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Wireless Personal Communication, Kluwer, No. 1 - 2, 1996

Special Issue on "Multi-Carrier Modulation"

 

By Jean-Paul Linnartz, Philips Research, Eindhoven, and

Shinsuke Hara, Osaka University and Delft University of Technology

 

The growing interest in Multi-Carrier Transmission by researchers and product developers motivated us to propose this topic for a special issue of Wireless Personal Communications. Judging from the response to our Call for Papers and from the growing number of sessions on this topic at international conferences, Multi-Carrier issues receive widespread interest. The number of contributed papers substantially exceeded what we could accommodate in a single issue, so a second issue will be dedicated to Multi-Carrier Communication soon.

 

Multi-Carrier Modulation (MCM) is the principle of transmitting data by dividing the stream into several parallel bit streams, each of which has a much lower bit rate, and by using these substreams to modulate several carriers. The first systems using MCM were military HF radio links in the late 1950s and early 1960s. Orthogonal Frequency Division Multiplexing (OFDM), a special form of MCM with densely spaced subcarriers and overlapping spectra was patented in the U.S. in 1970 [1]. OFDM abandoned the use of steep bandpass filters that completely separated the spectrum of individual subcarriers, as it was common practice in older Frequency Division Multiplex (FDMA) systems (e.g. in analogue SSB telephone trunks), in Multi-Tone telephone modems and still occurs in Frequency Division Multiple Access radio. In stead, OFDM time-domain waveforms are chosen such that mutual orthogonality is ensured even though subcarrier spectra may overlap. It appeared that such waveforms can be generated using a Fast Fourier Transform at the transmitter and receiver [2, 3]. For a relatively long time, the practicality of the concept appeared limited. Implementation aspects such as the complexity of a real-time Fourier Transform appeared prohibitive, not to speak about the stability of oscillators in transmitter and receiver, the linearity required in RF power amplifiers and the power back-off associated with this. After many years of further intensive research in the 1980's, e.g. [4, 5, 6], today we appear to be on the verge of a breakthrough of MCM techniques. Many of the implementational problems appear solvable [7] and MCM has become part of several standards.

As guest- editors, we are happy to see that so many researchers responded to our call for contributions, despite the tight time schedule. We hope that our authors manage to convey their enthusiasm to you, as readers of this special issue. Many papers describe and further investigate the interesting behaviour of MCM signals in channels that are essentially different from the ideal Linear Time-Invariant Memoryless Additive White Gaussian Noise Channel. Meanwhile, Multi-Carrier Systems such as Digital Audio Broadcasting are now close to market introduction.

 

Progress in Multi-Carrier Modulation

MCM benefited from considerable research interest for the military applications, but certainly to a much lesser extent than direct-sequence (DS) spread spectrum. The current overwhelming attention to spread spectrum and Code Division Multiple Access (CDMA) can at least partly be explained by many years of active exploration of this field in military labs. CDMA led to new insight in communication theory, that proved extremely valuable for finding reliable and efficient transmission methods suitable for adverse, i.e., both dispersive and time-varying communication channels with severe limitations by interference. DS-CDMA and MCM have in common that investigation into both schemes heavily relies on the insight in communications provided by Shannon, in particular, in his "geometric" theory, considering waveforms to be a point in a Euclidean space, allowing definitions of orthogonality.

 

It was known from earlier experiments with wireless data transmission that the selection of the modulation technique is highly critical. In the early days of mobile communications, many attempts to connect a telephone modem to a cellular phone failed miserably, mainly because of the poor anticipation to the mobile channel anomalies. Although entrepreneurs rapidly recognized the demand for wireless data communications, experiments and product tests rapidly revealed that the mobile fading channel needed specific solutions for the modulation scheme, bit rate, packet length and other aspects. Among the many proposals, Multi- Carrier Modulation appeared one of the most elegant solutions for wireless digital transmission at high symbol rate. The signal waveform used for Multi- Carrier transmission has intriguing properties. The rapid increase in digital signal processing power in (software programmable) radio receivers has opened the way for large scale use of this idea. The next sections illustrate why OFDM nowadays is considered to be particularly suitable for high-performance digital radio links.

