We consider massive grant-free random access in a massive multiple-input multiple-output (mMIMO) system. Users transmit a preamble selected at random from a pool, together with data in a grant-free manner. While superposed users with different preambles can be separated and their data decoded, colliding users selecting the same preamble may not be separated. We introduce a preamble collision resolution mechanism, where the multiuser channel of colliding users is resolved with a combination of preamble-based and data-aided channel estimation. For this, we use the sample covariance matrix of the data to estimate the superposition channel from the preamble. For the most likely case of two colliding users, based on the knowledge of the modulation alphabet is used to resolve a phase ambiguity in the multiuser channel. Through numerical evaluations, we validate the efficacy of the proposed method in effectively resolving preamble collisions.

5G-Advanced and likely 6G will support a new low-power wake-up signal (LP-WUS) enabling low-power devices, equipped with a complementary ultra low-power receiver to monitor wireless traffic, to completely switch off their main radio. This orthogonal frequency-division multiplexed (OFDM) signal will emulate an on-off keying (OOK) modulation to enable very low-energy envelope detection at the receiver. Higher rate LP-WUS, containing multiple OOK symbols within single OFDM symbol, will be generated using the time-domain pulse multiplexing of discrete Fourier transform spread (DFT-s-) OFDM. In this context, this paper presents a comprehensive signal design framework for DFT-s-OFDM-based OOK generation. General properties of subcarrier coefficients are derived demonstrating that only DFT of the bits needs to be computed online and repeated over the band before applying appropriate frequency-domain processing. The conventional approach of generating rectangular-like OOK waveforms is then addressed by a combination of pre-DFT bit-spreading and post-DFT processing; and the least-squares (LS) method from Mazloum and Edfors, proposed for 5G LP-WUS and also Ambient-IoT, is shown to be implementable as such. Even though aesthetically pleasing and of independent interest, rectangular-like OOK waveforms are not optimal for 5G LP-WUS scenarios due to their limited robustness to channel frequency-selectivity and timing offset, and so shaping methods for spreading the OOK spectrum and concentrating the OOK symbol energy are analyzed and shown to improve the bit error rate performance under practical conditions.

We investigate an unsourced coded slotted random access (RA) protocol which combines physical and MAC layer approaches. In contrast to the literature, we consider MAC-layer slotting which carries information. We distinguish three categories w.r.t. the amount of information carried by the slotting principle; non/partial/full information carrying setups. We model physical layer performance in a slot with a pilot sequence transmission selected based on information, combined with a finite block length code. For MAC-layer non/partial/full information carrying slotting, we use interference-free (IF) constant weight codes with different numbers of packet repetitions, and compare averaged per user block error rate performance with grant-free 5G NR 2-step RA. We observe that the full information carrying setup provides the best results for all slot repetition schemes, and in addition such schemes have the potential to significantly outperform 5G-NR RA. Also, partial information carrying schemes can provide a large portion of the gain over non-information carrying schemes for the same receiver complexity.

Cellular communication systems are currently evolving to provide non-terrestrial networks (NTNs) connectivity. However, due to large link path loss and realistic antenna capabilities of commercial smartphones, direct access to low Earth orbiting (LEO) satellites can so far only provide very small data rates. In this paper, we investigate the potential in using multi-dimensional constellations (MDC) for improving NTN connectivity. MDC allows non-coherent detection over coherent fading blocks, which can reduce the pilot overhead for channel estimation and remove sensitivity to channel estimation quality in low signal-to-noise ratio links. Our simulation results show that the considered MDC scheme can almost double the data rate compared to a NR-type scheme in the considered coverage-limited LEO scenario of small transport block transmission under NTN line-of-sight channel.

Motivated by using non-coherent transmission for coverage enhancement of 5G uplink control channel, this paper proposes a symbol-likelihood based successive cancellation list (SCL) polar decoder that takes into account the impact of constellation modulation. The conventional SCL polar decoding is based on likelihoods of individual coded bits, implicitly assuming independence among them. To circumvent the issue that in practice bit-dependency may occur for bits transmitted in the same constellation symbol, an interleaver is typically inserted before bit-to-symbol mapping. However, interleaving cannot be effective if the transmission is made of only few symbols, as in short packet non-coherent communications typically using high-order multi-dimensional constellations. The proposed decoder is shown to effectively solve this problem and improves the block error rate in a short packet regime, without needs for changing the encoder. Moreover, this symbol-based decoding can still be efficiently performed in a recursive manner by using a data flow graph with butterfly structure as in conventional polar decoding.

