In the quest for efficient multiple access schemes for future wireless systems, sparse code-domain non-orthogonal multiple access (NOMA) has gained considerable interest, potentially achieving significant performance enhancement in overloaded settings at feasible complexity. This paper revisits an uplink model with two classes of users distinguished by their received powers, each employing regular sparse code-domain NOMA (where a fixed and finite number of orthogonal resources is occupied by each user and vice versa). Introducing random coordinate transformations, the achievable ergodic class throughput region is analytically specified in the large system limit, and shown to strictly contain the achievable region with randomly spread dense code-domain NOMA, while closing the gap to the Cover-Wyner capacity region. Furthermore, harnessing tools from free probability theory, an exact closed form expression is derived for the total achievable sum-rate, which has been so far characterized in analogous settings by means of lower and upper bounds. The analysis significantly broadens the information theoretic perspective on code-domain NOMA applications, and establishes key tools for generalizing the results to more complex models for future systems.

Spectrally efficient non-orthogonal multiple access (NOMA) schemes are of paramount importance for 5G and beyond wireless networks, among which code-domain NOMA is a prominent technology. Two extreme paradigms have lead to analytically tractable benchmarks for code-domain NOMA performance. The first relies on independent random dense spreading signatures (fully utilizing the available orthogonal resources) and suits settings with sporadic user activity, where signature coordination is hard to enforce. The second paradigm is regular sparse NOMA (where a small fixed number of resources is allocated to each user, and vice versa). It exhibits superior performance, while facilitating near-optimal multiuser detection using iterative message-passing algorithms. However, it also requires fully coordinated signatures and might be impractical in certain use-cases. In this paper, we investigate for the first time a mixed setting, where one class of users obeys the latter paradigm, while a second class obeys the former. The achievable ergodic class-throughput region is derived, while considering the large-system limit. Particularly, the total achievable sum-rate is characterized by means of a free additive convolution of probability measures, while relying on a recent strong representation theorem. The corresponding low-SNR characterization is further shown to admit closed-form expressions. The analysis provides insightful tools for investigating various use-cases of interest for future networks.

Non-orthogonal multiple access (NOMA) is a promising technology in the design of efficient state-of-the-art communication, particularly 5G and beyond cellular systems. Understanding its fundamental information-theoretic limits is hence of paramount interest. This paper focuses on regular sparse NOMA (where only a fixed and finite number of orthogonal resources is allocated to any designated user, and vice versa), and extends a previous analysis by the authors to a setting where the system comprises two classes of users with different power constraints. Explicit rigorous closed-form analytical inner and outer bounds on the achievable rate (total class throughput) region in the large-system limit are derived. The inner bound is based on the conditional vector entropy power inequality (EPI), while the outer bound relies on a recent strengthened version of the EPI by Courtade. The closed-form bounds provide valuable insights into the potential performance gains of regular sparse NOMA in practically oriented settings, comprising, e.g., a combination of low-complexity devices and broadband users with higher transmit power capabilities, or combinations of cell-edge users with users located close to the cell center. Conditions are identified where superior performance over dense code-domain NOMA is guaranteed, and a relatively small gap to the ultimate performance limits is attainable. The bounds may also serve as a useful tool for future analyses involving interference networks, as, e.g., Wyner-type cellular models.

Understanding fundamental limits of the various technologies suggested for future 5G and beyond cellular systems is crucial for developing efficient state-of-the-art designs. A leading technology of major interest is non-orthogonal multiple-access (NOMA). In this paper, we derive an explicit rigorous closed-form analytical expression for the optimum spectral efficiency in the large-system limit of regular sparse NOMA, where only a fixed and finite number of orthogonal resources are allocated to any designated user, and vice versa. The basic Verdú-Shamai formula for (dense) randomly-spread code-division multiple-access (RS-CDMA) turns out to coincide with the limit of the derived expression, when the number of orthogonal resources per user grows large. Furthermore, regular sparse NOMA is rigorously shown to be spectrally more efficient than RS-CDMA across the entire system load range. It may therefore serve as an efficient means for reducing the throughput gap to orthogonal transmission in the underloaded regime, and to the ultimate Cover-Wyner bound in overloaded systems. The results analytically reinforce preliminary conclusions in [1], which mostly relied on heuristics and numerical observations. The spectral efficiency is also derived in closed form for the sub-optimal linear minimum-mean-square-error (LMMSE) receiver, which again extends the corresponding Verdti-Shamai LMMSE formula to regular sparse NOMA.

