Wireless Communications

What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.

What Will 5G Be

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

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

We propose an efficient way to support quality of service of multiple real-time data users sharing a wireless channel. We show how scheduling algorithms exploiting asynchronous variations of channel quality can be used to maximize the channel capacity (i.e., maximize the number of users that can be supported with the desired QoS).

Providing quality of service over a shared wireless link

We are concerned with the allocation of the base station transmitter time in time-varying mobile communications with many users who are transmitting data. Time is divided into small scheduling intervals, and the channel rates for the various users are available at the start of the intervals. Since the rates vary randomly, in selecting the current user there is a conflict between full use (by selecting the user with the highest current rate) and fairness (which entails consideration for users with poor throughput to date). The proportional fair scheduler of the Qualcomm High Data Rate system and related algorithms are designed to deal with such conflicts. The aim here is to put such algorithms on a sure mathematical footing and analyze their behavior. The available analysis, while obtaining interesting information, does not address the actual convergence for arbitrarily many users under general conditions. Such algorithms are of the stochastic approximation type and results of stochastic approximation are used to analyze the long-term properties. It is shown that the limiting behavior of the sample paths of the throughputs converges to the solution of an intuitively reasonable ordinary differential equation, which is akin to a mean flow. We show that the ordinary differential equation (ODE) has a unique equilibrium and that it is characterized as optimizing a concave utility function, which shows that PFS is not ad-hoc, but actually corresponds to a reasonable maximization problem. These results may be used to analyze the performance of PFS. The results depend on the fact that the mean ODE has a special form that arises in problems with certain types of competitive behavior. There is a large set of such algorithms, each one corresponding to a concave utility function. This set allows a choice of tradeoffs between the current rate and throughout. Extensions to multiple antenna and frequency systems are given. Finally, the infinite backlog assumption is dropped and the data is allowed to arrive at random. This complicates the analysis, but the same results hold.

Convergence of proportional-fair sharing algorithms under general conditions

The relative delay tolerance of data applications, together with the bursty traffic characteristics, opens up the possibility for scheduling transmissions so as to optimize throughput. A particularly attractive approach, in fading environments, is to exploit the variations in the channel conditions, and transmit to the user with the currently 'best' channel. We show that the 'best' user may be identified as the maximum-rate user when the feasible rates are weighed with some appropriately determined coefficients. Interpreting the coefficients as shadow prices, or reward values, the optimal strategy may thus be viewed as a revenue-based policy. Calculating the optimal revenue vector directly is a formidable task, requiring detailed information on the channel statistics. Instead, we present adaptive algorithms for determining the optimal revenue vector on-line in an iterative fashion, without the need for explicit knowledge of the channel behavior. Starting from an arbitrary initial vector, the algorithms iteratively adjust the reward values to compensate for observed deviations from the target throughput ratios. The algorithms are validated through extensive numerical experiments. Besides verifying long-run convergence, we also examine the transient performance, in particular the rate of convergence to the optimal revenue vector. The results show that the target throughput ratios are tightly maintained, and that the algorithms are well able to track changes in the channel conditions or throughput targets.

/pdf/dynamic-rate-control-algorithms-for-hdr-throughput-iwr7xewcih.pdf

Dynamic rate control algorithms for HDR throughput optimization

We consider multi-receiver networks with diversity reception from an information-theoretic point of view. In particular, we find their capacity and investigate how the frequency spectrum should be allocated to the users. We conclude that efficient transmission schemes cannot be built based on reuse partitioning and therefore advocate a spread spectrum approach. We also show that differences in received power levels can be exploited to advantage in multi-access coding and suggest that diversity reception should play an important role. Finally, we consider a sequence of random networks (to include mobility and fading) and show that a notion of network capacity emerges as a law of large numbers.

Information-theoretic capacity of multi-receiver networks

We evaluate the asymptotic normalized average distributions of a class of combinatorial configurations in random, regular and irregular, binary low-density parity-check (LDPC) code ensembles. Among the configurations considered are trapping and stopping sets. These sets represent subsets of variable nodes in the Tanner graph of a code that play an important role in determining the height and point of onset of the error-floor in its performance curve. The techniques used for deriving the spectra include large deviations theory and statistical methods for enumerating binary matrices with prescribed row and column sums. These techniques can also be applied in a setting that involves more general structural entities such as subcodes and/or minimal codewords, that are known to characterize other important properties of soft-decision decoders of linear block codes

Philip Whiting

Papers

Providing quality of service over a shared wireless link

Convergence of proportional-fair sharing algorithms under general conditions

Dynamic rate control algorithms for HDR throughput optimization

Information-theoretic capacity of multi-receiver networks

Asymptotic Spectra of Trapping Sets in Regular and Irregular LDPC Code Ensembles