 

Dispersion

 

In conventional modulation methods, dispersion (experienced in terms of a channel delay spread and intersymbol interference) reduces the maximum achievable rate. Equalization can mitigate this to some extent, but typically at the cost of increased noise, so it leads to a transmit power penalty or an increased vulnerability to interference. In contrast to this, several results showed that with a well-designed Coded OFDM system, modest dispersion can improve, rather than deteriorate, the bit error rate. This interesting, counter-intuitive phenomenon can be explained using arguments of diversity. If the entire MCM signal is subject to flat fading, i.e., if all subcarriers experience the same fading, bit errors occur on subcarriers are highly correlated. Error correction wiuth code words spread across subcarriers may not be able to correct erased or wrong bits. In a channel with a larger delay spread, the coherence bandwidth can be such that fading only affects a limited number of subcarriers at a time. Forward error correction coding can successfully repair poor reception at those subcarriers. Experiments within the DAB project revealed that under typical (outdoor) propagation conditions, 1.5 MHz is a minimum bandwidth to exploit such diversity gains.

Interleaving in frequency domain, i.e., across subcarriers is used to further improve the performance. Signals from different applications or programs are interleaved to achieve greater independence of fading of subcarriers for individual user data streams.

 

Time Dispersion, Synchronization and Doppler Spreading

 

In contrast to the delay dispersion, Doppler spreading" is caused by time variations of the channel. While most engineers in the field now think of Coded-MCM as a means to combat dispersion of the channel, in one of the pioneering papers, Cimini [4] proposed its use in rapidly time-varying channels. If the symbol duration is relatively large, it is unlikely that the symbol energy completely vanishes during a signal fade. However, OFDM subcarriers loose their mutual orthogonality if rapid time-variations of the channel occur, which typically leads to increased bit error rates. Similarly, phase jitter or receiver frequency offsets also lead to InterChannel Interference.

InterCarrier Interference

Input parameters:

Carrier frequency
MHz
Speed
m/s
Frame size
(excluding guard time)
subcarriers
Symbol rate
Number of QAM symbols per second
ksymbol/sec
 
 

Result:

P0
Local mean of wanted signal component.
dB ()
P1
Variance of first-order ICI, i.e., from neighboring subcarriers.
dB ()
P2
Variance of second-order ICI.
dB ()
P3
Variance of third-order ICI.
dB ()
P0 / SUM P3
Signal-to-ICI ratio
dB ()

A tutorial on OFDM and MC-CDMA in Doppler channels.

A recent paper

 

This sensitivity to frequency offsets, as well as to nonlinear amplification (see below), is often pointed out to be one of major MCM disadvantages. A (time-varying) frequency error not only erodes the subcarrier orthogonality, but also makes subcarrier synchronization much more difficult to achieve and maintain. There have been surprisingly few contributions on this topic so far, however, it is interesting to see that several researchers are proposing coherent detection schemes based on a frequency-time interpolation, inherent to MCM signalling in this issue.

 