A closed-form analytical expression is derived for the limiting empirical squared singular value density of a spreading (signature) matrix corresponding to sparse low-density code-domain (LDCD) non-orthogonal multiple-access (NOMA) with regular random user-resource allocation. The derivation relies on associating the spreading matrix with the adjacency matrix of a large semiregular bipartite graph. For a simple repetition-based sparse spreading scheme, the result directly follows from a rigorous analysis of spectral measures of infinite graphs. Turning to random (sparse) binary spreading, we harness the cavity method from statistical physics, and show that the limiting spectral density coincides in both cases. Next, we use this density to compute the normalized input-output mutual information of the underlying vector channel in the large-system limit. The latter may be interpreted as the achievable total throughput per dimension with optimum processing in a corresponding multiple-access channel setting or, alternatively, in a fully-symmetric broadcast channel setting with full decoding capabilities at each receiver. Surprisingly, the total throughput of regular LDCD-NOMA is found to be not only superior to that achieved with irregular user-resource allocation, but also to the total throughput of dense randomly-spread NOMA, for which optimum processing is computationally intractable. In contrast, the superior performance of regular LDCD-NOMA can be potentially achieved with a feasible message-passing algorithm. This observation may advocate employing regular, rather than irregular, LDCD-NOMA in 5G cellular physical layer design.

Interference mitigation is central in enhancing the total throughput of wireless systems. Efficient mitigation requires, however, accurate channel state information, which puts a heavy load on the wireless control channels. In this paper, we focus on the multiple-input single-output (MISO) interference channel, and propose a novel enhanced CSI feedback scheme that reduces the feedback overhead required for conveying cross-link CSI to the transmitters. For simplicity, we consider a two-user setting, where single user decoding is employed while treating interference as noise. The proposed scheme creates, by projecting the original channels into an appropriately chosen low-dimensional subspace, an effective cross-link channel which can be quantized more accurately for a given number of quantization bits. The idea is to choose the new subspace such that the effective cross-link channel, as well as the direct channel, maintain their array gain. We show via a comprehensive numerical study that the proposed scheme offers a significant reduction of CSI feedback overhead. By providing much more accurate CSI at the transmitters, while maintaining high array gains, the scheme allows for enhanced interference mitigation, and increases the total network throughput.

This paper studies the Rayleigh fading two-user multiple-input single-output interference channel with single user decoding and limited channel state information (CSI) feedback. Two contributions are presented. First, the achievable rate-region with partial CSI at the transmitters due to channel quantization errors is analyzed. We derive an analytically tractable inner bound on that region, which provides insights into the problem. It is shown that, similarly to the case of perfect transmitter CSI, beamforming is optimal for achieving every boundary point of the inner bound. The second contribution is a novel CSI feedback scheme that reduces the cross-link CSI feedback overhead, and enhances throughput for any rate-limited feedback scheme. Such feedback reduction is crucial when control channels for sharing information between transmitters and unintended receivers are rate limited. The proposed scheme takes feedback into account already at the channel estimation stage. While maintaining a high array gain in the direct channel towards the intended user, the scheme induces an effective low-dimensional cross-link channel, which can be quantized more accurately than the full-dimensional channel, leading to enhanced performance.