We consider low-complexity decoding of generalized second-order Reed-Muller frames. Second-order Reed-Muller frames are highly non-coherent, highly-structured, sets of $2^{m_{-}}$ dimensional complex vectors with fourth root-of-unity alphabet, that come by design with a low-complexity chirp reconstruction algorithm (ChirpRA). In this paper, we extend ChirpRA to expanded frames in 2m-dimension with same alphabet, and we also generalized it to Reed-Muller frames in other dimensions constructed from different alphabets.

5G physical random access channel (PRACH) uses several new preamble formats with less Zadoff-Chu (ZC) sequences available for the network than with formats inherited from LTE. We thus recently proposed an enlarged 5G PRACH preamble construction by covering ZC sequences with cubic-phase Alltop sequences. This construction significantly increases the PRACH sequence set while maintaining a similar intra-cell detection performance from a guaranteed low-correlation zone, and with limited inter-cell interference. However, unlike ZC, the new sequences did not come with a low-complexity PRACH detection which then had to naively rely on an exhaustive search, significantly increasing the PRACH receiver complexity. In this paper, we revisit this extended PRACH sequence construction and modify it to enable a detection of the same complexity-order as current 5G PRACH sequence set, without impacting the detection performance and promised PRACH capacity. Moreover, we describe a symmetrical but slightly non-equivalent PRACH sequence construction that achieves a similar performance and enables the same low-detection capability. Interestingly, this latter construction can be reduced to show that only pure Alltop and ZC sequences may concurrently be used in the network.

In the context of coverage enhancement of 5G uplink control channel, we propose a non-coherent signaling based on 2nd-order Reed-Muller constellations that come by design with a low-complexity chirp reconstruction algorithm (ChirpRA). Non-coherent multi-dimensional constellations are known to provide performance gains but often believed to be at the cost of an increased detection complexity. We show, in a practical and realistic setting, that in fact the proposed non-coherent design with the discussed low-complexity decoding algorithms still enables improving the 5G uplink control channel performance and decreasing the receiver complexity. The presented detection algorithms notably include: a low-complexity principal component computation enabling to apply ChirpRA to multiple receiver antenna signals without extra complexity, as well as enhancements of the original ChirpRA that improve performance and/or decrease detection complexity; which both are of independent interest.

A channel delay spread larger than the cyclic prefix (CP) creates inter-carrier/symbol interference (ISI/ICI) in orthogonal frequency-division multiplexing (OFDM). Recent interests in low-latency applications have motivated the usage of shorter OFDM symbols where one can either downscale the CP at the cost of interference, or maintain it but with larger overhead. Alternatively, this paper studies channel shortening methods exploiting the properties of large multi-antenna precoding in order to steer the transmitted signal energy toward channel paths inside an insufficient CP. It is shown that ISI/ICI can asymptotically be canceled by conventional subcarrier-based precoding with an infinite number of antennas. This is achieved by introducing time-delay selectivity inside frequency-selective precoders in order to remove undesired delayed signals, providing a trade-off between interference mitigation and multi-path combining gains, and leading to subsequent gains in high SNR. This frequency-domain precoding method, coined time-frequency (TF) precoding, is compared to time-reversal (TR) filtering whose asymptotic rate is optimal but introduces post-modulation processing with channel-dependent signal distortion. In addition to maintain the legacy precoded multi-antenna OFDM structure, finite-size analysis shows that TF-precoding converges faster to its asymptotic rate than TR-filtering, so that TF-precoding can outperform TR-filtering in the high-SNR regime with not-so-many antennas.

Grassmannian frames in composite dimensions D are constructed as a collection of orthogonal bases where each is the element-wise product of a mask sequence with a generalized Hadamard matrix. The set of mask sequences is obtained by exponentiation of a q-root of unity by different quadratic forms with m variables, where q and m are the product of the unique primes and total number of primes, respectively, in the prime decomposition of D. This method is a generalization of a well-known construction of mutually unbiased bases, as well as second-order Reed-Muller Grassmannian frames for power-of-two dimension D = 2m, and allows to derive highly symmetric nested families of frames with finite alphabet. Explicit sets of symmetric matrices defining quadratic forms leading to constructions in non-prime-power dimension with good distance properties are identified.

