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- Figure 1: OFDM Spectrum List of Figures
- Figure 2: Multipath Effects
- Figure 3 Multi-path Delay Spread
- Figure 4: Frequency Domain Distribution of Symbols.......................................................
- Figure 5: OFDM Sytem Block Diagram
- Figure 6: Guard Time..........................................................................................................
- Figure 7: Synchronisation using training sequence
- Figure 8: Simulation results
- Figure 9: Simulation Result
- Figure 10: Simulation Result
- Figure 11 : Simulation Result
Introduction to OFDM
Orthogonal Frequency Division Multiplexing is a digital multi-carrier modulation scheme, which uses a large number of closely-spaced orthogonal sub-carriers. Each sub- carrier is modulated with any of the modulation schemes such as quadrature amplitude modulation (QAM) or quadrature phase shift key (QPSK) while assuring that the data rates are similar to single carrier modulation schemes in the given bandwidth.
Figure 1: OFDM Spectrum
While using Frequency Division Multiplexing in multi-channel system the total bandwidth is divided into N over-lapping. Each sub-channel is modulated with a separate symbol stream and the N sub-channels are frequency multiplexed. Even though the prevention of spectral overlapping of sub-carriers reduces Inter-channel Interference, this leads to an inefficient use of spectrum.
Delay Spread
The received radio signal from a transmitter consists of typically a direct signal, plus reflections of object such as buildings, mountings, and other structures. The reflected signals arrive at a later time than the direct signal because of the extra path length, giving rise to a slightly different arrival time of the transmitted pulse, thus spreading the received energy. Delay spread is the time spread between the arrival of the first and last multi-path signal seen by the receiver. In a digital system, the delay spread can lead to inter-symbol interference. This is due to the delayed multi-path signal overlapping with the following symbols. This can cause significant errors in high bit rate systems, Figure 6 shows the effect of inter-symbol interference due to delay spread on the received signal. As the transmitted bit rate is increased the amount of inter-symbol interference also increases. The effect starts to become very significant when the delay spread is greater then ~50% of the bit time.
Figure 3 Multi-path Delay Spread
Inter-symbol interference can be minimized in several ways. One method is to reduce the symbol rate by reducing the data rate for each channel (i.e. split the bandwidth into more channels using frequency division multiplexing).
Doppler Shift
When a wave source and a receiver are moving relative to one another the frequency of the received signal will not be the same as the source. When they are moving toward each other the frequency of the received signal is higher then the source, and when they are approaching each other the frequency decreases. This is called the Doppler Effect. An example of this is the change of pitch in a car’s horns it approaches then passes by. This effect becomes important when developing mobile radio systems. The amount the frequency changes due to the Doppler effect depends on the relative motion between the source and receiver and on the speed of propagation of the wave. The
Doppler shift in frequency can be written:
Where delta f is the change in frequency of the source seen at the receiver, f 0 is the frequency of the source, v is the speed difference between the source and transmitter, and c is the speed of light.
For example: Let f 0 = 1GHz, and v = 60km/hr (16.7m/s) then the Doppler shift will be:
This shift of 55Hz in the carrier will generally not effect the transmission. However, Doppler shift can cause significant problems if the transmission technique is sensitive to carrier frequency offsets (for example COFDM) or the relative speed is higher (for example in low earth orbiting satellites).
For example, a receiver may see a signal via a direct path as well as a path that bounces off a building. Finally, clipping simulates the problem of amplifier saturation. This addresses a practical implementation problem in OFDM where the peak to average power ratio is high.
The receiver performs the inverse of the transmitter. First, the OFDM data are split from a serial stream into parallel sets. The Fast Fourier Transform (FFT) converts the time domain samples back into a frequency domain representation. The magnitudes of the frequency components correspond to the original data. Finally, the parallel to serial block converts this parallel data into a serial stream to recover the original input data.
OFDM System Design
Figure 5: OFDM Sytem Block Diagram
OFDM system design, as in any other system design, involves a lot of tradeoff’s and conflicting requirements. The following are the most important design parameters of an OFDM System. The following parameters could be a part of a general OFDM system Bit Rate required for the system Bandwidth available BER requirement (Power Efficiency)
Guard Time
Guard time in an OFDM system usually results in an SNR loss in an OFDM system, since it carries no information. The choice of the guard time is straightforward once the multi-path delay spread is known. As a rule of thumb, the guard time must be at least 2- times the RMS delay spread of the multi-path channel. Further, higher-order modulation schemes (like 32 or 64 QAM) are more sensitive to ISI and ICI than simple schemes like QPSK. This factor must also be taken into account while deciding on the guard-time.
Figure 6: Guard Time
Symbol Duration
To minimize the SNR loss due to the guard-time, the symbol duration must be set much larger than the guard time. But an increase in the symbol time implies a corresponding increase in the number of sub-carriers and thus an increase in the system complexity. A
Another associated problem with OFDM systems is the effect of phase noise. Phase noise is present in all practical oscillators and it manifests itself in the form of random phase modulation of the carrier. Both phase-noise and frequency offset cause significant mount of ICI in an OFDM receiver. The effect these are worse in OFDM than single carrier systems. The use of efficient frequency and phase estimation schemes can help reduce these effects.
Synchronization using Training Sequences
In cases like packet data transmission in which a training sequence is available, a much more efficient method of timing recovery is to correlate the received signal with the known training sequence and to find the peaks in the co-realtors output. This method is illustrated in figure.
Here T is the sampling interval and ci are the matched filter coefficients, which are in turn, the complex conjugates of the known training sequence. From the correlation peaks in the output signal, both the symbol timing and the frequency offset can be estimated.
Figure 7: Synchronisation using training sequence
Optimal Timing in the Presence of Multi-path
The effect of multi-path is the introduction of ICI and ISI in the OFDM symbol. These effects are significant only if the delay spread of the channel exceeds the guard interval. CI is caused mainly because the FFT interval is no longer flat (because the roll-off regions due the multi-path components interfere with the flat region of the FFT interval). ISI is caused mainly because of the overlap between the previous OFDM symbol and the
current OFDM symbol in the FFT interval. The solution to this timing problem is to find the delay window with a width equal to the guard time-that contains the maximum signal power. The optimal FFT starting time is then equal to the starting delay of the found delay window, plus the delay that occurs between a matched filter peak output from a single OFDM pulse and the delay of the last sample from the flat part of the OFDM signal envelope, minus the length of the FFT interval.
Figure 8: Simulation results 1
We want to transmit the following binary data using OFDM [0 0 0 1 1 0 1 1] The plot above show the binary data
Figure 9: Simulation Result 2
Figure 11 : Simulation Result 4
Finally an FFT (Fast Fourier Transform) is used to recover the binary data as shown in the plot. Note that the binary FFT is the opposite of IFFT used to generate the OFDM signal.
Figure 12: Simulink Model of OFDM Transciever
Figure 13: SImualtion Result 5