Precoding schemes in the framework of vector perturbation (VP) for the multiple-input multiple-output (MIMO) Gaussian broadcast channel (GBC) are investigated. The VP scheme, originally a “one-shot” technique, is generalized to encompass processing over multiple time instances. Using lattice-based extended alphabets (“perturbations”), and considering the infinite time-span extension limit, a lower bound on the achievable sum-rate using the generalized VP scheme is analytically obtained. The lower bound is shown to asymptotically achieve the optimum sum-rate in the high signal-to-noise ratio (SNR) regime (both in terms of degrees-of-freedom and power offset), for any number of users and transmit antennas. For the two-user cases, it is shown that the lower bound coincides with the sum-capacity for low SNR. The above lower bound is constructively obtained by means of an efficient practically oriented suboptimal transmit energy minimization algorithm, which exhibits a polynomial complexity in the number of users. The proposed precoding scheme demonstrates that the “shaping gain” is achievable for VP schemes, when employing “good” multidimensional lattices. It is also shown that the suboptimum algorithm has its merits, even when processing over multiple time instances is not employed. For the $2\times 2$ MIMO GBC, the VP scheme is generalized further, and an inner bound for the entire achievable rate region is obtained, by which an interesting correspondence is identified with the ultimate capacity region, as obtained by “dirty paper coding”.

Virtually rotating antennas, which rotate once or several times during a symbol interval, have been considered in recent years as a compact (in volume) alternative for achieving additional degrees of freedom compared to standard multiple antenna receivers. Antenna rotation effectively induces bandwidth expansion at the receiver, which in turn increases the effective dimensionality, and may potentially allow for spatial multiplexing. However, in a licensed spectrum such bandwidth expansion also introduces interference from signals transmitted in adjacent frequency bands. This paper investigates to what extent such adjacent channel interference can be mitigated by appropriate signal processing. The potentially achievable throughput of systems employingmultiplevirtually rotating antennas is examined analytically in a multiuser setting, while considering the large system limit, and employing random matrix theory tools. The analysis focuses on the linear minimum mean-square error (MMSE) receiver, and a receiver that optimally decodes the transmissions of desired users, while being unaware of the codebooks of interferers. The achievable throughput is compared to the corresponding throughputs of standard multiple antenna receivers employing the same number of physicalactiveantenna elements. Conditions for virtually rotating antennas to be beneficial are identified, which when met are shown to lead to significant performance enhancement over standard multiple antenna receivers.

In this paper, we consider the finite-state multiple access channel (MAC) with partially cooperative encoders and delayed channel state information (CSI). Here, partial cooperation refers to the communication between the encoders via finite-capacity links. The channel states are assumed to be governed by a Markov process. Full CSI is assumed at the receiver, while at the transmitters, only delayed CSI is available. The capacity region of this channel model is derived by first solving the case of the finite-state MAC with a common message. Achievability for the latter case is established using the notion of strategies, however, we show that optimal codes can be constructed directly over the input alphabet. This results in a single codebook construction that is then leveraged to apply simultaneous joint decoding. Simultaneous decoding is crucial here because it circumvents the need to rely on the capacity region's corner points, a task that becomes increasingly cumbersome with the growth in the number of messages to be sent. The common message result is then used to derive the capacity region for the case with partially cooperating encoders. Next, we apply this general result to the special case of the Gaussian vector MAC with diagonal channel transfer matrices, which is suitable for modeling, e.g., orthogonal frequency division multiplexing-based communication systems. The capacity region of the Gaussian channel is presented in terms of a convex optimization problem that can be solved efficiently using numerical tools. The region is derived by first presenting an outer bound on the general capacity region and then suggesting a specific input distribution that achieves this bound. Finally, numerical results are provided that give valuable insight into the practical implications of optimally using conferencing to maximize the transmission rates.

“Layered” rate-splitting based transmission strategies are investigated for the uplink of cellular communication systems employing clustered cooperative processing. Accordingly, partial decoding of some received out-of-cluster “layers” is employed, while undecoded “layers” are treated as noise. A two-dimensional Wyner-type system model is considered, by which only adjacent cell interference is present and characterized by a single parameter α ∊ (0, 1]. Focusing on the average throughput per cell, the setting is shown to be equivalent to a certain multiple-input multiple-output (MIMO) multiple access channel (MAC). An achievable average throughput is then obtained by efficiently solving an appropriately formalized Complementary Geometric Programming (CGP) problem. Singnificant performance enhancement is demonstrated compared to non-cooperative single-cell processing, as well as to “naive” cooperation, where out-of-cluster interference is treated as noise.

