arXiv subjects

Giuseppe Durisi

Publications and source records attributed to Giuseppe Durisi.

At least 109 records · Page 6Linked to original sources

arXiv2016

Minimum Energy to Send $k$ Bits Over Multiple-Antenna Fading Channels

This paper investigates the minimum energy required to transmit $k$ information bits with a given reliability over a multiple-antenna Rayleigh block-fading channel, with and without channel state information (CSI) at the receiver. No feedback is assumed. It is well known that the ratio between the minimum energy per bit and the noise level converges to $-1.59$ dB as $k$ goes to infinity, regardless of whether CSI is available at the receiver or not. This paper shows that lack of CSI at the receiver causes a slowdown in the speed of convergence to $-1.59$ dB as $k\to\infty$ compared to the case of perfect receiver CSI. Specifically, we show that, in the no-CSI case, the gap to $-1.59$ dB is proportional to $((\log k) /k)^{1/3}$, whereas when perfect CSI is available at the receiver, this gap is proportional to $1/\sqrt{k}$. In both cases, the gap to $-1.59$ dB is independent of the number of transmit antennas and of the channel's coherence time. Numerically, we observe that, when the receiver is equipped with a single antenna, to achieve an energy per bit of $ - 1.5$ dB in the no-CSI case, one needs to transmit at least $7\times 10^7$ information bits, whereas $6\times 10^4$ bits suffice for the case of perfect CSI at the receiver.

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arXiv2016

Quantized Massive MU-MIMO-OFDM Uplink

Coarse quantization at the base station (BS) of a massive multi-user (MU) multiple-input multiple-output (MIMO) wireless system promises significant power and cost savings. Coarse quantization also enables significant reductions of the raw analog-to-digital converter (ADC) data that must be transferred from a spatially-separated antenna array to the baseband processing unit. The theoretical limits as well as practical transceiver algorithms for such quantized MU-MIMO systems operating over frequency-flat, narrowband channels have been studied extensively. However, the practically relevant scenario where such communication systems operate over frequency-selective, wideband channels is less well understood. This paper investigates the uplink performance of a quantized massive MU-MIMO system that deploys orthogonal frequency-division multiplexing (OFDM) for wideband communication. We propose new algorithms for quantized maximum a-posteriori (MAP) channel estimation and data detection, and we study the associated performance/quantization trade-offs. Our results demonstrate that coarse quantization (e.g., four to six bits, depending on the ratio between the number of BS antennas and the number of users) in massive MU-MIMO-OFDM systems entails virtually no performance loss compared to the infinite-precision case at no additional cost in terms of baseband processing complexity.

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arXiv2016

Towards Massive, Ultra-Reliable, and Low-Latency Wireless Communication with Short Packets

Most of the recent advances in the design of high-speed wireless systems are based on information-theoretic principles that demonstrate how to efficiently transmit long data packets. However, the upcoming wireless systems, notably the 5G system, will need to support novel traffic types that use short packets. For example, short packets represent the most common form of traffic generated by sensors and other devices involved in Machine-to-Machine (M2M) communications. Furthermore, there are emerging applications in which small packets are expected to carry critical information that should be received with low latency and ultra-high reliability. Current wireless systems are not designed to support short-packet transmissions. For example, the design of current systems relies on the assumption that the metadata (control information) is of negligible size compared to the actual information payload. Hence, transmitting metadata using heuristic methods does not affect the overall system performance. However, when the packets are short, metadata may be of the same size as the payload, and the conventional methods to transmit it may be highly suboptimal. In this article, we review recent advances in information theory, which provide the theoretical principles that govern the transmission of short packets. We then apply these principles to three exemplary scenarios (the two-way channel, the downlink broadcast channel, and the uplink random access channel), thereby illustrating how the transmission of control information can be optimized when the packets are short. The insights brought by these examples suggest that new principles are needed for the design of wireless protocols supporting short packets. These principles will have a direct impact on the system design.