The high-SNR capacity of a block-faded non-coherent channel can be achieved by a multi-dimensional Grassmannian modulation. This paper proposes an analytical quasi-Gray labelling for Reed-Muller Grassmannian constellations. The proposed labelling method enables to reduce the block error rate (BLER) of a system with error correction code, by minimizing the average Hamming distance between labels of neighboring modulation symbols. In particular, we first define an inherent generation label from which the Reed-Muller Grassmannian constellation is constructed, and show it fulfills a homogeneity property. Based on this, a bijective linear mapping between a quasi-Gray labelling and the former labelling is proposed, where the bijective linear mapping matrix is obtained by a low-complexity algorithm. Numerical results show that the proposed quasi-Gray labelling method can achieve 40% reduction of the average Hamming distance between neighboring modulation symbols compared to the generation label or random labelling. Finally, link-level simulation results further demonstrate that the proposed quasi-Gray labelling can effectively reduce the BLER.

5G physical random access channel (PRACH) will use new preamble formats based on short Zadoff-Chu (ZC) sequences to enable new use cases. These formats result however in a PRACH capacity shortfall where the number of sequences available for network planning may just be enough to support few cells without sequence reuse. To overcome this issue, two enlarged constant-amplitude sequence constructions that include ZC sequences, and thus being backward-compatible with the current 5G PRACH design, are presented. Both constructions feature a desirable subset structure from which follows a natural cellular network sequence allocation where each cell-specific sequence subset has a controllable low-correlation zone similar to ZC sequences, and thus enables a similar detection performance inside a cell. The two extensions are meanwhile structurally different and offer different network allocations, as for one, new sequences are distributed among all cells, while for the other, they are in separated cells. With both proposed supersets and the new 5G PRACH formats, hundred-times more cells without sequence reuse can be supported compared to ZC sequences for a moderately larger inter-cell correlation than intra-cell correlation. Simulation results confirm that using the proposed supersets instead of reusing sequences in the network can significantly improve detection performance.

We consider measures of time-frequency localization (TFL) for stochastic signals. The approach is complementary to the use of TFL in prototype filter design; here, TFL is instead applied to multiplexed waveform packets with the objective to evaluate multi-user interference in a multiple access scenario rather than combat channel dispersion. We show that a generalization of the Heisenberg parameter to N-D stochastic signals directly characterizes the localization of the inter-user interference in the time-frequency phase space. A tight bound is provided, which shows the fundamental tradeoff between the TFL of a packet and the orthogonality among the multiplexed waveforms inside the packet. The Hermite-Gauss waveforms are optimally localized with regard to this measure. We also derive the expressions for the TFL of a Gabor system consisting of Nttime and Nffrequency shifts of a prototype, on the conventional and staggered lattices. In the limit of large N, the particular properties of the prototype yield diminishing returns to the overall localization. Finally, we compare the performance of waveforms in a connectionless and asynchronous random access scenario. At lower access intensities, where the out-of-band emissions are the significant limiting factor, the outage probability for smaller access packets is shown to vary significantly between the modulations. This variability diminishes when N is increased, which is consistent with the presented theory.

A cyclic prefix (CP) for an orthogonal frequency division multiplexing (OFDM) transmission shorter than the maximum delay spread of the channel results into inter-symbol interference (ISI) and inter-carrier interference (ICI). This paper shows that an appropriate frequency-domain multi-antenna (MIMO) precoding for OFDM can asymptotically cancel out ISI/ICI as the number of antennas goes to infinity. The method is based on introducing time-delay selectivity over the channel taps from which a conventional frequency-domain precoding method can be based on. This time-selectivity enables to asymptotically remove undesired delayed signals, while the frequency-selectivity in the precoders is preserved to suit the conventional MIMO-OFDM air interface where precoding is applied on a subcarrier level. Analysis reveals an optimization trade-off in the precoding design between interference removal and multi-path diversity gain. The resulting optimized precoders are shown to provide subsequent gains in asymptotic achievable rate with infinite number of antennas, as well as in symbol-error-rate performance of a moderate finite-antenna system.

