Corso di Comunicazioni Mobili Data Transmission By OFDM Modulation Prof. Carlo Regazzoni
References  M.L. Doelz, E.T. Heald, D. Martin, “Binary Data Transmission Techniques for Linear Systems”, Proceedings of IRE, Maggio 1957, pp. 656-661.  B. Hirosaki, “An Orthogonally Multiplexed QAM System Using the Discrete Fourier Transform”, IEEE Trans on Comm, Vol. 29, No. 7, Luglio 1981, pp. 982-989.  J.A.C. Bingham, “Multicarrier Modulation for Data Transmission: An Idea Whose Time Has Come”, IEEE Comm. Magazine, Maggio 1990, pp. 5- 14.  T. De Cousanon, R. Monnier, J.B. Rault, “OFDM for digital TV broadcasting”; Signal Processing, Vol. 39 (1994), pp. 1-32.  B. Le Floch, M. Alard, C. Berrou, “Coded Orthogonal Frequency Division Multiplex”, Proceedings of IEEE, Vol. 83, No.6, Giugno 1995, pp. 982-996.  E. Ayanoglu, et al, “VOFDM Broadband Wireless Transmission and Its Advantages over Single Carrier Modulation”, Proc of ICC 2001 Conference, Helsinki (SF) 11-14 Giugno 2001, Vol. 6, pp. 1660- 1664.
Introduction The OFDM modulation (Orthogonal Frequency Division Multiplexing) is the basic technique among the multi-carrier modulations a clear example of multi-carrier modulation is the DMT that is employed in the ADSL standard for transmissions on twisted pair with high bit-rate. Another example is comprised by the MC-CDMA techniques (Multi-carrier CDMA) which are the spread-spectrum version of the OFDM modulation. The basic concept of multi-carrier modulation is the transmission in diversity, i.e. the transmission of information on sub-channels with different bandwidth, where the distortion effects of the channel are different. As contrary to the single-carrier techniques, transmitted message will suffer, in a different measure, of the frequency selective effects of the channel. But a substantial improvement of performances in terms of BER is possible.
Historical Mentions Multi-carrier modulation techniques are considered the fourth generation (4G) communication systems used for fixed and mobile digital transmission. The idea of multi-carrier modulation dates at the end of fifties (Doelz, Heald, Martin, Procedings of IRE, May 1957, pp. 656-661). This work showed a practical implementation of a digital transmission system (called KINEPLEX) with bit multiplexing on orthogonal carriers, which is the basis principles of the OFDM. KINEPLEX demodulator KINEPLEX S/P converter
Historical Mentions The main problem of KINEPLEX lies in the totally analogical implementation of multiplexer (RLC resonance oscillators) which involves the huge dimension of the equipments. The theoretical evolution, which allowed the practical implementation of an OFDM system, was studied by B. Hirosaki in 1981 (IEEE Trans on Comm, July 1981, pp. 982-989), i.e. the multiplexing mapping in frequency on a structure like Fast Fourier Transform (FFT). An FFT structure can be implemented in a totally digital and software way. Ten years after the evolution of digital processing technology (such as DSP) allowed the practical implementation of an OFDM system (see J.C. Bingham, IEEE Comm. Magazine, May 1990, pp. 5-14). The first commercial prototypes of OFDM systems were announced in 2001 (Cisco’s VOFDM presented in the conference ICC2001) and their commercialization is expected for 2005
OFDM Modulation: Introduction The OFDM is a multi-carrier modulation in which carriers are frequency spaced by a multiple of 1/T, where T is the modulation period, and it is characterized by an overlap of the spectrum of the signals transmitted on different carriers. A possible OFDM modulator could be the following:
OFDM Modulation: Introduction The previous figure shows a symbol stream, codified in-phase and in-quadrature components (an , bn) is cyclically multiplexed on N branches containing a QAM digital modulator. The output of the k-th modulation branch is an M-QAMsignal, modulated on carrier frequency fk which is orthogonal to each other. In this way it is possible, at the receiver, to recover the symbol streams transmitted in every branch and to rebuild, after a de-multiplexing operation, the original symbol stream.
