Orthogonal Frequency Division Multiplexing-OFDM

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Introduction of Orthogonal Frequency-Division Multiplexing (OFDM):
Orthogonal frequency-division multiplexing (OFDM) is a method of digital modulation in which a signal is split into several narrowband channels at different frequencies. The technology was first conceived in the 1960s and 1970s during research into minimizing interference among channels near each other in frequency. Now, it is becoming the chosen modulation techniques because it can provide large data rates with sufficient robustness to radio channel impairments. This modulation technique is widely used in a number of communication systems such as IEEE 802.11a/b/g/n, IEEE 802.16, HIPERLAN/2, ADSL, Digital Audio Broadcasting (DAB), and Digital Video Broadcasting (DVB). The spread spectrum technique of OFDM distributes the data over a large number of carriers that are spaced apart at precise frequencies. This spacing provides the ?orthogonally? in this technique which prevents the demodulators from seeing frequencies other than their own, so bandwidth efficiency increase.
Figure 2.1 shows an illustration of the multicarrier transmission in OFDM system.

Principles of OFDM:
The basic principle of OFDM is Channel bandwidth is divided into multiple subchannels to reduce ISI and frequency-selective fading. OFDM is a block transmission technique. In the baseband, complex-valued data symbols modulate a large number of tightly grouped carrier waveforms. The transmitted OFDM signal multiplexes several low-rate data streams ? each data stream is associated with a given subcarrier. The main advantage of this concept in a radio environment is that each of the data streams experiences an almost flat fading channel. In slowly fading channels, the intersymbol interference (ISI) and intercarrier interference (ICI) within an OFDM symbol can be avoided with a small loss of transmission energy using the concept of a cyclic prefix.

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Signal characteristics:
An OFDM signal consists of orthogonal subcarriers modulated by parallel data streams. Each baseband subcarrier is of the form
, (1)
where is the frequency of the th subcarrier. One baseband OFDM symbol (without a cyclic prefix) multiplexes modulated subcarriers:
where is the th complex data symbol (typically taken from a PSK or QAM symbol constellation) and is the length of the OFDM symbol. The subcarrier frequencies are equally spaced
which makes the subcarriers on orthogonal. The signal (2) separates data symbols in frequency by overlapping subcarriers, thus using the available spectrum in an efficient way. The left half of Figure 1 illustrates the quadrature component of some of the subcarriers of an OFDM symbol. The right half of Figure 1 illustrates how the subcarriers are packed in the frequency domain.

Figure 1

Figure 2 shows time and frequency characteristics of an OFDM signal with 1024 subcarriers. As the OFDM signal is the sum of a large number of independent, identically distributed components its amplitude distribution becomes approximately Gaussian due to the central limit theorem. Therefore, it suffers from large peak-to-average power ratios. In addition, OFDM symbols of the form (2) can have large out-of-band power as illustrated in Figure 2. Large peak-to-average power ratios also cause out-of-band emission because of amplifier non-linearities. Section 3 discusses ways to deal with high peak-to-average power ratios and out-of-band power.

Figure 2

The OFDM symbol (2) could typically be received using a bank of matched filters. However, an alternative demodulation is used in practice. T-spaced sampling of the in-phase and quadrature components of the OFDM symbol yields (ignoring channel impairments such as additive noise or dispersion)
, (4)
which is the inverse discrete Fourier transform (IDFT) of the constellation symbols . Accordingly, the sampled data is demodulated with a DFT. This is one of the key properties of OFDM, first proposed by Weinstein and Ebert, [1971]. The DFT, typically implemented with an FFT, actually realizes a sampled matched-filter receiver in systems without a cyclic prefix.

OFDM with a cyclic prefix:
Two difficulties arise when the signal in is transmitted over a dispersive channel. One difficulty is that channel dispersion destroys the orthogonality between subcarriers and causes intercarrier interference (ICI). In addition, a system may transmit multiple OFDM symbols in a series so that a dispersive channel causes intersymbol interference (ISI) between successive OFDM symbols. The insertion of a silent guard period between successive OFDM symbols would avoid ISI in a dispersive environment but it does not avoid the loss of the subcarrier orthogonality. This problem is solved with the introduction of a cyclic prefix. This cyclic prefix both preserves the orthogonality of the subcarriers and prevents ISI between successive OFDM symbols. Therefore, equalization at the receiver is very simple. This often motivates the use of OFDM in wireless systems. The cyclic prefix with guard interval is illustrated in Figure 3.

Figure 3: The Cyclic Prefix
Between consecutive OFDM signals a guard period is inserted that contains a cyclic extension of the OFDM symbol. The cyclic prefix is a copy of the last portion of the data symbol which is appended in front of the data symbol during the guard interval. The ISI as it occurs if the tail of one symbol distorts the head of the next symbol when passing through the multipath fading channel, can be prevented from occurring with the help of cyclic prefix. As a copy of the last part of the OFDM symbol is appended to the front of the transmitted symbol which makes it periodic and plays a decisive role in identifying the frames correctly so as to avoid ISI and ICI. The guard interval allows time for the multipath signals from the previous symbol to die away before the information from the current symbol is gathered. Using this cyclic extended symbol, the samples required for performing the FFT (to decode the symbol) can be taken anywhere over the length of the cyclic prefix. This provides multipath immunity as well as symbol time synchronization tolerance.
The project used 16 last samples of the frame which were copied and placed at the beginning of the frame. The total numbers of bits after addition was 80 bits. The addition of these bits enables synchronization as the bits were used to detect the beginning and end of each frame.

Quantization is the process of converting a continuous range of values into a finite range of discreet values. This is a function of analog-to-digital converters, which create a series of digital values to represent the original analog signal. The bit depth (number of bits available) determines the accuracy and quality of the quantized value. A quantizer that uses n bits can have M = 2n discrete amplitude levels.
(There are more things to write in quantization)

There are mainly two types of algorithm companding. One is A-law algorithm and the other is ?-law algorithm. In this project we use the A-law algorithm. A-law algorithm is a standard companding algorithm, used in European digital communications systems to optimize, i.e., modify, the dynamic range of an analog signal for digitizing.

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