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arXiv2016

A Beta-Beta Achievability Bound with Applications

A channel coding achievability bound expressed in terms of the ratio between two Neyman-Pearson $β$ functions is proposed. This bound is the dual of a converse bound established earlier by Polyanskiy and Verdú (2014). The new bound turns out to simplify considerably the analysis in situations where the channel output distribution is not a product distribution, for example due to a cost constraint or a structural constraint (such as orthogonality or constant composition) on the channel inputs. Connections to existing bounds in the literature are discussed. The bound is then used to derive 1) an achievability bound on the channel dispersion of additive non-Gaussian noise channels with random Gaussian codebooks, 2) the channel dispersion of the exponential-noise channel, 3) a second-order expansion for the minimum energy per bit of an AWGN channel, and 4) a lower bound on the maximum coding rate of a multiple-input multiple-output Rayleigh-fading channel with perfect channel state information at the receiver, which is the tightest known achievability result.

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arXiv2015

Short-Packet Communications over Multiple-Antenna Rayleigh-Fading Channels

Motivated by the current interest in ultra-reliable, low-latency, machine-type communication systems, we investigate the tradeoff between reliability, throughput, and latency in the transmission of information over multiple-antenna Rayleigh block-fading channels. Specifically, we obtain finite-blocklength, finite-SNR upper and lower bounds on the maximum coding rate achievable over such channels for a given constraint on the packet error probability. Numerical evidence suggests that our bounds delimit tightly the maximum coding rate already for short blocklengths (packets of about 100 symbols). Furthermore, our bounds reveal the existence of a tradeoff between the rate gain obtainable by spreading each codeword over all available time-frequency-spatial degrees of freedom, and the rate loss caused by the need of estimating the fading coefficients over these degrees of freedom. In particular, our bounds allow us to determine the optimal number of transmit antennas and the optimal number of time-frequency diversity branches that maximize the rate. Finally, we show that infinite-blocklength performance metrics such as the ergodic capacity and the outage capacity yield inaccurate throughput estimates.

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arXiv2015

Finite-SNR Bounds on the Sum-Rate Capacity of Rayleigh Block-Fading Multiple-Access Channels with no a Priori CSI

We provide nonasymptotic upper and lower bounds on the sum-rate capacity of Rayleigh block-fading multiple-access channels for the setup where a priori channel state information is not available. The upper bound relies on a dual formula for channel capacity and on the assumption that the users can cooperate perfectly. The lower bound is derived assuming a noncooperative scenario, where each user employs unitary space-time modulation (independently from the other users). Numerical results show that the gap between the upper and the lower bound is small already at moderate SNR values. This suggests that the sum-rate capacity gains obtainable through user cooperation are minimal.

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arXiv2015

Optimum Power Control at Finite Blocklength

This paper investigates the maximal channel coding rate achievable at a given blocklength $n$ and error probability $ε$, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The second-order term in the large-$n$ expansion of the maximal channel coding rate is characterized both for additive white Gaussian noise (AWGN) channels and for quasi-static fading channels with perfect channel state information available at both the transmitter and the receiver. It is shown that in both cases the second-order term is proportional to $\sqrt{n^{-1}\ln n}$. For the quasi-static fading case, this second-order term is achieved by truncated channel inversion, namely, by concatenating a dispersion-optimal code for an AWGN channel subject to a short-term power constraint, with a power controller that inverts the channel whenever the fading gain is above a certain threshold. Easy-to-evaluate approximations of the maximal channel coding rate are developed for both the AWGN and the quasi-static fading case.

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arXiv2015

One-Bit Massive MIMO: Channel Estimation and High-Order Modulations

We investigate the information-theoretic throughout achievable on a fading communication link when the receiver is equipped with one-bit analog-to-digital converters (ADCs). The analysis is conducted for the setting where neither the transmitter nor the receiver have a priori information on the realization of the fading channels. This means that channel-state information needs to be acquired at the receiver on the basis of the one-bit quantized channel outputs. We show that least-squares (LS) channel estimation combined with joint pilot and data processing is capacity achieving in the single-user, single-receive-antenna case. We also investigate the achievable uplink throughput in a massive multiple-input multiple-output system where each element of the antenna array at the receiver base-station feeds a one-bit ADC. We show that LS channel estimation and maximum-ratio combining are sufficient to support both multiuser operation and the use of high-order constellations. This holds in spite of the severe nonlinearity introduced by the one-bit ADCs.

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arXiv2015

Broadcasting a Common Message with Variable-Length Stop-Feedback Codes

We investigate the maximum coding rate achievable over a two-user broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. Specifically, upon decoding the common message, each decoder sends a stop signal to the encoder, which transmits continuously until it receives both stop signals. For the point-to-point case, Polyanskiy, Poor, and Verdú (2011) recently demonstrated that variable-length coding combined with stop feedback significantly increases the speed at which the maximum coding rate converges to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, a result a.k.a. zero dispersion. In this paper, we show that this speed-up does not necessarily occur for the broadcast channel with common message. Specifically, there exist scenarios for which variable-length stop-feedback codes yield a positive dispersion.