OFDM Modulation: Transmitted Signal Every QAM modulator has an assigned constellation that can be equal in every branch. Given and , polar coordinates of the transmitted symbol in the QAM constellation relative to the k-th carrier in the interval [(j - 1)T, jT ], the transmitted signal can be written as: Signal transmitted by the k-th carrier Signal transmitted on the channel where Fundamental frequency Rectangular Pulse N : number of sinusoidal carriers
OFDM Modulation: Transmitted Signal The signal transmitted on the channel is a summation of a huge number of sinusoidal carriers, modulated with arbitrary phase and amplitude. The result, in the time domain, is a noise-like signal:
OFDM Modulation: Transmitted Signal The duration T of an OFDM modulation impulse is fixed and it’s equal to: where • D is the source bit-rate; • a is the number of bit for each transmitted symbol; • Tsis the duration time of a symbol ( N multiplexed symbols are transmitted in the duration time of an OFDM modulation pulse);
OFDM Modulation: Transmitted Signal The spectrum of the signal transmitted by every carrier assumes the shape of the function and zero crossing every 1/T Hz. The spectrum of the overall transmitted signal is a succession of functions spaced by 1/T Hz. The spectral components given by the single carriers are overlapped, as shown in figure:
OFDM Modulation: Bandwidth Occupation The spectrum of the OFDM signal has theoretically unlimited bandwidth. But it needs a truncation to compute the significant bandwidth occupied by the signal. The truncation is performed to remove all the components of the power spectrum which are at least 20 dB under the amplitude of main lobe. In this case only two side lobes are conserved, as shown in the following figure:
OFDM Modulation: Bandwidth Occupation The bandwidth occupied by the N carriers of the OFMD signal is equal to: It can be interesting to compute the spectral efficiency of the QAM modulation, given by the ratio (source bit-rate)/(occupied bandwidth). Supposing to have an M-QAM constellation (or M-PSK) in two dimensions with 2a points (where a is the number of bits for every transmitted symbol); since in T are transmitted N symbols, source bit-rate can be expressed as: Hz. Bit/sec. Now it’s easy to compute the spectral efficiency of the QAM modulation, that is given by:
OFDM Modulation: Bandwidth Occupation In the following figure the power spectral density of an OFDM modulated signal with T = 125 nsec, f0 = 8 MHz, number of carriers N = 32, 128, 512 is shown. Signal spectrum is inclined to become ideal (without using spectral shaping filters, like Nyquist filter with low roll-off) when N is high. In this case the spectral efficiency can be written as: The figure points out that (ideal value, difficult to reach with a QAM modulation, even using Nyquist filters) for high values (but finite) of N.
OFDM Demodulation In the following figure a possible modulator/demodulator schematic is shown. The demodulator is based on the orthogonality of the carriers. It is composed by a bench of demodulators with matched filter used both for in-phase and in-quadrature components. Demodulator Modulator
OFDM Demodulation These orthogonality conditions on the carriers, both for in-phase and in-quadrature components, allow to demodulate the signal, as pointed out in the following formulas: To have a correct demodulation process, other two conditions, which are considered guaranteed for simplicity, are necessary: • strict synchronization on the carrier (coherent demodulation); • strict synchronization of the clock on the receiver side (clock recovery)
OFDM Modulation A modulation/demodulation schematic, such as the previous one, cannot be implemented via hardware with analog oscillators: it would be too much expensive and the imperfections of the oscillators (frequency drift, phase noise) would cause critical malfunctions. But it can easily implemented via software, in a totally digital way, using the FFT (Fast Fourier Transform). In fact, if the k-th symbol (k = 1,…,N , where N is the number of transmitted symbols in a modulation period), mapped in the chosen M-QAM constellation, is written as: Set of symbols transmitted in T sec.
OFDM Modulation The OFDM signal transmitted on the channel can be obtained by the following steps: • computing the Inverse FFT (IFFT) on a set of symbols transmitted in a modulation period T • performing the digital-to-analog conversion (D/A) of the signal obtained in the previous step. In fact a sequence s(n) is generated by using an IFFT operation performed on the set of symbols transmitted in the modulation period T, with a number of samples NFFT (generally it is a power of 2).
OFDM Modulation The operation, previous described, is the following: This result is obtained remembering one of the fundamental properties of the W coefficients of the FFT, i.e. : Since the set of N symbols has to be transmitted every T seconds, the sampling frequency has to be:
OFDM Modulation Then, the s(n) sequence is sent to a D/A converter which works with a smaplig frequency equal to . The s(t) signal, which is the output of the converter, can be written as: but it can also rewritten as: This is the base band OFDM signal!
OFDM Modulation The following figure shows the complete schematic of and OFDM modulator/demodulator system which uses the FFT modulator demodulator k0=0 for simplicity
OFDM Modulation This schematic can be implemented in a totally software way on a DSP architecture because an FFT (or IFFT) structure can be mapped on this signal processing architecture with well known algorithms. With the actual technology a full-digital implementation is impossible; only the base band stage and intermediate frequency stage are developed. The radio frequency stage is still implemented with analogical components.
