In this paper we revisit hybrid analog-digital precoding systems with emphasis on their modelling
and radio-frequency (RF) losses, to realistically evaluate their benefits in 5G system implementations.
For this, we decompose the analog beamforming networks (ABFN) as a bank of commonly used RF
components and formulate realistic model constraints based on their S-parameters. Specifically, we
concentrate on fully-connected ABFN (FC-ABFN) and Butler networks for implementing the discrete
Fourier transform (DFT) in the RF domain. The results presented in this paper reveal that the performance
and energy efficiency of hybrid precoding systems are severely affected, once practical factors are
considered in the overall design. In this context, we also show that Butler RF networks are capable of
providing better performances than FC-ABFN for systems with a large number of RF chains.
Modeling and simulation of nonlinear systems provide communication system designers
with a tool to predict and verify overall system performance under nonlinearity and
complex communication signals. Traditionally, RF system designers use deterministic
signals (discrete tones), which can be implemented in circuit simulators, to predict the
performance of their nonlinear circuits/systems. However, RF system designers are usually
faced with the problem of predicting system performance when the input to the system
is real-world communication signals which have a random nature.
Before delving into the details of orthogonal frequency division multiplexing (OFDM), relevant
background material must be presented first. The purpose of this chapter is to provide the necessary
building blocks for the development of OFDM principles. Included in this chapter are reviews of stochastic
and random process, discrete-time signals and systems, and the Discrete Fourier Transform (DFT). Tooled
with the necessary mathematical foundation, we proceed with an overview of digital communication
systems and OFDM communication systems. We conclude the chapter with summaries of the OFDM
wireless LAN standards currently in existence and a high-level comparison of single carrier systems versus
OFDM.
Many good textbooks exist on probability and random processes written at the under-
graduate level to the research level. However, there is no one handy and ready book
that explains most of the essential topics, such as random variables and most of their
frequently used discrete and continuous probability distribution functions; moments,
transformation, and convergences of random variables; characteristic and generating
functions; estimation theory and the associated orthogonality principle; vector random
variables; random processes and their autocovariance and cross-covariance functions; sta-
tionarity concepts; and random processes through linear systems and the associated
Wiener and Kalman filters.
There exist two essentially different approaches to the study of dynamical systems, based on
the following distinction:
time-continuous nonlinear differential equations ? time-discrete maps
One approach starts from time-continuous differential equations and leads to time-discrete
maps, which are obtained from them by a suitable discretization of time. This path is
pursued, e.g., in the book by Strogatz [Str94]. 1 The other approach starts from the study of
time-discrete maps and then gradually builds up to time-continuous differential equations,
see, e.g., [Ott93, All97, Dev89, Has03, Rob95]. After a short motivation in terms of nonlinear
differential equations, for the rest of this course we shall follow the latter route to dynamical
systems theory. This allows a generally more simple way of introducing the important
concepts, which can usually be carried over to a more complex and physically realistic
context.
Current field forecast verification measures are inadequate, primarily because they compress the comparison
between two complex spatial field processes into one number. Discrete wavelet transforms (DWTs) applied to
analysis and contemporaneous forecast fields prove to be an insightful approach to verification problems. DWTs
allow both filtering and compact physically interpretable partitioning of fields. These techniques are used to
reduce or eliminate noise in the verification process and develop multivariate measures of field forecasting
performance that are shown to improve upon existing verification procedures.