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arXiv2015

Capacity of SIMO and MISO Phase-Noise Channels with Common/Separate Oscillators

In multiple antenna systems, phase noise due to instabilities of the radio-frequency (RF) oscillators, acts differently depending on whether the RF circuitries connected to each antenna are driven by separate (independent) local oscillators (SLO) or by a common local oscillator (CLO). In this paper, we investigate the high-SNR capacity of single-input multiple-output (SIMO) and multiple-output single-input (MISO) phase-noise channels for both the CLO and the SLO configurations. Our results show that the first-order term in the high-SNR capacity expansion is the same for all scenarios (SIMO/MISO and SLO/CLO), and equal to $0.5\ln (ρ)$, where $ρ$ stands for the SNR. On the contrary, the second-order term, which we refer to as phase-noise number, turns out to be scenario-dependent. For the SIMO case, the SLO configuration provides a diversity gain, resulting in a larger phase-noise number than for the CLO configuration. For the case of Wiener phase noise, a diversity gain of at least $0.5 \ln(M)$ can be achieved, where $M$ is the number of receive antennas. For the MISO, the CLO configuration yields a higher phase-noise number than the SLO configuration. This is because with the CLO configuration one can obtain a coherent-combining gain through maximum ratio transmission (a.k.a. conjugate beamforming). This gain is unattainable with the SLO configuration.

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arXiv2015

Analysis of Massive MIMO With Hardware Impairments and Different Channel Models

Massive Multiple-Input Multiple-Output (MIMO) is foreseen to be one of the main technology components in next generation cellular communications (5G). In this paper, fundamental limits on the performance of downlink massive MIMO systems are investigated by means of simulations and analytical analysis. Signal-to-noise-and-interference ratio (SINR) and sum rate for a single-cell scenario multi-user MIMO are analyzed for different array sizes, channel models, and precoding schemes. The impact of hardware impairments on performance is also investigated. Simple approximations are derived that show explicitly how the number of antennas, number of served users, transmit power, and magnitude of hardware impairments affect performance.

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arXiv2014

On the Impact of Hardware Impairments on Massive MIMO

Massive multi-user (MU) multiple-input multiple-output (MIMO) systems are one possible key technology for next generation wireless communication systems. Claims have been made that massive MU-MIMO will increase both the radiated energy efficiency as well as the sum-rate capacity by orders of magnitude, because of the high transmit directivity. However, due to the very large number of transceivers needed at each base-station (BS), a successful implementation of massive MU-MIMO will be contingent on of the availability of very cheap, compact and power-efficient radio and digital-processing hardware. This may in turn impair the quality of the modulated radio frequency (RF) signal due to an increased amount of power-amplifier distortion, phase-noise, and quantization noise. In this paper, we examine the effects of hardware impairments on a massive MU-MIMO single-cell system by means of theory and simulation. The simulations are performed using simplified, well-established statistical hardware impairment models as well as more sophisticated and realistic models based upon measurements and electromagnetic antenna array simulations.

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arXiv2014

Degrees of Freedom of Generic Block-Fading MIMO Channels without A Priori Channel State Information

We studynthe high-SNR capacity of generic MIMO Rayleigh block-fading channels in the noncoherent setting where neither transmitter nor receiver has a priori channel state information but both are aware of the channel statistics. In contrast to the well-established constant block-fading model, we allow the fading to vary within each block with a temporal correlation that is "generic" (in the sense used in the interference-alignment literature). We show that the number of degrees of freedom of a generic MIMO Rayleigh block-fading channel with $T$ transmit antennas and block length $N$ is given by $T(1-1/N)$ provided that $T<N$ and the number of receive antennas is at least $T(N-1)/(N-T)$. A comparison with the constant block-fading channel (where the fading is constant within each block) shows that, for large block lengths, generic correlation increases the number of degrees of freedom by a factor of up to four.

