Integrated sensing and communication is regarded as a key enabler for next-generation wireless networks. To optimize the transmitted waveform for both sensing and commu-nication, various performance metrics must be considered. This work focuses on sensing, and specifically on the mean square error (MSE) of channel estimation. Given the complexity of deriving the MSE, the Bayesian Cramer-Rae Bound (BCRB) is commonly recognized as a lower bound on the minimum MSE. However, the BCRB is not applicable to channels with discrete or mixed distributions. To address this limitation, a new lower bound based on a Poincare inequality is proposed and applied to fading MIMO AWGN channels with blockage probability, and the behavior of the lower bound at high SNR is precisely characterized.

In this paper, the definition of threshold of elementary absorbing sets is extended to scaled Min-Sum low-density parity-check (LDPC) decoding. Based on the analysis of the behavior of scaled Min-Sum LDPC decoders in the Tanner graph of the absorbing set, it is proven that correct decoding is guaranteed with received channel messages above threshold. A fast algorithm for the threshold computation is derived. Many examples of absorbing sets taken from LDPC codes of various variable node degrees are investigated, and it is shown that all of them can be deactivated with low enough scaling factors.

Absorbing sets (ASs) cause the error floor phenomenon in many Low-Density Parity-Check (LDPC) codes. A recent, simplified system model for Min-Sum (MS) LDPC decoding [1] predicts that ASs exhibit a threshold behavior: if all variable nodes in an AS have channel messages above the threshold, the AS cannot trap the decoder. The threshold is a real-valued parameter that depends on the topology of the AS, and can be evaluated by a nonlinear optimization. In this paper we describe a simple, fast algorithm for evaluating the AS threshold. Additionally, we show that the algorithm is valid also for scaled-MS decoding. We show with an example that the threshold values under scaled-MS decoding are smaller than under MS decoding. Accordingly, scaling decreases the error floor.

The error floor phenomenon in many low-density parity-check (LDPC) codes is caused by combinatorial objects in their Tanner graph, known as absorbing sets. In this paper, we highlight a threshold behavior for the min-sum decoding algorithm in the graph of an absorbing set with fixed-point representation of messages. For an absorbing set of interest in a binary LDPC code we can compute the threshold, a novel real-valued parameter that is closely related to its harmfulness. We show that absorbing sets with negative thresholds cannot trap the decoder if the dynamic range of the extrinsic messages is large enough. We also prove that, in regular LDPC codes, absorbing sets with negative thresholds exist if the variable node degree is odd. The examples presented in this paper show that odd-column-weight LDPC codes can have many absorbing sets with negative thresholds, but that these absorbing sets do not trap a well-designed decoder. Simulations show a good agreement between the results of the analysis presented in this paper and the performance of practical decoders with fixed-point messages.

High-performance storage class memories could benefit from a fast decoding error correcting code (ECC), able to correct a few errors in just a few nanoseconds. The class of BCH codes provides excellent candidates to play this role. The low latency requirement prevents adopting iterative or sequential processes in the encoding and decoding phases-as traditionally done for storage application based on Flash NAND technology. Therefore, we propose an architecture for fast decoding of double and triple ECCs. In our architecture, any time-consuming iterative computation is eliminated, and the most complex evaluations are isolated and carried in parallel with the other terms, to avoid bottlenecks in the decoder. In particular, the error locator polynomial is computed by a combinatorial logic, and its roots are searched by testing all the bits simultaneously. Here, we describe a gate-level design of these architectures. We also give an in-depth analysis of hardware-oriented implementations of finite field operations, and of bases for element representation.

In this paper, we consider Block Differential Modulation (BDM), to tackle the phase slip problem in digital communication systems. When the received signal phase can drift, the synchronizer can suddenly choose a wrong reference phase, e.g. adding multiples of 2π/M in case of M-ary Phase Shift Keying. Phase slips are detrimental for any coherent system since they cause long error bursts, till an opposite phase slip occurs. BDM is a generalization of Differential Modulation (DM). Neither of them relies on the absolute carrier phase. However, BDM differentially encodes information between small blocks of symbols and exploits couples of adjacent blocks to decode. This allows simple and practical demapping, without sacrificing capacity. We show that for low and moderate phase slip probabilities, BDM approaches the constrained capacity of coherent transmission, in particular at high spectral efficiencies. We provide closed-form results for the constrained capacity in absence of phase slips for Phase Shift Keying and Quadrature Amplitude Modulation, and we evaluate numerically the constrained capacity through an efficient Monte Carlo method, when phase slips occur. Besides, we provide simple upper and lower bounds.

