This paper investigates the decoding of a remarkable set of lattices: We treat in a unified framework the Leech lattice in dimension 24, the Nebe lattice in dimension 72, and the Barnes-Wall lattices. A new interesting lattice, named$L_{3\cdot 24}$, is constructed as a simple application of the single parity check on the Leech lattice. The common aspect of these lattices is that they can be obtained via a single parity check or via the$k$-ing construction. We exploit these constructions to introduce a new efficient paradigm for decoding. This leads to efficient list decoders and quasi-optimal decoders on the Gaussian channel. Both theoretical and practical performance (point error probability and complexity) of the new decoders are provided.

We characterize the complexity of the lattice decoding problem from a neural network perspective. The notion of Voronoi-reduced basis is introduced to restrict the space of solutions to a binary set. On the one hand, this problem is shown to be equivalent to computing a continuous piecewise linear (CPWL) function restricted to the fundamental parallelotope. On the other hand, it is known that any function computed by a ReLU feed-forward neural network is CPWL. As a result, we count the number of affine pieces in the CPWL decoding function to characterize the complexity of the decoding problem. It is exponential in the space dimension$n$, which induces shallow neural networks of exponential size. For structured lattices we show that folding, a technique equivalent to using a deep neural network, enables to reduce this complexity from exponential in$n$to polynomial in$n$. Regarding unstructured MIMO lattices, in contrary to dense lattices many pieces in the CPWL decoding function can be neglected for quasi-optimal decoding on the Gaussian channel. This makes the decoding problem easier and it explains why shallow neural networks of reasonable size are more efficient with this category of lattices (in low to moderate dimensions).

We present new efficient recursive decoders for the Barnes-Wall lattices based on their squaring construction. The analysis of the new decoders reveals a quasi-quadratic complexity in the lattice dimension. The error rate is shown to be close to the universal lower bound in dimensions 64 and 128.

Point lattices and their decoding via neural networks are considered in this paper. Lattice decoding in ℝn, known as the closest vector problem (CVP), becomes a classification problem in the fundamental parallelotope with a piecewise linear function defining the boundary. Theoretical results are obtained by studying root lattices. We show how the number of pieces in the boundary function reduces dramatically with folding, from exponential to linear. This translates into a two-layer ReLU neural network requiring a number of neurons growing exponentially in n to solve the CVP, whereas this complexity becomes polynomial in n for a deep ReLU neural network.

A novel static sequence assisted discrete Fourier transform (DFT)-spread-orthogonal frequency division multiplexing (OFDM) waveform is proposed to suppress out-of-band (OoB) emission. In the proposed scheme, a deterministic sequence, which functions as cyclic prefix (CP), is used to suppress OoB emission. A measure of continuity is proposed to determine the location of the static sequence to maximize the amount of OoB suppression. Perturbation is added to the static sequence to further improve phase continuity at block transitions. It is shown that the spectra of the proposed static sequence assisted waveforms are more compact that those of the conventional waveforms. A frequency offset estimation method using the static sequence is described and its performance is evaluated by simulations.

We describe a new family of integer lattices built from construction A and non-binary LDPC codes. An iterative message-passing algorithm suitable for decoding in high dimensions is proposed. This family of lattices, referred to as LDA lattices, follows the recent transition of Euclidean codes from their classical theory to their modern approach as announced by the pioneering work of Loeliger (1997), Erez, Litsyn, and Zamir (2004-2005). Besides their excellent performance near the capacity limit, LDA lattice construction is conceptually simpler than previously proposed lattices based on multiple nested binary codes and LDA decoding is less complex than real-valued message passing.

In this paper we compare and test several channel estimation algorithms in the case of LTE (Long Term Evolution) Systems applied in a high mobility environment. In particular, we propose a novel algorithm, based on the observation of OFDM block energy, to perform a semi-blind tracking of the channel between pilot blocks. This algorithm is compared to more traditional approach based on 1D estimation and interpolation. In addition, an Expectation Maximization (EM) is used to improve the overall channel estimation.

