The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

The ever-increasing demand for higher data rates in wireless communications in the face of limited or underutilized spectral resources has motivated the introduction of cognitive radio. Traditionally, licensed spectrum is allocated over relatively long time periods and is intended to be used only by licensees. Various measurements of spectrum utilization have shown substantial unused resources in frequency, time, and space [1], [2]. The concept behind cognitive radio is to exploit these underutilized spectral resources by reusing unused spectrum in an opportunistic manner [3], [4]. The phrase cognitive radio is usually attributed to Mitola [4], but the idea of using learning and sensing machines to probe the radio spectrum was envisioned several decades earlier (cf., [5]).

Spectrum Sensing for Cognitive Radio : State-of-the-Art and Recent Advances

Cyclostationarity: half a century of research

/pdf/statistical-theory-of-communication-4wy4yg9ato.pdf

Statistical Theory of Communication

Cyclostationarity: New trends and applications

The relative motion between the transmitter and the receiver modifies the nonstationarity properties of the transmitted signal. In particular, the almost-cyclostationarity property exhibited by almost all modulated signals adopted in communications, radar, sonar, and telemetry can be transformed into more general kinds of nonstationarity. A proper statistical characterization of the received signal allows for the design of signal processing algorithms for detection, estimation, and classification that significantly outperform algorithms based on classical descriptions of signals. Generalizations of Cyclostationary Signal Processing addresses these issues and includes the following key features:

Generalizations of Cyclostationary Signal Processing : Spectral Analysis and Applications

Continuous-phase modulated (CPM) signals play a prominent role in modern communication systems due to their desirable constant-modulus property and the ability to control their power and bandwidth efficiencies. Popular CPM signals include the classical minimum-shift keyed (MSK) signal, the LREC family of signals also known as continuous-phase frequency-shift-keyed (CPFSK) signals, and Gaussian MSK, which is used in state-of-the-art GSM and PCS mobile communication systems. CPM signals, like virtually all man-made communication signals, are known to exhibit cyclostationarity, which implies that their probabilistic parameters, such as mean, second moment, and higher order cumulants, are almost-periodic functions of time. A novel representation of CPM signals as a sum of PAM signals is presented for both integer and noninteger modulation index cases. Then, the Nth-order cyclostationarity properties of binary CPM signals are derived in terms of Nth-order temporal and spectral moment and cumulant functions. Moreover, the case of M-ary CPM signals is briefly addressed. The results are illustrated with simulations involving MSK, LREC, and GMSK signals.

Antonio Napolitano

Papers

Cyclostationarity: half a century of research

Cyclostationarity: New trends and applications

Generalizations of Cyclostationary Signal Processing : Spectral Analysis and Applications

Cyclic spectral analysis of continuous-phase modulated signals

Cyclic higher-order statistics: input/output relations for discrete- and continuous-time MIMO linear almost-periodically time-variant systems