This chapter seeks keywords and concepts that will enable us to grasp the contradictory and conflictive globality of the current moment and sharpen our analysis of equally contradictory and conflictive global pasts. In a plea to move beyond equating the global with openness, connection, and integration, I address the role of closure, boundaries, and limits in global history in a wider sense. For this purpose, I explore in an experimental and deliberately open-ended fashion how thinking about global spherescan be utilised fruitfully for the current practice of history writing. The first part explores the radically inclusive yet claustrophobic vision of the globe as a closed sphere from which there is no escape. Building on earlier closed-world and one-world discourses, this thinking gained prominence after the Second World War in the face of the threat of nuclear destruction and environmental degradation. I then move to think about the globe as composed of many bounded spheres – geopolitical but also social. Here, I take central examples from the realm of communication and language and discusses the public sphere as an exclusionary rather than inclusionary figure of thought.

Intersymbol interference (ISI) occurs for linear dispersive channels (i.e., channels where the transfer function is not flat within the transmission band). Hence, an obvious strategy to avoid ISI is to divide the transmission band into a large number of subbands, which are used individually in parallel. If these bands are small enough, such fluctuations of the channel transfer function can be ignored and no linear distortions occur that would have to be equalized. In this chapter, we study this idea in the particular form of orthogonal frequency-division multiplexing (OFDM). It is shown that even starting from the frequency-division multiplexing idea, the key principle behind OFDM is blockwise transmission and the use of suitable transformations at transmitter and receiver. We analyze OFDM in detail and show how the resulting parallel data transmission can be used in an optimum way. OFDM is compared with the equalization schemes discussed in the previous chapter, and incorporated in the unified description framework.

In carrier-modulated (digital) communication, the transmit signal has spectral components in a band around a so-called carrier frequency. Here, a baseband transmit signal is upconverted to obtain the radio-frequency (RF) transmit signal and the RF receive signal is downconverted to obtain the baseband receive signal. The processing of transmit and receive signals is done as far as possible in the baseband domain. The aim of the chapter is to develop a mathematically precise compact representation of real-valued RF signals independent of the actual center frequency (or carrier frequency) by equivalent complex baseband (ECB) signals. In addition, transforms of corresponding systems and stochastic processes into the ECB domain and back are covered in detail. Conditions for wide-sense stationary and cyclic-stationary stochastic processes in the EBC domain are discussed.

In digital frequency modulation, in particular frequency-shift keying (FSK), information is represented solely by the instantaneous frequency, whereas the amplitude of the ECB signal and thus the envelope of the RF signal are constant. Therefore, efficient power amplification is possible, an important advantage of digital frequency modulation. Even though the frequency and phase of a carrier signal are tightly related (the instantaneous frequency is given by the derivative of the phase), differentially encoded PSK and FSK fall into different families. Moreover, in FSK, the continuity of the carrier phase plays an important role, resulting in continuous-phase FSK (CPFSK). A generalization of CPFSK leads to continuous-phase modulation (CPM), similar to the generalization of MSK to Gaussian MSK discussed in Chapter 4. A brief introduction to CPM is presented and we especially enlighten the inherent coding of CPFSK and CPM. For the characterization and analysis, the general signal space concept derived in Chapter 6 is applied.

An overview of digital communications techniques is given. The notions of source, transmitter, channel, receiver, and sink are explained. Examples of digital communication schemes and respective applications are given. The main quantities and performance measures are introduced and summarized. The fundamental trade-off between both power efficiency and bandwidth efficiency is characterized.

In practice, channels often cause linear dispersive signal distortions (e.g., due to low-pass properties of cables or multipath propagation in wireless communications). Consequently, in this chapter we study PAM transmission over time-invariant linear dispersive channels, where so-called intersymbol interference (ISI) occurs. First, receiver-side equalization strategies for linear dispersive channels are introduced and analyzed. Besides the optimum procedure, which follows immediately from the general signal space concept, we assess low-complexity receivers, specifically linear equalization and decision-feedback equalization. In each case, we are interested in the achievable error performance; the loss caused by ISI is quantified. In addition, transmitter-side techniques for pre-equalization are addressed. The duality between receiver-side and transmitter-side schemes is highlighted. A unified theoretic framework for filter design and the calculation of the error performance of the various strategies for digital transmission over linear dispersive channels is presented.

In some situations, it is convenient to apply modifications to the conventional digital PAM scheme, in order to achieve desired properties of the transmit signal and/or in order to modify the demodulation process. First, we have a look at the crest factor or peak-to-average power ratio of the transmit signal, which should be as low as possible. In this context, offset QAM, minimum-shift keying, and Gaussian minimum-shift keying are studied. Moreover, the replacement of the coherent I/Q demodulator by different principles is addressed. First, “carrierless” amplitude and phase modulation is treated as an alternative approach to PAM. Here, no explicit mixing of the pulse-shaped continuous-time baseband signal to the RF domain is required. Second, in some cases (e.g., fiber-optical transmission), coherent reception is possible in principle but very costly. Here it is desired that even when demodulating without phase information (i.e., by conducting energy detection), a performance close to a coherent receiver is enabled. We study in detail an advanced scheme, called the Kramers–Kronig coherent receiver, which meets this aim by performing more complex operations at the digital part.