There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Wireless Communications

Mobile users' data rate and quality of service are limited by the fact that, within the duration of any given call, they experience severe variations in signal attenuation, thereby necessitating the use of some type of diversity. In this two-part paper, we propose a new form of spatial diversity, in which diversity gains are achieved via the cooperation of mobile users. Part I describes the user cooperation strategy, while Part II (see ibid., p.1939-48) focuses on implementation issues and performance analysis. Results show that, even though the interuser channel is noisy, cooperation leads not only to an increase in capacity for both users but also to a more robust system, where users' achievable rates are less susceptible to channel variations.

http://dns2.asia.edu.tw/~ysho/YSHO-English/2000%20Engineering/PDF/IEE%20Tra%20Com51,%201927.pdf

User cooperation diversity. Part I. System description

Multi-user MIMO offers big advantages over conventional point-to-point MIMO: it works with cheap single-antenna terminals, a rich scattering environment is not required, and resource allocation is simplified because every active terminal utilizes all of the time-frequency bins. However, multi-user MIMO, as originally envisioned, with roughly equal numbers of service antennas and terminals and frequency-division duplex operation, is not a scalable technology. Massive MIMO (also known as large-scale antenna systems, very large MIMO, hyper MIMO, full-dimension MIMO, and ARGOS) makes a clean break with current practice through the use of a large excess of service antennas over active terminals and time-division duplex operation. Extra antennas help by focusing energy into ever smaller regions of space to bring huge improvements in throughput and radiated energy efficiency. Other benefits of massive MIMO include extensive use of inexpensive low-power components, reduced latency, simplification of the MAC layer, and robustness against intentional jamming. The anticipated throughput depends on the propagation environment providing asymptotically orthogonal channels to the terminals, but so far experiments have not disclosed any limitations in this regard. While massive MIMO renders many traditional research problems irrelevant, it uncovers entirely new problems that urgently need attention: the challenge of making many low-cost low-precision components that work effectively together, acquisition and synchronization for newly joined terminals, the exploitation of extra degrees of freedom provided by the excess of service antennas, reducing internal power consumption to achieve total energy efficiency reductions, and finding new deployment scenarios. This article presents an overview of the massive MIMO concept and contemporary research on the topic.

/pdf/massive-mimo-for-next-generation-wireless-systems-1eydagg3js.pdf

Massive MIMO for next generation wireless systems

Multiuser diversity is a form of diversity inherent in a wireless network, provided by independent time-varying channels across the different users. The diversity benefit is exploited by tracking the channel fluctuations of the users and scheduling transmissions to users when their instantaneous channel quality is near the peak. The diversity gain increases with the dynamic range of the fluctuations and is thus limited in environments with little scattering and/or slow fading. In such environments, we propose the use of multiple transmit antennas to induce large and fast channel fluctuations so that multiuser diversity can still be exploited. The scheme can be interpreted as opportunistic beamforming and we show that true beamforming gains can be achieved when there are sufficient users, even though very limited channel feedback is needed. Furthermore, in a cellular system, the scheme plays an additional role of opportunistic nulling of the interference created on users of adjacent cells. We discuss the design implications of implementing. this scheme in a complete wireless system.

https://web.stanford.edu/~dntse/papers/oppbf_it.pdf

Opportunistic beamforming using dumb antennas

Maddah-Ali and Tse have recently shown that delayed transmitter channel state information (CSIT) can still be useful in increasing the degrees-of-freedom (DoF) over the MIMO broadcast channel. This was achieved by constructing a scheme that, in the presence of two transmit antennas, of two single-antenna receivers, and of CSIT that is delayed by one coherence time, manages to provide each user with 2/3 DoF, improving upon the 1/2 DoF corresponding to no CSIT. This same scheme though, as well as all subsequent schemes pertinent schemes, achieve DoF gains by suppressing the inherent diversity of the broadcast parallel channel. The current work proposes a novel broadcast scheme which, over the above described setting of the delayed CSIT broadcast channel, employs a form of interference alignment to achieve both full DoF as well as full diversity.

