Journal ArticleDOI
On the complexity of sphere decoding in digital communications
Joakim Jalden,Bjorn Ottersten +1 more
TLDR
It is found that sphere decoding can be efficient for some SNR and problems of moderate size, even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size.Abstract:
Sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications. In some cases, the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure. Another claim is that although worst-case complexity is exponential, the expected complexity of the algorithm is polynomial. Herein, we study the expected complexity where the problem size is defined to be the number of symbols jointly detected, and our main result is that the expected complexity is exponential for fixed signal-to-noise ratio (SNR), contrary to previous claims. The sphere radius, which is a parameter of the algorithm, must be chosen to ensure a nonvanishing probability of solving the detection problem. This causes the exponential complexity since the squared radius must grow linearly with problem size. The rate of linear increase is, however, dependent on the noise variance, and thus, the rate of the exponential function is strongly dependent on the SNR. Therefore sphere decoding can be efficient for some SNR and problems of moderate size, even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size.read more
Citations
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Journal ArticleDOI
Scaling Up MIMO: Opportunities and Challenges with Very Large Arrays
Fredrik Rusek,Daniel Persson,Buon Kiong Lau,Erik G. Larsson,Thomas L. Marzetta,Fredrik Tufvesson +5 more
TL;DR: The gains in multiuser systems are even more impressive, because such systems offer the possibility to transmit simultaneously to several users and the flexibility to select what users to schedule for reception at any given point in time.
Journal ArticleDOI
Semidefinite Relaxation of Quadratic Optimization Problems
TL;DR: This article has provided general, comprehensive coverage of the SDR technique, from its practical deployments and scope of applicability to key theoretical results, and showcased several representative applications, namely MIMO detection, B¿ shimming in MRI, and sensor network localization.
Journal ArticleDOI
Scaling up MIMO: Opportunities and Challenges with Very Large Arrays
Fredrik Rusek,Daniel Persson,Buon Kiong Lau,Erik G. Larsson,Thomas L. Marzetta,Ove Edfors,Fredrik Tufvesson +6 more
TL;DR: Very large MIMO as mentioned in this paper is a new research field both in communication theory, propagation, and electronics and represents a paradigm shift in the way of thinking both with regards to theory, systems and implementation.
Journal ArticleDOI
Fifty Years of MIMO Detection: The Road to Large-Scale MIMOs
Shaoshi Yang,Lajos Hanzo +1 more
TL;DR: In this article, the authors provide a recital on the historic heritages and novel challenges facing massive/large-scale multiple-input multiple-output (LS-MIMO) systems from a detection perspective.
Journal ArticleDOI
An introduction to convex optimization for communications and signal processing
Zhi-Quan Luo,Wei Yu +1 more
TL;DR: This tutorial gives an interpretation of Lagrangian duality in a multiuser multi-antenna communication problem; it illustrates the role of semidefinite relaxation inMultiuser detection problems; and methods to formulate robust optimization problems via second-order cone programming techniques are reviewed.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Digital communications
TL;DR: This month's guest columnist, Steve Bible, N7HPR, is completing a master’s degree in computer science at the Naval Postgraduate School in Monterey, California, and his research area closely follows his interest in amateur radio.
Book
Integer and Combinatorial Optimization
TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
Book
Multiuser Detection
TL;DR: This self-contained and comprehensive book sets out the basic details of multiuser detection, starting with simple examples and progressing to state-of-the-art applications.