OFDM: performances on AWGN channel The performances of the OFDM modulation/demodulation systems on a noisy channel depend on the chosen M-QAM constellation. Supposing to transmit data on an AWGN channel, the signal received by the matched filter associated to the k-th carrier, is the following: An error occurs when the noise components are greater than the half of the distance d between two points of the constellation. Then the error probability on the symbol in an OFDM system has the following expression: d depends on the chosen constellation and can be expressed as a function of the average energy of the constellation. (in-phase component) (in-quadrature component)
OFDM: performances on AWGN channel Practically the error probability of an OFDM system is the same of an M-QAM system on a single carrier. 16 points QAM Constellation 32 points QAM Constellation 64 points QAM Constellation 128 points QAM Constellation Number of points in the constellation where
OFDM: performances with pulse noise The OFDM modulation offers remarkable robustness properties against impulsive noises, where impulsive noise is defined as a rectangular pulse with limited amplitude and duration (generally inferior than the symbol time). Hence it is a wide band disturb. Since the information is coded in the frequency domain, the energy of the noise pulse is distributed on the entire bandwidth of the spectrum. This fact reduce its effect on the signal sub-carriers. The following figure shows the error probability versus the impulsive signal-to-noise ratio.
OFDM: performances with jamming noise OFDM is much vulnerable respect to the narrow band interferences like jamming ones, composed by sinusoidal tones which interfere with the signal (man-made noise, ingress-noise); it offers worse performances than a normal QAM (see the following figure with N=512 carriers). The power of the OFDM signal is concentrated in a reduced portion of the spectrum; a noisy pulse which hits in the bandwidth of the signal is able to alter the bits transmitted by various sub-carriers.
OFDM: performances with jamming noise A possible solution consist in switching off the sub-carriers corrupted by the jamming pulse. This solution succeed if the position of the interfering tone in the frequency domain is fixed and known. It can be implemented without any additional hardware, by using the IFFT properties. If the position of the interfering tone is not fixed known, a FEC coding has to be introduced before the modulator (called Coded-OFDM or COFDM)
OFDM: behave on multipath channel After a multipath channel, a series of delayed and out of phase replica of the desired signal are received. Hence, sampling the signal on a certain instant, a linear combination of the previous symbol of the current symbol, and of the following symbol is obtained (ISI); then the channel behaves like a linear filter. Theoretically, it could be possible to use the inverse equalizers, which are digital filters whose the coefficients are dynamically updated by proper algorithms. The coefficients updating is a computationally heavy operation and substantially inefficient if the delay spread of the channel is greater than the modulation period (this condition is equivalent to the frequency selectivity for the multipath fading) The OFDM techniques allow to increase the modulation period and to generate a modulated signal for which the channel is not frequency selective; but the bit-rate remain the same.
OFDM: behave on multipath channel Supposing to introduce a multipath channel with discreet paths, it can be represented by the following impulse response: Without losing generality, an extremely simplified model of the multipath channel can be assumed: The signal received by every single carrier can be written as a summation of the LoS signal and its delayed echo. It is impossible to insulate (see figure) an interval of T seconds which contains only one symbol: ISI appears.
OFDM: behave on multipath channel A possible solution to remove this kind of interference consists in increasing the duration of the OFDM symbol to (T+τ) where τ is called cyclic prefix. Sampling properly the received signal between the instants T1and T2, it’s possible to extract a portion of the signal, with duration T seconds, which contains information only about the j-th symbol, which is the desired; ISI is removed. To realize this mechanism, keeping the orthogonality, an expansion of the duration of the modulated carriers on the left (as shown in the figure) of τ seconds is needed.
OFDM: behave on multipath channel To use the OFDM on a channel where the delay spread is equal to τp, this process has to be applied to every single sub-carrier with a cyclic prefix of τp. The ISI-free demodulation is possible if the received signal is processed in an interval comprised between τp and (T+ τp),where T is the modulation period. The cyclic prefix can be inserted by modulating quickly the N carriers during a modulation period: before inserting, afterwards, the cyclic prefix. To keep orthogonality, N carriers spaced by should be used, before inserting, afterwards, the cyclic prefix. The transmitted signal will be the following: The demodulation will be performed during the period T’.
OFDM: behave on multipath channel The use of the cyclic prefix can limit the spectral efficiency of the modulation. It can be shown that the spectral efficiency of an OFDM system with cyclic prefix τp is equal to: Where T is fixed and it’s equal to: The following figure shows the required bandwidth as a function of the number of the orthogonal carriers, with D=34Mb/s, a=3,4,5,6 e τp = 8msec.