On maximum-likelihood detection and the search for the closest lattice point
TL;DR: A novel algorithm is developed that is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder and is supported by intuitive arguments and simulation results in many relevant scenarios.
Abstract: Maximum-likelihood (ML) decoding algorithms for Gaussian multiple-input multiple-output (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using number-theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr-Euchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near-ML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.
Citations
More filters
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.
Abstract: In this article, we have provided general, comprehensive coverage of the SDR technique, from its practical deployments and scope of applicability to key theoretical results. We have also showcased several representative applications, namely MIMO detection, B? shimming in MRI, and sensor network localization. Another important application, namely downlink transmit beamforming, is described in [1]. Due to space limitations, we are unable to cover many other beautiful applications of the SDR technique, although we have done our best to illustrate the key intuitive ideas that resulted in those applications. We hope that this introductory article will serve as a good starting point for readers who would like to apply the SDR technique to their applications, and to locate specific references either in applications or theory.
2,996 citations
Cites background from "On maximum-likelihood detection and..."
..., [49]), with problem size (M,N) = (40, 40)....
[...]
..., [49]) that the same model as in (7) can be used to formulate detection problems in many other communication scenarios, such as multiuser systems, space-time coding systems, spac efrequency coding systems, and combinations such as multius er multi-antenna systems....
[...]
TL;DR: A simple encoding algorithm is introduced that achieves near-capacity at sum-rates of tens of bits/channel use and a certain perturbation of the data using a "sphere encoder" can be chosen to further reduce the energy of the transmitted signal.
Abstract: Recent theoretical results describing the sum-capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achieves near-capacity at sum-rates of tens of bits/channel use. The algorithm is a variation on channel inversion that regularizes the inverse and uses a "sphere encoder" to perturb the data to reduce the energy of the transmitted signal. The paper is comprised of two parts. In this second part, we show that, after the regularization of the channel inverse introduced in the first part, a certain perturbation of the data using a "sphere encoder" can be chosen to further reduce the energy of the transmitted signal. The performance difference with and without this perturbation is shown to be dramatic. With the perturbation, we achieve excellent performance at all signal-to-noise ratios. The results of both uncoded and turbo-coded simulations are presented.
972 citations
TL;DR: The implementation results show that it is feasible to achieve near-ML performance and high detection throughput for a 4/spl times/4 16-QAM MIMO system using the proposed algorithms and the VLSI architecture with reasonable complexity.
Abstract: K-best Schnorr-Euchner (KSE) decoding algorithm is proposed in this paper to approach near-maximum-likelihood (ML) performance for multiple-input-multiple-output (MIMO) detection. As a low complexity MIMO decoding algorithm, the KSE is shown to be suitable for very large scale integration (VLSI) implementations and be capable of supporting soft outputs. Modified KSE (MKSE) decoding algorithm is further proposed to improve the performance of the soft-output KSE with minor modifications. Moreover, a VLSI architecture is proposed for both algorithms. There are several low complexity and low-power features incorporated in the proposed algorithms and the VLSI architecture. The proposed hard-output KSE decoder and the soft-output MKSE decoder is implemented for 4/spl times/4 16-quadrature amplitude modulation (QAM) MIMO detection in a 0.35-/spl mu/m and a 0.13-/spl mu/m CMOS technology, respectively. The implemented hard-output KSE chip core is 5.76 mm/sup 2/ with 91 K gates. The KSE decoding throughput is up to 53.3 Mb/s with a core power consumption of 626 mW at 100 MHz clock frequency and 2.8 V supply. The implemented soft-output MKSE chip can achieve a decoding throughput of more than 100 Mb/s with a 0.56 mm/sup 2/ core area and 97 K gates. The implementation results show that it is feasible to achieve near-ML performance and high detection throughput for a 4/spl times/4 16-QAM MIMO system using the proposed algorithms and the VLSI architecture with reasonable complexity.
723 citations
Cites background from "On maximum-likelihood detection and..."
...is commonly preprocessed in various practical MIMO detectors [23], [24]....
[...]