Inter-cell interference is a major issue in current wireless cellular systems, in particular with the development of femto-cells. We propose a semi-centralized uplink femto-macro ICIC approach with low network signalling in which a coordinator defines a power control function for all femto base stations in a given area based on long-term statistics they build. The power control function takes path gains as arguments and the transmit power of each femto mobile terminal is set according to the short-term path gains it reports. The proposed power control function achieves good results in terms of femto-macro performance trade-off and mobile terminal transmit power.

Inter-cell interference is a major issue in current wireless cellular systems, in particular with the development of femto-cells. Indeed, macro-femto inter-cell interference coordination is not an easy task and should be performed with a minimum communication between macro- and femto-base stations. We propose a blind inter-cell interference coordination approach, in which each femto base station configures its transmission power autonomously. This power setting aims at maintaining a constant macro-cell performance impact of the femto base station, whatever its location in the macro-cell, i.e., it equalises the macro-degradation. In a 3GPP-LTE context, this approach exhibits a good femto-macro performance trade-off compared to fixed femto base station transmission power.

Expectation-maximization (EM) based iterative algorithms are investigated in order to estimate the impulse response of a frequency-selective multipath channel in a coded OFDM system. Two ways of choosing the EM complete data are compared: a complete data built from observations and transmitted symbols (CL-EM) and a complete data chosen by decomposing noise and observation components (NCD-EM). Both CL-EM and NCD-EM algorithms are derived for a coded OFDM system. The rate of convergence of both EM algorithms is theoretically determined. It is found that the rate of convergence of CL-EM is independent from the number of channel taps at high signal-to-noise ratio (SNR), while that of NCD-EM varies with the number of taps. It is shown that CL-EM converges in a few iterations. Furthermore, considering the complexity per iteration, CL-EM has a lower complexity than its counterpart. We also establish a Cramer-Rao bound (CRB) for coded OFDM transmission. Simulation results show that CL-EM has a good performance-complexity trade-off and it achieves the CRB.

Joint channel estimation and decoding using belief propagation on factor graphs requires the quantization of probability densities since continuous parameters are involved. We propose to replace these densities by standard messages where the channel estimate is accurately modeled as a Gaussian mixture over multipath channel. Upward messages include symbol extrinsic information and downward messages carry mean values and variances for the Gaussian modeled channel estimate. Such unquantized message propagation leads to a complexity reduction and a performance improvement. Over multipath channel, the proposed belief propagation almost achieves the performance of iterative APP equalizer and outperforms MMSE equalizer.

Joint channel estimation and decoding using belief propagation on factor graphs requires the quantization of probability densities since continuous parameters are involved. We propose to replace these densities by standard messages where the channel estimate is accurately modeled as a Gaussian mixture. Upward messages include symbol extrinsic information and downward messages carry a mean and a variance for the Gaussian modeled channel estimate. Such unquantized message propagation leads to a complexity reduction and a performance improvement. For QAM modulated symbols, the proposed belief propagation almost achieves the performance of expectation-maximization under good initialization and surpasses it under bad initialization.

In order to increase the performance of joint channel estimation and decoding through belief propagation on factor graphs, we approximate the distribution of channel estimate in the factor graph as a mixture of Gaussian distributions. The result is a continuous downward and upward message propagation in the factor graph instead of discrete probability distributions. Using continuous downward messages, the computation complexity of belief propagation is reduced without performance degradation. With both continuous upward and downward messages, belief propagation almost achieves the same performance as expectation-maximization under good initialization and outperforms it under bad initialization.

This paper provides a link and system level study of the downlink in a B3G system using MIMO OFDMA techniques. A 3GPP/LTE-like scenario, in terms of frame structure and system main parameters, is considered in this study. At the link level, the double Alamouti MIMO scheme is studied and the performances of various modulation and coding schemes (MCS) are provided. The impact of real MIMO channel estimation (including RF impairments, CFO compensation and automatic gain control AGC) on the MCSs link performance is also presented. System level study is thus carried out to assess the performance of the downlink OFDMA in terms of coverage and cell throughput. Several scheduling disciplines and MIMO schemes are investigated and the impact of the spatial diversity on the cell throughput is provided. This study has been carried out in the scope of the French RNRT OPUS project.