The use of Fourier transforms in both the transmitter and receiver, allows MCM communication systems to invoke any measure that was previously used against time dispersion in an attempt to mitigate the effect of frequency dispersion, and vice versa [13]. For instance, it is well known that a maximum-length Linear Feedback Shift Register sequence can be used to find the delay profile of a time dispersive, i.e., frequency selective channel. If such a sequence is transmitted in multi-carrier format, i.e., after Fourier Transformation, it can be used to find the Doppler components of the frequency dispersive channel. In a mobile multipath channel, signal waves coming from different paths often exhibit different Doppler shifts. A MCM receiver can detect the individual components by searching shifted versions of the sequence at the output pins of the FFT. The resulting correlation pattern can be used to steer the Local Oscillator to better track the signal. This idea can further be exploited if a special form of CDMA transmission is used, which is the Fourier Transform of Direct Sequence CDMA (called Multi Carrier CDMA, see below and [9, 10]). It maps each bit to all subcarriers, but each subcarrier uses a time-constant phase offset according to a code pattern. Of course, in an ideal frequency non-selective and time-invariant channel, the receiver adds the energy from all subcarriers according to the code pattern. In a frequency-dispersive channel however, multiple shifted versions of the signal can be recognized at the output of the receive FFT. The receiver may "rake" together energy dispersed in the frequency domain. Implementationwise, it is the dual of the conventional rake receiver designed to combat time-dispersion as now commonly used in Direct Sequence CDMA. This "frequency-domain rake" adds multiple frequency-shifted versions of the signal [13]. Hence, the frequency-domain rake does not address time dispersion, but rather it combats frequency dispersion.

 

Linerarity

 

In an extreme case, MCM signals can be seen as the addition of many independent subcarrier signals, so the amplitude of resulting signal becomes approximately Gaussian. Amplification of such signals by power-efficient Class C amplifiers leads to severe distortion. This affects the MCM link performance as it leads to InterChannel Interference (ICI). Typically a significant power back-off is needed to ensure low distortion at the transmitter, or a nonlinearity compensation at the receiver [16]. One countermeasure can be the selection of a specific set of interdependent subcarrier waveforms that minimizes the peak-to-average power ratio of the total signal.

 

Special Forms of MultiCarrier Modulation

 

Coded OFDM (C-OFDM)

 

Multi-Carrier Modulation on its own is not the solution to the problems of communication over unreliable multipath channels. The channel time dispersion will excessively attenuate some subcarriers such that the throughput on these sub-channels would be unacceptable small. Only if the joint signal of many subcarriers is processed appropriately, the diversity advantages of MCM can be exploited fully. The need for coding across subcarriers was addressed by Sari et al., e.g. [14], warning against overly enthusiastic pursuit of MCM. The advantages of frequency-domain implementations of equalizers (using an FFT) should not be mistaken for an "inherent" diversity gain of OFDM, which may not exist.

 

But of course coding across subcarriers is not the only mechanism that can be invoked against dispersion or to exploit diversity. Other possibilities are

If in a point-to-point MCM link, the receiver and the transmitter can cooperate by adaptively distributing of their power budget over the individual subcarriers. For instance, the signal-to-noise ratios selected according to Gallager's water-pouring theorem can (under certain conditions) be proved to be optimum. Efficient loading of the various subcarriers can for instance significantly enhance the performance of MCM over twisted pair telephone subscriber loops with crosstalk from other nearby copper pairs.

 

MC-CDMA

 

Multi-Carrier Code Division Multiplexing or Multiple Access is another interesting approach to intentionally disperse the signal over different subcarriers. It uses DS-CDMA merely for multiplexing, but chooses the signal waveforms using the OFDM principle. Signals to different users are added linearly onto a multiplex of Multi-Carrier CDMA signals. This scheme was first disclosed at PIMRC '93 in Yokohama by Linnartz, Yee and Fettweis [9] and a similar scheme was presented under a different name by Fazal and Papke [10]. The latter paper reported the performance of a receiver with Maximum Likelihood combining of different subcarriers. Linnartz and Yee showed that MC-CDMA signals can also be detected with fairly simple receiver structures, using an FFT and a variable gain diversity combiner, in which the gain of each branch is controlled only by the channel attenuation at that subcarrier. Chouly et al. presented similar ideas at the ICC conference, November 1993.

