Introduction

OFDM stands for Orthogonal Frequency Division Multiplexing. OFDM is a combination of multiplexing and modulation technique. In OFDM a wideband channel is split inro narrow channel. These narrow band channels are modulated by the data and are then remultiplexed to create OFDM carrier. In OFDM sub-system the subcarriers are orthogonal to each other. The independent subchannel are multiplexed by Frequency Division Multiplexing called multicarrier transmission.
The main idea involved in OFDM is orthogonality of the subcarriers. The orthogonality of subcarrier allows simultaneous transmission on subcarrier which are tightly placed in the spectrum without interference from each other.
OFDMA is a derivative radio-technology, which can be used for shared access.

Background of OFDM

Orthogonal Frequency Division Multiplexing or OFDM has been in commercial usage since the 1980s. In 1990, the OFDM technique was selected as the transmission technology for the Digital Audio Broadcast project [Jacobsen95]. At this time, it was also known as Synchronized Multiple Discrete Tone or SMDT. For a long time, OFDM was considered prohibitively complex to use; however, the ingenious technique based on inverse FFT was proposed by Weinstein, Ebert and others. Starting from a seminal paper by [Cimini85] there was interest in using this technique in the wireless domain as well. Currently OFDM is being used as the radio transmission technology for wimax, LTE, Power line communications and many other areas.

OFDM is an improved form of FDM, designed to take on TDMA/CDMA as a shared access technology. The principal advantages of FDM over, for example, TDMA, are the flat power profile over time (since the transmitter transmits continuously, not in bursts as in TDMA) and the ease of time-synchronization due to relatively large symbol durations. The principal difficulty in FDM is the effect of frequency-selective fading, which creates correlated noise across the signal and requires extremely complex pre-shaping and equalization; this pretty much limits the application of FDM over broadband channels. OFDM aims to retain the advantages of FDM, mitigate the disadvantages and squeeze additional efficiency out of the wireless air interface.

In trying to improve FDM, the immediate idea would be to use multiple narrow-band carriers in parallel. This does not solve the multipath issue entirely, but makes it easier to deal with, since, within each narrow-band carrier (subcarrier in wimax terminology), we can treat the fading as flat. However, there is a requirement for banks of filters (filters are CPU intensive and complex to develop) and the efficiency is further compromised by requiring additional guard-bands (the 3dB points) between sub-carriers to prevent ACI. In FDM the subcarriers are not orthogonal to each other. Either we need to have subcarrier placed far apart in the spectrum or the system can experience interference. For a PSK carrier of bandwith b, symbol rate is given by

The relationship assumes a perfect Nyquist bandwidth with roll off equal to 0.0. Since this is not achievable; root raised cosine filtering is used. In this case the rate is given by

Thus if we need two carrier of data rate 10 Mbps; then if we have to place our BPSK carrier with spacing 15 MHz(10*1.25+2.5) apart allowing for a 10% guard band.

What is OFDM

OFDM is an ingenious technique which works around these issues:

The popularity of OFDM stems from its ability to transform a wideband frequency-selective channel to a set of parallel flat fading narrowband channels, which substantially simplifies the channel equalization problem.
It directly modulates the incoming symbol sequence onto the sub-carriers without pulse shaping. Since rectangular pulses (in the time domain) have a sinc curve response (in the frequency domain) and a sync curve response has spectral nulls at f_c +/- 1/T_s, the sub-carriers can be placed exactly 1/T_s apart, actually squeezing the carriers together.
Instead of separate modulators, the outgoing waveform is created by executing a high-speed inverse DFT on a set of time-samples of the transmitted data (post modulation). The output of the DFT can be directly modulated onto the outgoing carrier, without requiring any other components.

The BER performance of an OFDM signal in a fading channel is much better then the performance of FDM. The advantage is tacit from diversity of the multicarrier such that fading applies to only small subset. Because of the time–frequency granularity that it offers, OFDM appears to be a natural solution when the available spectrum is not contiguous, for overlay systems, and to cope with issues such as narrowband jamming. In the multiuser context, this granularity also accommodates variable quality-of-service (QoS) requirements and bursty data.

Implementation of OFDM

The principles OFDM described can be efficiently implemented by means of digital signal processing using the FFT algorithm to perform the N-point IFFT and FFT at the transmitter and at the receiver respectively. Figures displays a basic scheme of an OFDM Transmitter

At the transmitter, a high data-rate sequence b[n] is sent to a serial to parallel buffer from which N groups of bits {m₁,m₂,…,m_N} are mapped into N complex points Xi corresponding to each one of the subcarriers that the system handles. The X_i points are converted into a time -domain sequence xi via an FFT operation and a parallel to serial conversion. The addition of the Cyclic Prefix is necessary at this stage to combat the time dispersion of the channel and to avoid the ICI at the receiver. This can be easily done in a digital hardware implementation with a few memory storage and retrieval operations before the digital to analog conversion and frequency upconversion are performed. The interface towards the wireless channel is constructed with a High Power Amplifier (HPA) matched to the transmitter antenna.