In this paper, a single-letter characterization for the capacity region of finite-state multiple access channels (MACs) with partially cooperative encoders is derived. Partial cooperation here is in the sense that the encoders communicate with each other through finite-capacity links. The channel states are assumed to be governed by a Markov processes. Full channel state information (CSI) is assumed at the receiver, while only delayed CSI is available at transmitters. The capacity region is derived by first solving the case of finite-state multiple access channels with common message, using rate splitting, multiplexing and simultaneous decoding in order to establish the achievability. The common message result is then used to derive the capacity region of the partially cooperative encoders case. Finally, we apply this result in order to obtain the capacity region for a finite-state Gaussian MAC with partially cooperative encoders.

The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of input alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

There are a number of corrections for the above titled paper (ibid., vol. 58, no. 3, pp. 1413-1440, Mar. 2012). They are presented here.

Precoding schemes in the framework of vector perturbation (VP) for the multiple-input multiple-output (MIMO) Gaussian broadcast channel (GBC) are investigated. The VP scheme, originally a “one-shot” technique, is generalized to encompass processing over multiple time instances. Using lattice-based extended alphabets (“perturbations”), and considering the infinite time-span extension limit, a lower bound on the achievable sum-rate using the generalized VP scheme is analytically obtained, by which it is shown to achieve the optimum sum-rate in the high signal-to-noise ratio (SNR) regime (both in terms of degrees-of-freedom and power offset). The above lower bound is constructively obtained by means of an efficient practically oriented suboptimum transmit energy minimization algorithm, which has merits of its own, and it demonstrates the significant performance enhancement that can be obtained by preprocessing over multiple symbol instances, potentially eliminating the gap to the ultimate performance at high SNRs. For the 2×2 MIMO GBC, the VP scheme is generalized further, and an inner bound for the entire achievable rate region is obtained, by which an interesting correspondence is identified to the ultimate capacity region, as obtained by “dirty paper” coding (DPC).

In this paper, we investigate the spectral efficiency of vector precoding with minimum mean square error (MMSE) linear preprocessing. We restrict the discussion to the spectral efficiency of MMSE vector precoding with quadrature phase-shift keying (QPSK) signaling. Spectral efficiency is investigated by numerical simulations, and plotted as a function of the energy per bit divided by the noise spectral density Eb/N0. The optimum system load α, given as the ratio of the number of transmit and receive antennas, that maximizes spectral efficiency is obtained. Previously obtained spectral efficiency results for: Dirty paper coding (DPC), linear zero forcing (ZF), ZF vector precoding, and linear MMSE precoding are provided for comparison. We quantify the performance enhancement that MMSE vector precoding obtains in comparison to vector precoding with ZF linear preprocessing, in the low to medium Eb/N0region. We also find that MMSE vector precoding does not significantly outperform its linear counterpart.

Recent information theoretic results on cooperation in cellular systems are reviewed, addressing both multicell processing (cooperation among base stations) and relaying (cooperation at the user level). Two central issues are addressed, namely, first multicell processing is studied with either limited-capacity backhaul links to a central processor or only local (and finite-capacity) cooperation among neighboring cells. The role of codebook information, decoding delay and network planning (frequency reuse) are specifically highlighted along with the impact of different transmission/ reception strategies. Next, multicell processing is considered in the presence of cooperation at the user level, focusing on both out-of-band relaying via conferencing users and in-band relaying by means of dedicated relays. Non-fading and fading uplink and downlink channels adhering to simple Wyner-type, cellular system models are targeted.