The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading multiple-input multiple-output (MIMO) channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upper bound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders, called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension. With turbo codes, they exhibit a frame error rate which does not increase with frame length.

This paper investigates the problem of channel quality indicator (CQI) estimation in the context of OFDMA systems in the downlink. The problem of CQI estimation is addressed for SINR-based CQI forms. In this paper, we present a technique for instantaneous SINR estimation which consists in using the channel estimator already present at the receiver to obtain the useful signal levels and signal regeneration (SR) estimator to get the level of interference plus noise. We show that SR estimator has an error floor caused by channel estimation errors, and then we introduce a compensation factor rho in order to remove this error floor. The compensation factor rho is defined as the ratio between the variance of channel estimation errors and the level of interference plus noise at the input of the channel estimator. Thanks to the compensation factor rho we achieve a gain of about 1 dB in term of RMSE for CQI estimation over a wide range of CQI values.

This paper presents uplink spatial scheduling with adaptive transmit beamforming, where terminals perform system-based transmit beamforming in multiuser multi-input multi-output (MIMO) systems. In the presented spatial scheduling, the base station (BS) selects appropriate combination of terminals and their transmit beamforming among possible terminals. In the selection process, a terminal and its transmit beamforming for a signal are successively selected, considering the effect of the other predetermined signals. In performance evaluation, we show that the spatial scheduling achieves much larger system throughput than the system without spatial scheduling. We also present a basic system configuration in which the BS reports the target transmit beamforming to the selected terminal efficiently in time-division duplex (TDD) system downlink

This paper presents downlink spatial scheduling which nullifies interference among multiplexed signals perfectly in multiuser MIMO systems. Under the base station's zero-forcing transmit beamforming, each terminal can receive packet of interest without interference from the other multiplexed packets. The scheduling algorithm successively selects appropriate terminals for packet transmission in the presence of already selected packets. We show that the downlink spatial scheduler is equivalent to the virtual uplink spatial scheduler in terms of received signal characteristics. Applying the uplink scheduling concept to downlink, the downlink spatial scheduler achieves much higher system throughput than the system without spatial scheduling. Also, it is shown that the spatial scheduler has similar system throughput in uplink and downlink

Time division duplex (TDD) technologies are necessary to deal with unpaired frequency bands and to allow low-complexity user equipments (UE) without duplexer in paired frequency bands. In TDD communications, a frame is divided into several sub-frames, each sub-frame being allocated to either uplink (UL) or downlink (DL). An idle period (IP) is required at a DL/UL switching point. It is usually dimensioned according to the cell radius and is identical for all UEs of the cell. In this paper, we propose a UE-specific IP duration, which increases the overall data rate of TDD communications for large cells. Numerical results show the potentially large benefit of the proposed dimensioning in term of spectral efficiency, which can be obtained without any specific signaling

Multidimensional binary mappings for bit-interleaved coded modulations (BICMs) on ergodic multiple-antenna channels with iterative decoding are presented. After derivation of a closed-form expression for the pairwise error probability under ideal maximum-likelihood (ML) decoding, the design criterion for mapping optimization is established from the ML performance of the ideally interleaved channel. It coincides with the figure of merit derived from the genie condition when the iterative receiver converges to perfect a priori information. Multidimensional mapping constructions that exhibit high signal-to-noise ratio (SNR) gains without increasing the complexity of the a posteriori probability (APP) detection are proposed. They allow for a reduced decoding complexity as they achieve near turbo code performance with a single convolutional code.

We present a linear preceding solution to achieve full diversity with iteratively decoded bit-interleaved coded modulation on multiple antenna channels while minimizing the detection complexity.

When performed using an exhaustive search, the maximum likelihood (ML) joint detection of all users in a multicarrier code-division multiple-access (MC-CDMA) system has a prohibitive complexity, growing exponentially with the number of users and the number of bits in each modulation symbol. In this paper, a novel ML multiuser detection algorithm is proposed, the complexity of which is a polynomial function of the number of users and is independent of the modulation size. The MC-CDMA system is modeled as a sphere packing lattice and a low-complexity optimum lattice decoder, the sphere decoder, is applied to jointly detect all users. Suboptimum simplifications, based on the orthogonal projection of the received signal on a facet of the lattice constellation, are also proposed to further decrease the complexity. Simulation results are shown with up to 64 users transmitting 16-quadrature-amplitude modulation symbols.