5G physical random access channel (PRACH) will use several new preamble formats in order to enable new use cases. These new formats, however, results in a PRACH capacity shortfall. In this paper, we propose a solution based on an extension of the LTE PRACH sequence set. Cell-specific sequences are derived from single-root Zadoff-Chu (ZC) sequences with a zero-correlation zone, and if necessary, different m-sequence covers instead of multiple roots as in LTE. While this construction is shown to preserve a similar low-correlation zone as with the LTE design, it does not consume the other ZC roots which can then be used to support more cells. The proposed PRACH design is evaluated by 5G link-level simulations to verify the expected good detection performance and low PAPR.

The density of a code is the fraction of the coding space covered by packing balls centered around the codewords. A high density indicates that a code performs well when used as a uniform point-wise discretization of an ambient space. This paper investigates the density of codes in the complex Stiefel and Grassmann manifolds equipped with the chordal distance arising from an Euclidean embedding, including the unitary group as a special case. The choice of distance enables the treatment of the manifolds as subspaces of Euclidean hyperspheres. In this geometry, the densest packings are not necessarily equivalent to maximum-minimum-distance codes. Computing a code's density follows from computing: 1) the normalized volume of a metric ball and 2) the kissing radius, the radius of the largest balls one can pack around the codewords without overlapping. First, the normalized volume of a metric ball is evaluated by asymptotic approximations. The volume of a small ball can be well-approximated by the volume of a locally equivalent tangential ball. In order to properly normalize this approximation, the precise volumes of the manifolds induced by their spherical embedding are computed. For larger balls, a hyperspherical cap approximation is used, which is justified by a volume comparison theorem showing that the normalized volume of a ball in the Stiefel or Grassmann manifold is asymptotically equal to the normalized volume of a ball in its embedding sphere as the dimension grows to infinity. Then, bounds on the kissing radius are derived alongside corresponding bounds on the density. Unlike spherical codes or codes in flat spaces, the kissing radius of Grassmann or Stiefel codes cannot be exactly determined from its minimum distance. It is nonetheless possible to derive bounds on density as functions of the minimum distance. Stiefel and Grassmann codes have larger density than their image spherical codes when dimensions tend to infinity. Finally, the bounds on density lead to refinements of the standard Hamming bounds for Stiefel and Grassmann codes.

This paper investigates the application of N-continuous spectral projection precoding design to single-carrier frequency-division multiple access (SC-FDMA). It first considers a general orthogonal projection-based precoded system with an improved iterative receiver and analyzes its ultimate performance in an additive white Gaussian noise channel, both in terms of achievable throughput and symbol-error rates. For N-continuous SC-FDMA, the distribution of the symbol errors is very much asymmetric; a few base pulses carry the lion share of the self-induced interference, resulting in a zero throughput. We show that an optimized transmission and reception scheme based on a polarized use of the base pulses can satisfactorily deal with this asymmetry, and the end-to-end throughput can be recovered to be close to optimal. Applying a similar scheme to N-continuous OFDM enables also an improved performance in the high-SNR regime, where the interference effect strikes the most.

Volume estimates of metric balls in manifolds find diverse applications in information and coding theory. In this paper, new results for the volume of a metric ball in unitary group are derived via tools from random matrix theory. The first result is an integral representation of the exact volume, which involves a Toeplitz determinant of Bessel functions. A simple but accurate limiting volume formula is then obtained by invoking Szegö's strong limit theorem for large Toeplitz matrices. The derived asymptotic volume formula enables analytical evaluation of some coding-theoretic bounds of unitary codes. In particular, the Gilbert-Varshamov lower bound and the Hamming upper bound on the cardinality as well as the resulting bounds on code rate and minimum distance are derived. Moreover, bounds on the scaling law of code rate are found. Finally, a closed-form bound on the diversity sum relevant to unitary space-time codes is obtained, which was only computed numerically in the literature.

