techniques, and channel estimation techniques, and training codeword symbols etc may all be needed to successfully recover the time-domain vector sequence.

Also noting that cyclic prefix was used to handle multi-path effects. Recovering the time domain sequence and removing cyclic prefix then allows the reverse procedure to be applied. The reverse of IFFT Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 4 years, 7 months ago.

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Add a comment. Active Oldest Votes. Improve this answer. I think the system still works perfectly, doesn't it? When you say "The Cyclic Prefix converts the linear convolution into a circular convolution".

However, the combination of many subcarriers enables data rates similar to conventional single-carrier modulation schemes within equivalent bandwidths. In FDM different streams of information are mapped onto separate parallel frequency channels. Each FDM channel is separated from the others by a frequency guard band to reduce interference between adjacent channels. A guard interval is added to each symbol to minimize the channel delay spread and intersymbol interference.

The following figure illustrates the main concepts of an OFDM signal and the inter-relationship between the frequency and time domains. In the frequency domain, multiple adjacent tones or subcarriers are each independently modulated with complex data. Then in the time domain, guard intervals are inserted between each of the symbols to prevent inter-symbol interference at the receiver caused by multi-path delay spread in the radio channel. Multiple symbols can be concatenated to create the final OFDM burst signal.

We will use a simple analog based implementation to show the basic principles of generating an OFDM signal. Each subcarrier transmits one bit of information N bits total as indicated by its presence or absence in the output spectrum.

The frequency of each subcarrier is selected to form an orthogonal signal set. These frequencies are also known at the receiver for signal recovery. Note that the output is updated at a periodic interval T that forms the symbol period. To maintain orthogonality, T must be the reciprocal of the subcarrier spacing. In the frequency domain, each transmitted subcarrier results in a sinc function spectrum with side lobes that produce overlapping spectra between subcarriers, see "OFDM Signal Frequency Spectra" figure below.