OFDM is a special case of multicarrier transmission, where a single data stream is transmitted over a number of low data rate subcarriers. OFDM can be thought of as a hybrid of multicarrier modulation (MCM) and frequency shift keying (FSK) modulation scheme. The principle of MCM is to transmit data by dividing the data stream into several parallel data streams and modulate each of these data streams onto individual subcarriers. FSK modulation is a technique whereby data is transmitted on one subcarrier from a set of orthogonal subcarriers in symbol duration.
Orthogonality between these subcarriers is achieved by separating these subcarriers
by an integer multiples of the inverse of symbol duration of the parallel data streams.
With the OFDM technique used, all orthogonal subcarriers are transmitted simultaneously. In other words, the entire allocated channel is occupied through the aggregated sum of the narrow orthogonal subbands.
The main reason to use OFDM systems is to increase the robustness against frequency-selective fading or narrowband interference. In a single carrier system, a single fade or interference can cause the entire link fail, but in a multicarrier system, only a small amount of subcarriers will be affected. Then the error correction coding techniques can be used to correct errors. The equivalent complex baseband OFDM signal can be expressed as
2 1 1
where Nc is the number of subcarriers, T is the symbol duration, dk is the transmitted subsymbol (M-PSK or M-QAM), φk( )t =ej2πf tk / T is the kth subcarrier with the frequency /fk =k T , and uT(t) is the time windowing function. Using the correlator-based OFDM demodulator, the output of the jth branch can be presented as
By sampling x(t) with the sampling period Td=T/Nc, the discrete time signal xn
can be expressed as
Note that xn is the Inverse Fast Fourier Transform (IFFT) output of the N input data subsymbols. Similarly, the output of the jth branch can also be presented in the digital form
In theory, the orthogonality of subcarriers in OFDM systems can be maintained and individual subcarriers can be completely separated by the Fast Fourier Transform (FFT) at the receiver when there are no intersymbol interference (ISI) and intercarrier interference (ICI) introduced by transmission channel distortions.
However, it is impossible to obtain these conditions in practice. In order to eliminate ISI completely, a guard interval is imposed into each OFDM symbol. The guard interval is chosen larger than the expected delay spread, such that the multipath from one symbol cannot interfere with the next symbol. The guard interval can consist of no signals at all. However, the effect of ICI would arise in that case due to the loss of orthogonality between subcarriers. To eliminate ICI, the OFDM symbol is cyclically extended in the guard interval to introduce cyclic prefix (CP) as shown in Figures 2.1 and 2.2. This ensures that delayed replicas of the OFDM symbol always have an integer number of cycles within the FFT interval, as long as the delay is smaller than the guard interval. As a result, the delayed multipath signals which are smaller than the guard interval will not cause ICI. The complete OFDM signal with CP is given by
where Ncp is the number of samples in CP. Due to CP, the transmitted OFDM symbol becomes periodic, and the linear convolution process of the transmitted OFDM
symbols with the channel impulse responses will become a circular convolution one.
Assuming the value of Ncp is larger than the channel length, the received data vector can be expressed as
= +
Applying SVD on the channel response, we have
= H
H UΣV (2.7) where U and V are unitary matrices, and Σ is a diagonal matrix. Substituting
Equation 2.7 and the equalities of x=V and X Y=UHy into Equation 2.6, the received data vector can be written as
( ) N guard interval can be written as
0 1
transform (DFT) matrix with the lth entry as
As in Equation 2.8, the received data y can be transformed into Y ( ) N
According to Equation 2.11, by adding CP to the OFDM symbol, the modulation in OFDM is equivalent to multiplying the frequency domain signals of the OFDM symbol with the channel’s frequency response Σ .
The block diagrams of the OFDM transceiver is shown in Figure 2.3, where the upper path is the transmitter chain and lower path corresponds to the receiver chain.
In the center, IFFT modulates a block of input values onto a number of subcarriers.
In the receiver, the subcarriers are demodulated by the FFT, which performs the reverse operation of the IFFT. In fact, the IFFT can be made using the FFT by conjugating input and output of the FFT and dividing the output by the FFT size.
This makes it possible to use the same hardware for both transmitter and receiver.
This complexity saving is only possible when the transceiver doesn’t have to transmit and receive simultaneously. The functions before the IFFT can be discussed as follows. Binary input data is first encoded by a forward error correction code. The encoded data is then interleaved and mapped onto QAM values. In the receiver path, after passing the radio frequency (RF) part and the analog-to-digital conversion (ADC), the digital signal processing starts with a training sequence to determine symbol timing and frequency offset. The FFT is used to demodulate all subcarriers.
The FFT outputs are mapped onto binary values and decoded to produce binary output data. In order to successfully map the QAM values onto binary values, the reference phases and amplitudes of all subcarriers have to be acquired first.
In conclusion, OFDM is a powerful modulation technique that simplifies the removal of distortion due to the multipath channel and increases bandwidth efficiency. The key advantages of OFDM transmission scheme can be summarized as follows:
1. OFDM is an efficient way to deal with multipath. For a given delay spread, the implementation complexity is significantly lower than that of a single carrier