The basic OFDM receiver depicted in figure takes the RF signal from the antenna and from its Low Noise Amplifier (LNA). Then, the signal is downconverted and transformed into a digital sequence after it passes an Analog-to-Digital Converter (ADC). If the receiver is synchronized the cyclic prefix is removed by eliminating the guard band from each OFDM symbol. The remaining symbol is passed through serial-to-parallel converter and an N-point FFT is computed. The resulting Y_i complex points are the complex baseband representation of the N modulated subcarriers.The Frequency Domain Equalizers(FEQ) compensates for the gain and phase introduced by the channel at the subchannel’s frequency due to decomposition of broadband channel into N sub-channels. The demapping from the complex symbols to bits follows

Explanation of the OFDM modulation sequence

The following is a step-by-step description of the transmission process. The receiving process is the inverse and fairly simple.

Let the input data stream be a sequence {s_k}.
Modulate this data stream as per chosen modulation, to get a sequence of complex symbols {c_k}
Do an inverse FFT to get the sequence {C_k} as . Note that the kth output is nothing but the kth time-sample of a signal which has modulated the complex symbols {c_k} into carriers spaced at NT_s^-1, where T_s is chosen appropriately.
Directly modulate this onto the carrier central frequency to get the outgoing signal as follows: . In this equation s_n is the nth sample of s(t).

OFDM design issues and challenges

In this section, we focus on the key technical issues regarding OFDM. Some of these issues show the advantage of OFDM over other systems, whereas some other ones reflect technical challenges that are to be overcome.

The role of the cyclic prefix

Cyclic prefix is a mechanism by which OFDM modulations combat inter-symbol interference. To achieve this, the ofdm symbol is slightly increased. Instead of keeping the guard times blank, the initial first few values from the vector {C_k} are copied into the guard band. This ensures the circularity of the transmission; thus the discrete fourier transform done at the receiver results in the deconvolution of the transmitted signal.
This is a very simple and effective possibility to compensate channel-sided frequency selective influences. The interval should be longer than the duration, the channel impulse response needs to decay or tune, because these are the the phases of ISI- or ICI-occurence. The disadvantage of using a cyclic extension is a less available bandwidth for the real data transmission. In most environments the length of the Guardinterval is equal to a quarter symbol duration. This is a stable compromise between the less bandwidth efficiency and the better performance due to interferences.
See this page for more details.

Combating multipath

One of the strengths of OFDM is that it can convert a multipath channel i.e. a Rayleigh fading channel to one that is nearly Gaussian in nature. This gives it close to 6-7 dB improvement over a standard single carrier transmission using optimal equalization. This happens because we can individually estimate the impairments in each sub-carrier, and generate an optimal correction signal which simultaneously protects against distortion and against interference by a co-channel interferer [Cimini94]. While the optimal correction sequence is complex to generate, Cimini shows that a simple gain limiting correction sequence is enough to give very good results compared to a standard, single channel coherent receiver.

OFDM channel estimation

However, for this to work, we need to have a good channel estimation mechanism available. The standard wimax technique is to use pilot based channel estimation. The pilots must be distributed through the entire transmission band, such that there is good correlation between the received pilot signal and adjacent carriers. Also, the estimators must be run separately for each pilot, leading to a fair amount of computation effort.

Frequency domain equalization for QAM signals

One oft-touted benefit of OFDM is that time-synchronization can be avoided completely. By adding a cyclic prefix to the waveform, any variations in time synchronization between the sender and the receiver can be taken care of. However, [Sari94] correctly points out that this merely moves the equalization problem into the frequency domain. Also, while phase shifting can be corrected relatively easily using a fixed correction at the output of the DFT stage in the receiver Sari shows that in case of QAM or other higher-order modulations, an adaptive DFE technique must be used.
Adaptive channel estimation is a subject in itself and we will not discuss it in detail here. deBeek etc. [deBeek95] suggest a maximum likelihood technique. Much further work has been carried out in this area. See [Giannakis99] for more.

Adaptive Loading

Adaptive loading is a technique of loading the carriers based on their individual channel transfer functions and noise functions. A technique of adaptive loading is discussed in [Bingham90] where bits are assigned to carriers based on the incremental power matrix at the target bit error rate. This technique is not in widespread use - rather, carriers with bad spectral noise patterns can be omitted entirely from the sub-carrier list in wimax::ofdma.

References

[Bingham90] J.A.C. Bingham, "Multicarrier Modulation: An idea whose time has come", IEEE Communications Magazine, May 1990

[Cimini85] Leonard Cimini, "Analysis and Simulation of a Digital Mobile Channel using Orthogonal Frequency Division Multiplexing", IEEE Transactions on Communications, July 1985

[Hanzo00] Hanzo, Keller, "Adaptive Multicarrier modulation: A convenient framework for time-frequency processing in wireless communications" Proceedings of the IEEE, May 2000

[Sari94] Sari, Karam, Jeanclaude, "An analysis of orthogonal frequency division multiplexing for mobile radio applications", IEEE Transactions on Communications 1994

[deBeek95] deBeek, Edfors, Sandell, Wilson, Borjesson, "On Channel estimation of OFDM systems", IEEE Conference on Vehicular Tech, 1995

[Giannakis99] Scaglione, Giannakis, Barbarrossa, "Redundant filterbank precoders and equalizers, I and II", IEEE Transactions on Signal Processing, July 99

Maintainer: abheek.saha@hsc.com, rajenish.jain@hsc.com
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