Soft output detection for signals transmitted on linear channels is investigated. A particular emphasis is made for signal detection on multiple antenna channels. The a posteriori information at the detector output is evaluated from a shifted spherical list of point candidates. The spherical list is centered on the maximum likelihood point, which has the great advantage of stabilizing the list size. Thus, the sphere radius is selected in order to control the list size and to cope with the boundaries of the finite multiple antenna constellation. Our new soft output sphere decoder is then applied to the computation of constrained channel capacity and to the iterative detection of a coded transmission. For example, we achieved a signal-to-noise ratio at 1.25 dB from capacity limit on a 4/spl times/4 MIMO channel with 16-QAM modulation and a 4-state rate 1/2 parallel turbo code.

A fast optimal algorithm based on the branch and bound (BBD) method is proposed for the joint detection of binary symbols of K users in a synchronous code-division multiple access (CDMA) channel with Gaussian noise. Relationships between the proposed algorithms (depth-first BBD and fast BBD) and both the decorrelating decision feedback (DF) detector and sphere decoding (SD) algorithm are clearly drawn. It turns out that decorrelating DF detector corresponds to a "one-pass" depth-first BBD; sphere decoding is in fact a type of depth-first BBD, but one that can be improved considerably via tight upper bounds and user ordering as in our fast BBD.

A new joint detection method based on sphere packing lattice decoding is presented in this paper. The algorithm is suitable for both synchronous and asynchronous multiple access direct-sequence code-division multiple-access (DS-CDMA) systems, and it may jointly detect up to 64 users with a reasonable complexity. The detection complexity is independent of the modulation size and large M-PAM or M-QAM constellations can be used. Furthermore, a theoretical gain analysis is performed in which the multiple-access system performance is derived from the lattice parameters.

When performed using an exhaustive search, the maximum likelihood (ML) joint detection of all users in a multi-carrier code division multiple access (MC-CDMA) system has a prohibitive complexity, growing exponentially with the number of users and the number of bits in each modulation symbol. An ML multiuser detection algorithm has previously been proposed, with a complexity growing polynomially with the number of users, independent of the modulation size. The MC-CDMA system is modelled as a sphere packing lattice and a low-complexity optimum lattice decoder, called the sphere decoder, is applied to jointly detect all users. We propose sub-optimum simplifications, based on orthogonal projection of the received signal on a facet of the lattice constellation, to further decrease the complexity. Simulation results are shown with up to 64 users transmitting 16-QAM symbols.

The maximum likelihood joint detection of all users in a multi-carrier code division multiple access (MC-CDMA) system has a prohibitive complexity, growing exponentially with the number of users, when it is performed using an exhaustive search. In this paper, a novel ML multiuser detection algorithm is proposed, whose complexity is a polynomial function of the number of users and is independent of the modulation size. The MC-CDMA system is modelled using a sphere packing lattice representation and an efficient lattice decoder, called the sphere decoder, is applied to jointly detect all users. Simulation results are proposed up to 64 users transmitting 16-QAM symbols.

Iterative multiuser interference cancellation schemes for direct sequence code division multiple access systems exhibit good performance results for a reasonable complexity. We study an efficient iterative scheme, combining interference cancellation, soft input soft output decoding and beamforming. To deal with unknown channels, we add a pilot-aided space-time channel estimation in each iteration. The iterative structure has two advantages: the observation signal used for estimation contains less interference from one iteration to the following and soft estimates of coded bits are available for data-aided estimation.

This paper investigates an adaptive iterative space-time interference cancellation receiver for wideband code division multiple access (W-CDMA). Each iteration of the interference cancellation includes adaptive beamforming, adaptive path-combining and soft-input soft-output decoding. The complexity of the demodulation process using very simple normalized least mean square (N-LMS) adaptive algorithms is limited with no need of space-time channel estimation. Adaptive space-time processing algorithms are shown to benefit from the iterative process. Simulation results on a UMTS-like scenario show that this receiver achieves performance that is very close to the single user bound, even for highly interfered networks.