In this paper, we consider joint estimation of the channel length and of the impulse response for OFDM systems, exploiting information criteria to find the best trade-off, in terms of Kullback-Leibler divergence, between noise rejection and channel description accuracy. So far, information criteria have not been used for practical channel length estimation methods, due to their prohibitive complexity. We show how to make them affordable, performing channel estimation in a recursive way that allows to establish the optimal channel length with a moderate incremental cost. With reference to IEEE 802.11 OFDM-based standards for WLAN, we investigate several cases, applying the joint channel length and impulse response estimation to many scenarios, ranging from the simplest pilot-aided channel estimation based on training sequences, to the most challenging data-aided channel tracking, driven either by detected or by decoded symbols. In all cases, the achieved performance and robustness are very good, with a very small increase in complexity w.r.t. estimation methods that assume fixed channel length.

In this paper, we consider joint estimation of the channel length and of the impulse response for OFDM systems, exploiting information criteria, to find the best trade-off between noise rejection and channel description accuracy. So far, information criteria have not been considered practical channel estimation methods, due to their prohibitive complexity. We show how to make them affordable, performing channel estimation in a recursive way that allows to establish the optimal channel length with a moderate incremental cost. Focusing on the 802.11 wireless LAN family, we investigate several cases, applying the joint channel length and impulse response estimation to many scenarios, ranging from the simplest pilot-aided channel estimation based on training sequences, to the most challenging data-aided channel tracking, driven either by detected or decoded symbols. In all cases, the performance and robustness are very good, with a very small increase in complexity w.r.t. estimation methods that assume fixed channel length.

We investigate a property that we have found in many efficient bilinear cyclic convolutions in GF (2m). We show that this property can reduce the additive complexity of cyclotomic FFTs. We explain how it arises, and why the most common constructions of cyclic convolutions yield this beneficial feature.

This paper is focused on cyclotomic Fourier transforms in GF(2m), and on their applications to algebraic decoding of Reed-Solomon codes, like the evaluation of syndromes and of error locator (or evaluator) polynomials. Cyclotomic transforms are much more efficient than straightforward evaluation. In particular, the number of multiplications is quite small. In this paper it is shown that also the number of additions can be considerably reduced with respect to previous analyses. A simple interpretation of the cyclotomic Fourier transform best suited for the evaluation of syndromes allows to assemble the required matrix easily and quickly, even in large fields. Fast construction of such matrices is important to obtain the best results, since as many matrices as possible must be generated and compared. It is shown that both the structure of the matrix and of bilinear convolutions need to be exploited, to reduce the complexity of the costly part of cyclotomic Fourier transforms, which is a matrix-vector product. Heuristic algorithms for matrix-vector product are to be run as many times as possible to obtain the best transform. It is shown with several examples that very good results can be obtained even with very simple algorithms.

In this paper a VLSI architecture of a high throughput and high performance soft-output (SO) MIMO detector (the recently presented Layered ORthogonal Lattice Detector, LORD) is presented. The baseline implementation includes optimal (i.e. maximum-likelihood - ML - in the max-log sense) SO generation. A reduced complexity variant of the SO generation stage is also described. To the best of the authors' knowledge, the proposed architecture is the first VLSI implementation of a max-log ML MIMO detector which includes QR decomposition and SO generation, having the latter a deterministic very high throughput thanks to a fully parallelizable structure, and parameterizability in terms of both the number of transmit and receive antennas, and the supported modulation orders. The two designs achieve a very high throughput making them particularly suitable for MIMO-OFDM systems like e.g. IEEE 802.11n WLANs: the most demanding requirements are satisfied at a reasonable cost of area and power consumption.