Volume of metric balls relates to rate-distortion theory and packing bounds on codes. In this paper, the volume of balls in complex Grassmann manifolds is evaluated for an arbitrary radius. The ball is defined as a set of hyperplanes of a fixed dimension with reference to a center of possibly different dimensions, and a generalized chordal distance for unequal dimensional subspaces is used. First, the volume is reduced to a 1-D integral representation. The overall problem boils down to evaluating a determinant of a matrix of the same size as the subspace dimensionality. Interpreting this determinant as a characteristic function of the Jacobi ensemble, an asymptotic analysis is carried out. The obtained asymptotic volume is moreover refined using moment-matching techniques to provide a tighter approximation in finite-size regimes. Finally, the pertinence of the derived results is shown by rate-distortion analysis of source coding on Grassmann manifolds.

We investigate the use of non-binary classical error-correcting codes in facilitating reliable, entanglement-assisted communication of classical information over quantum depolarising channels. A classical-quantum communication system is presented, which relies on error-correction in the classical domain to achieve an information rate that approaches the entanglement-assisted capacity of the quantum channel. Classical information is transmitted over the channel by means of the superdense coding protocol, and the impact of the noisy distribution of initial entanglement resources on the achievable information rate is considered. In this context, the transmission model is equivalent to a non-binary discrete symmetric classical channel, which motivates the use of non-binary error-correcting codes capable of exploiting correlations between the pairs of classical bits communicated via the superdense coding protocol. We illustrate this principle by showing that duo-binary turbo codes significantly outperform binary turbo codes in the considered scenarios.

Volume estimates of metric balls in manifolds find diverse applications in communications and information theory. In this paper, we derive some new results for the volume of a metric ball in unitary group under Frobenius norm topological metric. Our first result is an integral representation of the exact volume, which involves a Toeplitz determinant of Bessel functions. The connection to matrix-variate hypergeometric functions leads from the exact finite size formula to an asymptotic one. The convergence of the obtained limiting formula is exceptionally fast due to the underlying mock-Gaussian behavior.

This paper provides a proof of global convergence of gradient search for low-rank matrix approximation. Such approximations have recently been of interest for large-scale problems, as well as for dictionary learning for sparse signal representations and matrix completion. The proof is based on the interpretation of the problem as an optimization on the Grassmann manifold and Fubiny-Study distance on this space.

We consider product codebook strategy where a single small codebook is implemented at the receiver to quantize larger multi-input multi-output (MIMO) channels, e.g. aggregate channels of cooperative MIMO base stations. The present work focuses on the codebook design, codebook construction, and codeword selection under this scenario, for single- or multistream MIMO transmission. Designing point-to-point unitary precoding codebook is related to a discretization problem on the Grassmann manifold, where a Grassmannian codeword is an equivalence class of rectangular-unitary/Stiefel matrices. For practical needs, one has to choose the rectangular unitary matrix to represent each Grassmann codeword. In this paper, we choose appropriate representatives so that product codebook quantization becomes competitive with global Grassmannian quantization. For this, we propose a novel joint Grassmann-Stiefel codebook design aiming at good quantization/discretization of Grassmann and Stiefel manifolds with a single codebook. To find low-distortion codebooks, we present a vector quantizer generating a Stiefel codebook conditioned on a fixed Grassmann codebook. For this purpose, we provide an exact solution for computing centroids in the Stiefel manifold with chordal distance. Furthermore, concrete examples of analytical joint Grassmann-Stiefel packings are given. Finally, we discuss low-complexity codeword selection methods.

We discuss group orbits codes in homogeneous spaces for the unitary group, known as flag manifolds. The distances used to describe the codes arise from embedding the flag manifolds into Euclidean hyperspheres, providing a generalization of the spherical embedding of Grassmann manifolds equipped with the so-called chordal distance. Flag orbits are constructed by acting with a unitary representation of a finite group. In the construction, the center of the finite group has no effect, and thus it is sufficient to consider its inner automorphism group. Accordingly, some explicit constructions from projective unitary representations of finite groups in 2 and 4 dimensions are described. We conclude with examples of codes on the Stiefel manifold constructed as orbits of the linear representation of the projective groups, and thus expansion of the flag codes considered.