TL;DR: It is shown that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
Abstract: In this paper, we consider a multiple-input-multiple-output (MIMO) fading broadcast channel and compute achievable ergodic rates when channel state information (CSI) is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback schemes are analyzed and compared under various assumptions. Digital feedback is shown to be potentially superior when the feedback channel uses per channel state coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a minor effect even if simple uncoded modulation is used on the feedback channel. We discuss first the case of an unfaded additive white Gaussian noise (AWGN) feedback channel with orthogonal access and then the case of fading MIMO multiple access (MIMO-MAC). We show that by exploiting the MIMO-MAC nature of the uplink channel, a much better scaling of the feedback channel resource with the number of base station (BS) antennas can be achieved. Finally, for the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ? F < 1/2, a fraction 1 - 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
684 citations
Cites methods from "On maximum-likelihood detection and..."
...These codes can be optimally decoded by using a sphere decoder [59], [60] and achieve the performance promised by the above analysis....
[...]
27 Jun 2005
TL;DR: Two ASIC implementations of MIMO sphere decoders with efficient implementation of the enumeration approach recently proposed in .
Abstract: Multiple-input multiple-output (MIMO) techniques are a key enabling technology for high-rate wireless communications. This paper discusses two ASIC implementations of MIMO sphere decoders. The first ASIC attains maximum-likelihood performance with an average throughput of 73 Mb/s at a signal-to-noise ratio (SNR) of 20 dB; the second ASIC shows only a negligible bit-error-rate degradation and achieves a throughput of 170 Mb/s at the same SNR. The three key contributing factors to high throughput and low complexity are: depth-first tree traversal with radius reduction, implemented in a one-node-per-cycle architecture, the use of the /spl lscr//sup /spl infin//-instead of /spl lscr//sup 2/-norm, and, finally, the efficient implementation of the enumeration approach recently proposed in . The resulting ASICs currently rank among the fastest reported MIMO detector implementations.
666 citations
Cites background or methods from "On maximum-likelihood detection and..."
...Ever since its introduction in [6] and its application to wireless communications in [10], reduction of the computational complexity of the algorithm has received significant attention [11], [12], [10], [13]....
[...]
...A scheme proposed by Schnorr and Euchner [12] and modified for the finite lattice case in [13] traverses the members of the admissible sets in ascending order of their PEDs....
[...]
...As shown in [13], there is no need to explicitly compute the...
[...]
References
More filters
Book•
01 Jan 1983
25,017 citations
"On maximum-likelihood detection and..." refers background in this paper
...For the sake of simplicity, we assume that , where is a pulse amplitude modulation (PAM) signal set [1] of size , i....
[...]
...Let denote a squared QAM signal set with signal points [1]....
[...]
01 Nov 1999
TL;DR: In this paper, the authors investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading, and derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such formulas.
Abstract: We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such formulas. We show that the potential gains of such multi-antenna systems over single-antenna systems is rather large under independenceassumptions for the fades and noises at different receiving antennas.
12,542 citations
TL;DR: In this article, the authors examined the performance of using multi-element array (MEA) technology to improve the bit-rate of digital wireless communications and showed that with high probability extraordinary capacity is available.
Abstract: This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver.
We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon‘s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.
10,526 citations
Book•
01 Jan 1968TL;DR: This chapter discusses Coding for Discrete Sources, Techniques for Coding and Decoding, and Source Coding with a Fidelity Criterion.
Abstract: Communication Systems and Information Theory. A Measure of Information. Coding for Discrete Sources. Discrete Memoryless Channels and Capacity. The Noisy-Channel Coding Theorem. Techniques for Coding and Decoding. Memoryless Channels with Discrete Time. Waveform Channels. Source Coding with a Fidelity Criterion. Index.
6,684 citations
"On maximum-likelihood detection and..." refers background in this paper
...coding rates not too close to the channel capacity [32], [34]....
[...]
Book•
[...]
01 Aug 1998
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.
Abstract: From the Publisher:
The development of multiuser detection techniques is one of the most important recent advances in communications technology. 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. The only prerequisites assumed are undergraduate-level probability, linear algebra, and digital communications. The book contains over 240 exercises and will be a suitable textbook for electrical engineering students. It will also be an ideal self-study guide for practicing engineers, as well as a valuable reference volume for researchers in communications, information theory, and signal processing.
5,048 citations
"On maximum-likelihood detection and..." refers background or methods in this paper
..., a linear MMSE filter followed by symbol-by-symbol hard decisions [16]....
[...]
...The canonical baseband complex model for a -user synchronous code-division multiple access (CDMA) system is given by [16]...
[...]