 

At PIMRC '94 in The Hague [15], optimum gain control functions in the sense of the Mean-Square Error were presented, basedcon the Wiener Filtering Principle. Despite the theoretical need for a full matrix inversion, it apperared that for a MC-CDMA downlink the subcarrier combiner can exist of gain controls that depend only on the code phase offset and signal fading at that particular subcarrier. This simple subcarrier gain and phase correction combines the functions of the rake receiver and interference cancellation as used in multi-user DS-CDMA. Results showed that a fully loaded MC-CDMA system, i.e., one in which the number of users equals the spread factor, can operate in a highly time dispersive channel with satisfatory bit error rate. These results appeared in contrast to the behaviour of a fully loaded DS-CDMA link that often can not work satisfactorily in channels with substantial time dispersion. Since 1993, MC-CDMA rapidly has become a topic of research, with some new contributions appearing in these special issues.

 

MCM Applications

 

MCM has the elegant waveform properties that make it useful for a wide variety of applications. In particular, we mention digital transmission over telephone lines, applications in broadcasting and in wireless LANs.

 

Digital Transmission over the Telephone System

 

MCM has been tested successfully for digital transmission at high rates over the twisted-pair telephone subscriber loop. It is proposed for the Asymmetric Digital Subscriber Loop (ADSL) [8].

 

Digital Audio Broadcasting

 

The concept of Orthogonal Frequency Division Multiplexing (OFDM) for Digital Audio Broadcasting goes back to the end of the 1980s [5, 6]. Nowadays, experimental systems are in operation, and introduction to the mass-audience is soon to follow. It may substantially improve mobile reception of radio broadcasts. Chipsets for DAB are now being developed in the European JESSE project, a necessary step towards mass production of receivers at low price.

Marketers previously noticed that the introduction of a new technology is often more successful if it replaces an old existing service than if it only offers previously unknown services. But in our personal opinion, improved mobile radio reception by itself may not guarantee the real breakthrough of digital broadcasting. A lesson learned from High-Definition Television (HDTV) was that quality of reception is not the main motivation for customers to replace their equipment. However novel multi-media applications can easily be introduced once DAB is operational, which may form a substantial market in future.

Presumably, one of the reasons to choose OFDM as the DAB standard was the possibility to deploy single frequency networks. Main and relay broadcast transmitter may use the same set of subcarriers. In areas with reception from multiple transmitters, site diversity gains are experienced. This is in sharp contrast to the typical degradation by mutual interference seen with analogue transmission. As MCM is robust against fading caused by natural multipath, it can also work if signals are received from two different transmitter sites: the mutual interference is experienced as artificial multipath propagation. This possibility guarantees very efficient use of scarce radio spectrum, particularly if nationwide coverage is aimed at.

 

Digital Television

 

Developments in MPEG-2 video encoding showed that good quality television signals can be distributed over a channel of 3 to 8 Mbit/s. Multi-Carrier signals with FFT sizes on the order of 2k to 8k points have been proposed as the Digital Video Broadcasting (DVB) standard to ensure reliable mobile reception of digital Terrestrial Television broadcasting (dTTb), see e.g. [17]. In this issue, we also see a U.S. research interest in Digital Video Broadcasting.

As far as we can see, business plans for the introduction of dTTb appear not yet to be fully worked out. Mobile reception of television broadcasts may not justify the enormous costs of replacing the broadcast infrastructure: within DVB, marketing interests appear to focus on provision of television services over cable, the twisted pair telephone subscriber loop, or directly via satellite.

 

Wireless Local Area Networks

 

MCM was not adopted as a standard for the European HIgh PErformance Radio LAN (HIPERLAN), presumably because of the need for highly linear RF amplifiers which are difficult to build with the limited power available for PCMCIA add- ons. However, this does not imply that the race for Wireless LAN standards is completely run. The deregulation of the use of Industrial Scientific and Medical (ISM) bands for communication allows many manufacturers to develop their own wireless equipment independently from time-consuming standardization processes, that are mostly dominated by commercial interests of a few major players. It is particularly in this field that many small companies in the U.S. are researching novel modulation methods and improved access methods, including OFDM and MC-CDMA.