In this paper we introduce an innovative version of the recently proposed Layered ORthogonal lattice Detector (LORD). LORD is an attractive MIMO detection algorithm, which aims to approach the optimal Maximum-Likelihood (ML) detection performance with a reasonable complexity, quadratic in the number of transmitting antennas rather than exponential. LORD is also well suited to a hardware (e.g. ASIC or FPGA) implementation because of its regularity, deterministic latency and parallelism. Nevertheless, its complexity is still high in case of high cardinality constellations, such as the 64-QAM foreseen by the 802.11n standard. We show that, when only global latency constraints exist, e.g. a fixed time to detect the whole OFDM symbol, the LORD complexity can be remarkably reduced (up to 60%), still approaching the ML performance.

We propose a novel family of Soft-Input Soft-Output detectors for iterative, point-to-point, MIMO receivers. Compared to the optimal Maximum A Posteriori receiver, low complexity is achieved restricting the detector search to small subsets of the entire QAM hyper-symbol constellation, through simple criteria. These criteria are applied to an improved version of the non-iterative Layered ORthogonal lattice Detector. We show that, notwithstanding the suboptimal low-complexity implementation, this detector approaches the EXtrinsic Information Transfer of the MAP detector. Therefore, when included in an iterative receiver it delivers the same performance. Furthermore, the deterministic complexity and highly parallelizable structure of the proposed detector are well suited for HDL and ASIC implementation. To focus on a specific setting, we consider the indoor MIMO wireless LAN 802.11n standard, taking into account errors in Channel Estimation and a frequency selective, spatially correlated channel model.

In this paper we introduce an improved version of the turbo layered orthogonal lattice detector (T-LORD), recently presented. This implementation, namely K-Best T-LORD, misses the performance of the turbo MAP detector by only few tenths of dB in various configurations, like the fully enhanced T-LORD. However, its complexity is quadratic in the number of transmitting antennas instead of exponential. Moreover, we show that the K-Best T-LORD is robust also over realistic channels, with correlation between tones and antennas, and with imperfect channel state Information at the receiver. This behavior is shown not only via Monte Carlo simulations, but also with EXIT chart analysis.

We reconsider the role of user selection in multiuser MIMO broadcast channels (downlink), in the relevant regime where the number of users K is linear in the number of transmitter (base station) antennas M. User selection is known to achieve mutually quasi-orthogonal user channels and, at the same time, a multiuser diversity effect in terms of receiver SNR. These goals are achieved in the regime of fixed number of transmit antennas, and very large number of users. In contrast, we show that when K = O(M) these effects cannot be achieved, and the role of user selection is marginal. In terms of system design, our results suggest that only a small number K ¿ M of users should feedback their channel state information at each point in time. This greatly alleviates the burden of the channel state information feedback, while achieving essentially optimal performance.

In this paper a novel Soft-Input Soft-Output detector, namely Turbo-LORD, is proposed for iterative MIMO receivers. This is an improved version, capable of managing a priori information, of the Layered ORthogonal lattice Detector recently presented. The implementation is straight and efficient when there are only two transmitting antennas. However, problems arising with more than two antennas are also discussed, along with possible solutions. It is shown that notwithstanding the suboptimal low-complexity implementation, this iterative receiver misses the performance of the turbo MAP detector by only few tenths of dB in various configurations, with very high spectral efficiency.

We consider multiple input-multiple output orthogonal frequency division multiplexing indoor wireless communications, adopting training assisted channel estimation. We focus on the transmission of orthogonal training sequences over a generic number of spatial streams, possibly different from the number of antennas. We show how to cope with performance requirements, low latency and complexity, firstly reducing the problem to a series of easier single input-single output problems, and finally exploiting the correlation between adjacent tones to refine the previously obtained estimations. As a practical example, we consider the 802.11n ongoing standard.

In this paper we consider an iterative detection and decoding scheme for Space-Frequency-Bit-Interleaved Coded Modulation (SF-BICM) MIMO-OFDM systems as a candidate receiver architecture for Next Generation Wireless LANs. This work is focused on the implementation complexity reduction of the overall turbo MIMO scheme through the simplification of the three main blocks: the Soft-Interference-Canceller, the MMSE-MIMO detector and the MIMO Soft-Symbol demapper which uses extrinsic soft information, produced by a Soft-Output-Viterbi-Algorithm (SOVA), to perform the LLRs calculation of the coded bits. A new receiver architecture is proposed, its computational complexity is estimated and compared with a more classical turbo MMSE receiver, both for 16-QAM and 64-QAM constellations.