A new approach to relay and user selection is proposed using threshold-based transmission to reduce outage probability and save transmit power. By exploiting properties of dual-hop transmission using amplify-and-forward (AF) relaying, new threshold-based relay and user (TRU) selection protocols that employ one-bit channel state information (CSI) feedback are proposed for multiple-relay, multiple-user systems. These new protocols have the advantages of (1) economical feedback, and (2) optional adaptive power-saving transmission. Centralized selection (CS) and distributed selection (DS) policies as well as lower-complexity suboptimal selection schemes are investigated for downlink transmission. Exact expressions for outage probability, outage diversity and feedback requirement are provided to quantify the complexity/performance trade-offs. The analysis shows that selection threshold(s) can be chosen such that transmission is interrupted when system outage is certain, which allows power saving without impairing outage performance. These protocols are compared in terms of performance, energy-efficiency and system requirement to others that trade outage performance for additional energy saving and/or reduced complexity.

Base station cooperation is expected to enhance spectrum efficiency of future cellular system. Performance heavily depends on the channel state information available at the transmitter. In practical systems, channel information are acquire through a limited feedback channel. Typically, quantization of the channel at the receiver side is done with a fixed pre-designed codebook. In this paper, we consider the codebook design and codeword selection problem when a product codebook is employed, reusing a point-to-point codebook. Point-to-point codebooks are often designed as Grassmannian packings. To improve the performance of the codebook for base station cooperation without impairing the performance for single cell transmission, we propose a novel joint Grassmann-Stiefel codebook design. In addition, we propose a method for independently selecting the per-cell codewords by using a distance on the Stiefel manifold.

A construction of Grassmannian packings related to representation theory is applied to build implementation-friendly MIMO precoding codebooks when the number of transmit antennas is a power of a prime. Using the chordal distance as a metric, some of the corresponding packings appear to be optimal by meeting the othoplex bound. Also, by using only some of the codewords, smaller packings satisfying the equal power per antenna constraint may be found. Optimality with reference to this constraint may be shown by using a modification of the Conway-Hardin-Sloane's spherical embedding of the Grassmann manifold for equal per-antenna codebooks.

We investigate the density of codes in the complex Grassmann manifolds Gℂn,pequipped with the chordal distance. The density of a code is defined as the fraction of the Grassmannian covered by `kissing' balls of equal radius centered around the codewords. The kissing radius cannot be determined solely from the minimum distance, nonetheless upper and lower bounds as a function of minimum distance only are provided, along with the corresponding bounds on the density. This leads to a refinement of the Hamming bound for Grassmannian codes. Finally, we provide explicit bounds on code cardinality and minimum distance, notably a generalization of a bound on minimum distance previously proven only for line packing (p = 1).

Precoding codebook design for limited feedback MIMO systems is known to reduce to a discretization problem on a Grassmann manifold. The case of two-antenna beamforming is special in that it is equivalent to quantizing the real sphere. The isometry between the Grassmannian G2,1ℂand the real sphereS2shows that discretization problems in the Grassmannian G2,1ℂare directly solved by corresponding spherical codes. Notably, the Grassmannian line packing problem in ℂ2, namely maximizing the minimum distance, is equivalent to the Tammes problem on the real sphere, so that optimum spherical packings give optimum Grassmannian packings. Moreover, a simple isomorphism between G2,1ℂandS2enables to analytically derive simple codebooks in closed-form having low implementation complexity. Using the simple geometry of some of these codebooks, we derive closed-form expressions of the probability density function of the relative SNR loss due to limited feedback. We also investigate codebooks based on other spherical arrangements, such as solutions maximizing the harmonic mean of the mutual distances among the codewords, which is known as the Thomson problem. We find that in some special cases, Grassmannian codebooks based on these other spherical arrangements outperform codebooks from Grassmannian packing.

We investigate the impact of fixed relay station deployment in a single frequency network (SFN) using orthogonal frequency-division multiplexing (OFDM). We provide semi-analytical methods for relay-based SFN performance evaluation. Monte Carlo simulations are performed to provide numerical calculation of multi-cell network performance. The performance metric is the cumulative distribution function of the signal-to-interference-plus-noise-ratio (SINR) for different user positions in the network. Common relaying methods for two-hop amplify-and-forward (A&F) relay networks are evaluated. The impact on the SINR is compared for different relaying gains, locations and densities of relays, as well as different transmission protocols, such as full-duplex (FD) and half-duplex (HD). Overall, taking into account their different rates and physical layer performances, FD appears to outperform HD. In addition to showing the benefit of relay deployment for enhancing network performance, our simulations show that the fixed and variable gains perform equally well.