 

Scope of the Special Issue on "Multi-Carrier Modulation"

Wireless Personal Communication, Kluwer, No. 1 - 2, 1996

 

This issues starts with contributions on video broadcast systems using OFDM modulation. Fazel, Kaiser, Robertson and Ruf discuss hierarchical image coding to ensure graceful degradation for receivers in areas with poor reception or under adverse propagation conditions. Engels and Rohling analyse the performance OFDM transmission, with a focus on non-linearities. Their proposal involves non-coherent detection of 64-QAM multilevel transmission, to accommodate 34 Mbit/s in an 8 MHz channel. Rusell and Stueber investigate Doppler spreads and Interchannel Interference in OFDM systems for video broadcasting. Antenna diversity and trellis-coded modulation are proposed to improve reception.

 

Cimini discusses the pro and cons of MCM for indoor wireless LANs aiming at high rates, say up to 155 Mbit/s. Considering many channel and implementation issues, the OFDM scheme may be enhanced by subcarrier equalization if increasing the number of subcarriers appears impractical. Further implementation aspects are addressed in papers by Eetveld, Shepherd and Barton and by Vallet and Haj Taieb. The former paper addresses the theory of peak powers in OFDM signals in order to maximize the performance of peak- limited wireless MCM link. It appears that a few bits of redundancy can significantly improve the peak-to-average factor. Vallet and Haj Taieb propose time-domain pulse shaping to avoid spectral overlap of subcarriers, and to reduce interchannel interference.

 

CDMA systems relying on Multi-Carrier transmission formats are being discussed in several papers. Stirling-Gallacher and Povey study the performance of a path diversity receiver to detect MC-CDMA signals received over a slowly fading, time- dispersive channel. Their paper addresses two different implementations, i.e., the conventional rake structure, and one that operates in the frequency domain, using an FFT. Fazel, Kaiser and Schnell show, as part of their research for the RACE CODIT project, by analysis and by simulation that the combination of CDMA with OFDM can outperform DS-CDMA with a rake receiver. The MCM-based system can simultaneously combat channel dispersion and multi-user interference, a task that would require complex interference cancellation hardware in a DS system.

 

A contribution from Louvain-La-Neuve by Vandendorpe and Van de Wiel also combines OFDM with CDMA. However, their proposal differs from other MC-CDMA system in the sequence of performing the spreading and MC waveform generation. Their proposal is to modulate OFDM waveforms on a DS-CDMA carrier. Although the operations of CDMA spreading and an FFT operation both have the "involution" property that the inverse operation is, except for a multiplicative constant, identical to its inverse. However, this property does not hold for the concatenation of, say Walsh Hadamard, code sequences and an FFT. That is, the transmission schemes are different in nature, and have properties different from MC-CDMA.

Chen, Sousa and Pasupathy analyse a system with DS-signals on multiple subcarriers, called MC-DS-CDMA. The MCM scheme facilitates chip synchronization of DS CDMA signals from different users. It is well known from DS-CDMA that asynchronicity of user signals may cause of excessive bit errors because of substantial correlation of fractions of code sequences. Since in MC transmission the chip time at individual subcarriers is enlarged substantially, this allows relatively more accurate signal alignment.

 

In contrast to this MC-DS-CDMA scheme, the orthogonal MC-CDMA does not use DS signal spreading within subcarrier channels, but it can exploit the a code structure accross subcarriers, and combines different subcarrier signals in order to effectively reduce Multi-User Interference. The Multi-Carrier DS-CDMA benefits from interleaving and error correction coding across subcarriers.

 

Because of space limitations, several papers had to be deferred to the next special issue on Multi-Carrier Transmission. It deals among other things with frequency planning for DAB, interference cancellation in MC-CDMA and OFDM channel estimation by interpolation both in time and frequency domain.

 


Bibliography

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Wireless Communication © Jean-Paul M.G. Linnartz and Shinsuke Hara, 1995.

 

Learn more about OFDM and MC-CDMA
on the Wireless Communication, The Interactive Multimedia CD-ROM
Listen to Internet radio at wireless.per.nl.