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arXiv2014

Oversampling Increases the Pre-Log of Noncoherent Rayleigh Fading Channels

We analyze the capacity of a continuous-time, time-selective, Rayleigh block-fading channel in the high signal-to-noise ratio (SNR) regime. The fading process is assumed stationary within each block and to change independently from block to block; furthermore, its realizations are not known a priori to the transmitter and the receiver (noncoherent setting). A common approach to analyzing the capacity of this channel is to assume that the receiver performs matched filtering followed by sampling at symbol rate (symbol matched filtering). This yields a discrete-time channel in which each transmitted symbol corresponds to one output sample. Liang & Veeravalli (2004) showed that the capacity of this discrete-time channel grows logarithmically with the SNR, with a capacity pre-log equal to $1-{Q}/{N}$. Here, $N$ is the number of symbols transmitted within one fading block, and $Q$ is the rank of the covariance matrix of the discrete-time channel gains within each fading block. In this paper, we show that symbol matched filtering is not a capacity-achieving strategy for the underlying continuous-time channel. Specifically, we analyze the capacity pre-log of the discrete-time channel obtained by oversampling the continuous-time channel output, i.e., by sampling it faster than at symbol rate. We prove that by oversampling by a factor two one gets a capacity pre-log that is at least as large as $1-1/N$. Since the capacity pre-log corresponding to symbol-rate sampling is $1-Q/N$, our result implies indeed that symbol matched filtering is not capacity achieving at high SNR.

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arXiv2014

Diversity versus Multiplexing at Finite Blocklength

A finite blocklenth analysis of the diversity-multiplexing tradeoff is presented, based on nonasymptotic bounds on the maximum channel coding rate of multiple-antenna block-memoryless Rayleigh-fading channels.The bounds in this paper allow one to numerically assess for which packet size, number of antennas, and degree of channel selectivity, diversity-exploiting schemes are close to optimal, and when instead the available spatial degrees of freedom should be used to provide spatial multiplexing. This finite blocklength view on the diversity-multiplexing tradeoff provides insights on the design of delay-sensitive ultra-reliable communication links.

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arXiv2014

Quasi-Static Multiple-Antenna Fading Channels at Finite Blocklength

This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output (MIMO) fading channels, with and without channel state information (CSI) at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of them, or at neither of them. These results follow from analytically tractable converse and achievability bounds. Numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases. In the example of a particular $1 \times 2$ single-input multiple-output (SIMO) Rician fading channel, the blocklength required to achieve $90\%$ of capacity is about an order of magnitude smaller compared to the blocklength required for an AWGN channel with the same capacity. For this specific scenario, the coding/decoding schemes adopted in the LTE-Advanced standard are benchmarked against the finite-blocklength achievability and converse bounds.

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arXiv2014

Capacity of a Nonlinear Optical Channel with Finite Memory

The channel capacity of a nonlinear, dispersive fiber-optic link is revisited. To this end, the popular Gaussian noise (GN) model is extended with a parameter to account for the finite memory of realistic fiber channels. This finite-memory model is harder to analyze mathematically but, in contrast to previous models, it is valid also for nonstationary or heavy-tailed input signals. For uncoded transmission and standard modulation formats, the new model gives the same results as the regular GN model when the memory of the channel is about 10 symbols or more. These results confirm previous results that the GN model is accurate for uncoded transmission. However, when coding is considered, the results obtained using the finite-memory model are very different from those obtained by previous models, even when the channel memory is large. In particular, the peaky behavior of the channel capacity, which has been reported for numerous nonlinear channel models, appears to be an artifact of applying models derived for independent input in a coded (i.e., dependent) scenario.

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arXiv2014

Capacity bounds for MIMO microwave backhaul links affected by phase noise

We present bounds and a closed-form high-SNR expression for the capacity of multiple-antenna systems affected by Wiener phase noise. Our results are developed for the scenario where a single oscillator drives all the radio-frequency circuitries at each transceiver (common oscillator setup), the input signal is subject to a peak-power constraint, and the channel matrix is deterministic. This scenario is relevant for line-of-sight multiple-antenna microwave backhaul links with sufficiently small antenna spacing at the transceivers. For the 2 by 2 multiple-antenna case, for a Wiener phase-noise process with standard deviation equal to 6 degrees, and at the medium/high SNR values at which microwave backhaul links operate, the upper bound reported in the paper exhibits a 3 dB gap from a lower bound obtained using 64-QAM. Furthermore, in this SNR regime the closed-form high-SNR expression is shown to be accurate.

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