/pdf/interference-alignment-for-achieving-both-full-dof-and-full-356k2uuwje.pdf

Interference alignment for achieving both full DoF and full diversity in the broadcast channel with delayed CSIT

In ISIT'12 Brahma, Ozgur and Fragouli conjectured that in a half-duplex diamond relay network (a Gaussian noise network without a direct source-destination link and with $N$ non-interfering relays) an approximately optimal relay scheduling (achieving the cut-set upper bound to within a constant gap uniformly over all channel gains) exists with at most $N+1$ active states (only $N+1$ out of the $2^N$ possible relay listen-transmit configurations have a strictly positive probability). Such relay scheduling policies are said to be simple. In ITW'13 we conjectured that simple relay policies are optimal for any half-duplex Gaussian multi-relay network, that is, simple schedules are not a consequence of the diamond network's sparse topology. In this paper we formally prove the conjecture beyond Gaussian networks. In particular, for any memoryless half-duplex $N$-relay network with independent noises and for which independent inputs are approximately optimal in the cut-set upper bound, an optimal schedule exists with at most $N+1$ active states. The key step of our proof is to write the minimum of a submodular function by means of its Lovasz extension and use the greedy algorithm for submodular polyhedra to highlight structural properties of the optimal solution. This, together with the saddle-point property of min-max problems and the existence of optimal basic feasible solutions in linear programs, proves the claim.

The Approximate Optimality of Simple Schedules for Half-Duplex Multi-Relay Networks

In this work, we consider achievable rates for transmission strategies suited to Ultra-wideband (UWB) systems and focus non-coherent receivers (i.e. those which do not perform channel estimation, but may have prior knowledge of the secondorder channel statistics). Here we take a UWB system to be loosely defined as any wireless transmission scheme that occupies a bandwidth between 1 and 10 GHz and more than 25% of it’s carrier frequency in the case of a passband system. The most common UWB transmission scheme is based on transmitting information through the use of short-term impulses, whose positions are modulated by a binary information source [3]. This can be seen as a special case of gash signaling coined by Verdu in [2]. We focus on the case of non-coherent detection since it is well known [l] that coherent detection is not required to achieve the wideband AWGN channel capacity C,. In [2] Verdu addresses the spectral efficiency of signaling strategies in the wideband regime under different assumptions regarding channel knowledge a t the transmitter and receiver. He shows that approaching C, with non-cohcrent detection is impossible for practical data rates (>lo0 kbit/s) even for the vanishing spectral efficiency of UWB systems. This is due to the fact that the slope SO of the curve representing (Eb/No),i, versus spectral efficiency, is zero at the origin for non-coherent detection. We restrict our study to strictly time-limited memoryless real-valued signals, both at the transmitter and receivcr. The transmitted pulse, of duration Tp, is passed through a linear channel, h(t , U) of duration Td and corrupted by additive white Gaussian noise with power spectral density No/2. The transmitted signal is written as z( t ) = E,”=, S ( U k ) f i p ( t where k is the symbol index, T, the symbol duration, E, = PT, the transmitted symbol energy, uk E (1,. . . , m} is the transmitted symbol at time k , p ( t ) and s ( u ~ ) are the assigned pulse and amplitude for symbol U k . For all k, p ( t ) is a unit-energy pulse of duration Tp. The considered model encompasses modulation schemes such as flash signaling, mary PPM, amplitude, and differential modulations. A guard interval of length Td is left a t the end of each symbol (from our memoryless assumption) so that T, 2 T, + T d . We characterize UWB propagation channel in terms of statistical eigenvalue distributions and optimal transmit pulse shapes, and highlight the “no-fading”, or constant received energy, behavior these channels.

On the achievable rates of ultra-wideband systems in multipath fading environments

In this paper, we study a communication system consisting of three end-nodes, e.g. a single transceiver base station (BS), one transmitting and one receiving user equipments (UEs), and a common two-way relay node (RN) wherein the full-duplex BS transmits to the receiving UE in downlink direction and receives from the transmitting UE in uplink direction with the help of the intermediate full-duplex RN. We call this system model as interference two-way relay channel (ITWRC) with three end-nodes. Information theoretic bounds corresponding this system model are derived and analyzed so as to better understand the potentials of exploiting RN in future communication systems. Specifically, achievable rate regions corresponding to decode-and-forward (DF) relaying with and without rate splitting, and partial-DF and compress-and-forward (pDF+CF) relaying strategies are derived.

Interference Two-Way Relay Channel with Three End-nodes

Modern VLSI decoders for low-density parity-check (LDPC) codes require high throughput performance while achieving high energy efficiency on the smallest possible footprint. In this paper we present a valuable optimization to the processing step known as syndrome check. After each decoding iteration the updated posterior values are used to verify the validity of the codeblock and halt the decoding task. We partition this task and perform it on-the-fly in order to speed up the total task latency and eliminate hardware components. We present results for applying this technique to an LDPC decoder for the IEEE 802.11n standard.

Raymond Knopp

Papers

Interference alignment for achieving both full DoF and full diversity in the broadcast channel with delayed CSIT

The Approximate Optimality of Simple Schedules for Half-Duplex Multi-Relay Networks

On the achievable rates of ultra-wideband systems in multipath fading environments

Interference Two-Way Relay Channel with Three End-nodes

On-the-Fly Syndrome Check for LDPC Decoders