Achip-interleavedrandomly spread direct-sequence code-division multiple-access (DS-CDMA) scheme is considered, employed in two variants of Wyner's infinite linear cell-array model with flat fading. Focusing on the asymptotic setup in which both the number of users per cell and the processing gain go to infinity, while their ratio (the “cell load”) goes to some finite constant, the spectral efficiencies of the optimum and linear minimum mean-squared error (MMSE)joint multicell receiversare investigated. A dramatic performance enhancement as compared tosingle-cell-site processing is demonstrated. The asymptotic behavior of the two receivers in extreme signal-to-noise ratio (SNR) regimes and in a high cell-load regime are analyzed as well. The impact of chip interleaving versus symbol interleaving is also investigated. Chip-level interleaving is found beneficial in several cases of interests, and is conjectured to be beneficial in general.

The sum-rate capacity of a cellular system model is analyzed, considering the uplink and downlink channels, while addressing both nonfading and flat-fading channels. The focus is on a simple Wyner-like multicell model, where the system cells are arranged on a circle, and the cell sites are located at the boundaries of the cells. For the uplink channel, analytical expressions of the sum-rate capacities are derived for intra-cell time-division multiple-access (TDMA) scheduling, and a “wideband” (WB) scheme (where all users are active simultaneously utilizing all bandwidths for coding). Assuming individual equal per-cell power constraints, and using the Lagrangian uplink–downlink duality principle, an analytical expression for the sum-rate capacity of the downlink channel is derived for nonfading channels, and shown to coincide with the corresponding uplink result. Introducing flat-fading, lower and upper bounds on the average per-cell ergodic sum-rate capacity are derived. The bounds exhibit an$O(\log _{e} K)$multiuser diversity factor for a number of users per cell$K\gg 1$, in addition to the array diversity gain. Joint multicell processing is shown to eliminate out-of-cell interference, which is traditionally considered to be a limiting factor in high-rate reliable communications.

We consider a chip-interleaved randomly spread DS-CDMA scheme employed in Wyner's infinite linear cell-array model with flat fading. Focusing on the asymptotic setup, the per-cell spectral efficiencies of the optimum and linear MMSE joint multicell receivers are considered. Performance enhancement as compared to single-cell-site processing is demonstrated. The asymptotic behavior of the two receivers in extreme SNR regimes and in a high cell-load setup is analyzed as well. The impact of chip interleaving vs. symbol interleaving is also considered.

A simple multi-cell Rayleigh fading uplink communication model is suggested and analyzed for optimally coded randomly spread DS-CDMA with multiuser detection. The model adheres to Wyner's (1994) infinite linear cell-array setting, according to which only adjacent-cell interference is present, and characterized by a single parameter 0/spl les//spl alpha//spl les/1. The discussion is confined to asymptotic analysis where both the number of users per cell and the processing gain go to infinity, while their ratio goes to some finite constant. The spectral efficiency of various multiuser detection strategies is evaluated assuming single cell-site processing, and equal transmit powers for all users in all cells. Comparative results demonstrate how performance is affected by the introduction of inter-cell interference (with and without fading), and what is the penalty associated with the randomly spread coded DS-CDMA strategy.

A simple multicell uplink communication model is suggested and analyzed for optimally coded randomly spread direct sequence code-division multiple access (DS-CDMA). The model adheres to Wyner's (1994) infinite linear cell-array model, according to which only adjacent-cell interference is present, and characterized by a single parameter 0/spl les//spl alpha//spl les/1. The discussion is confined to asymptotic analysis where both the number of users and the processing gain go to infinity, while their ratio goes to some finite constant. Single cell-site processing is assumed and four multiuser detection strategies are considered: the matched-filter detector, "optimum" detection with adjacent-cell interference treated as Gaussian noise, the linear minimum mean square error (MMSE) detector and a detector that performs MMSE-based successive interference cancellation for intracell users with linear MMSE processing of adjacent-cell interference. Spectral efficiency is evaluated under three power allocation policies: equal received powers (for all users), equal rates, and a maximal spectral efficiency policy. Comparative results demonstrate how performance is affected by the introduction of intercell interference, and what is the penalty associated with the randomly spread coded DS-CDMA strategy. Finally, the effect of intercell time-sharing protocols as suggested by Shamai and Wyner (1997) is also examined, and a significant system performance enhancement is observed.