Efficient evaluation of the error probability for pilot-assisted URLLC with Massive MIMO

We propose a numerically efficient method for evaluating the random-coding union bound with parameter $s$ on the error probability achievable in the finite-blocklength regime by a pilot-assisted transmission scheme employing Gaussian codebooks and operating over a memoryless block-fading channel. Our method relies on the saddlepoint approximation, which, differently from previous results reported for similar scenarios, is performed with respect to the number of fading blocks (a.k.a. diversity branches) spanned by each codeword, instead of the number of channel uses per block. This different approach avoids a costly numerical averaging of the error probability over the realizations of the fading process and of its pilot-based estimate at the receiver and results in a significant reduction of the number of channel realizations required to estimate the error probability accurately. Our numerical experiments for both single-antenna communication links and massive multiple-input multiple-output (MIMO) networks show that, when two or more diversity branches are available, the error probability can be estimated accurately with the saddlepoint approximation with respect to the number of fading blocks using a numerical method that requires about two orders of magnitude fewer Monte-Carlo samples than with the saddlepoint approximation with respect to the number of channel uses per block

Pilot-Assisted Short-Packet Transmission over Multiantenna Fading Channels: A 5G Case Study

Leveraging recent results in finite-blocklength information theory, we investigate the problem of designing a control channel in a 5G system. The setup involves the transmission, under stringent latency and reliability constraints, of a short data packet containing a small information payload, over a propagation channel that offers limited frequency diversity and no time diversity. We present an achievability bound, built upon the random-coding union bound with parameter s (Martinez & Guill\ue9n i F\ue0bregas, 2011), which relies on quadrature phase-shift keying modulation, pilot-assisted transmission to estimate the fading channel, and scaled nearest-neighbor decoding at the receiver. Using our achievability bound, we determine how many pilot symbols should be transmitted to optimally trade between channel-estimation errors and rate loss due to pilot overhead. Our analysis also reveals the importance of using multiple antennas at the transmitter and/or the receiver to provide the spatial diversity needed to meet the stringent reliability constraint

Low-Complexity Joint Channel Estimation and List Decoding of Short Codes

A pilot-assisted transmission (PAT) scheme is proposed for short blocklengths, where the pilots are used only to derive an initial channel estimate for the list construction step. The final decision of the message is obtained by applying a non-coherent decoding metric to the codewords composing the list. This allows one to use very few pilots, thus reducing the channel estimation overhead. The method is applied to an ordered statistics decoder for communication over a Rayleigh block-fading channel. Gains of up to $1.2$ dB as compared to traditional PAT schemes are demonstrated for short codes with QPSK signaling. The approach can be generalized to other list decoders, e.g., to list decoding of polar codes.Comment: Accepted at the 12th International ITG Conference on Systems, Communications and Coding (SCC 2019), Rostock, German

Multiantenna Wireless Architectures with Low Precision Converters

One of the main key technology enablers of the next generation of wireless communications is massive multiple input multiple output (MIMO), in which the number of antennas at the base station (BS) is scaled up to the order of tens or hundreds. It provides considerable energy and spectral efficiency by spatial multiplexing, which enables serving multiple user equipments (UEs) on the same time and frequency resource. However, the deployment of such large-scale systems could be challenging and this thesis is aimed at studying one of the challenges in the optimal implementation of such systems. More specifically, we consider a fully digital setup, in which each antenna at the BS is connected to a pair of data converters through a radio-frequency (RF) chain, all located at the remote radio head (RRH), and there is a limitation on the capacity of the fronthaul link, which connects the RRH to the baseband unit (BBU), where digital signal processing is performed. The fronthaul capacity limitation calls for a trade-off between some of the design parameters, including the number of antennas, the resolution of data converters and the over-sampling ratio. In this thesis, we study the aforementioned trade-off considering the first two design parameters.First, we consider a quasi-static scenario, in which the fading coefficients do not change throughout the transmission of a codeword. The channel state information (CSI) is assumed to be unknown at the BS, and it is acquired through pilot transmission. We develop a framework based on the mismatched decoding rule to find lower bounds on the achievable rates. The bi-directional rate at 10% outage probability is selected as the performance metric to determine the recommended architecture in terms of number of antennas and the resolution of data converters. Second, we adapt our framework to a finite blocklength regime, considering a realistic mm-wave multi-user clustered MIMO channel model and a well suited channel estimation algorithm. We start our derivations by considering random coding union bound with parameter s (RCUs) and apply approximations to derive the corresponding normal approximation and further, an easy to compute outage with correction bound. We illustrate the accuracy of our approximations, and use the outage with correction bound to investigate the optimal architecture in terms of the number of antennas and the resolution of the data converters.Our result show that at low signal to noise (SNR) regime, we benefit from lowering the resolution of the data converters and increasing the number of antennas, while at high SNR for a practical scenario, the optimal architecture could move to 3 or 4 bits of resolution since we are not in demand of large array gain anymore

Short Packets over Block-Memoryless Fading Channels: Pilot-Assisted or Noncoherent Transmission?

We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no \emph{a priori} channel state information available at the transmitter and at the receiver. An upper bound built upon the min-max converse is compared to two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver; the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number of diversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, for the case when a coded packet of $168$ symbols is transmitted using a channel code of rate $0.48$ bits/channel use, over a block-fading channel with block size equal to $8$ symbols, PAT requires an additional $1.2$ dB of energy per information bit to achieve a packet error probability of $10^{-3}$ compared to a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics decoding, whose performance are close ($1$ dB gap at $10^{-3}$ packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes.Comment: 30 pages, 5 figures, journa

Reliable Transmission of Short Packets through Queues and Noisy Channels under Latency and Peak-Age Violation Guarantees

This work investigates the probability that the delay and the peak-age of information exceed a desired threshold in a point-to-point communication system with short information packets. The packets are generated according to a stationary memoryless Bernoulli process, placed in a single-server queue and then transmitted over a wireless channel. A variable-length stop-feedback coding scheme---a general strategy that encompasses simple automatic repetition request (ARQ) and more sophisticated hybrid ARQ techniques as special cases---is used by the transmitter to convey the information packets to the receiver. By leveraging finite-blocklength results, the delay violation and the peak-age violation probabilities are characterized without resorting to approximations based on large-deviation theory as in previous literature. Numerical results illuminate the dependence of delay and peak-age violation probability on system parameters such as the frame size and the undetected error probability, and on the chosen packet-management policy. The guidelines provided by our analysis are particularly useful for the design of low-latency ultra-reliable communication systems.Comment: To appear in IEEE journal on selected areas of communication (IEEE JSAC

Short-Packet Transmission over a Bidirectional Massive MIMO link

We consider the transmission of short packets over a bidirectional communication link where multiple devices, e.g., sensors and actuators, exchange small-data payloads with a base station equipped with a large antenna array. Using results from finite-blocklength information theory, we characterize the minimum SNR required to achieve a target error probability for a fixed packet length and a fixed payload size. Our nonasymptotic analysis, which applies to the scenario in which the bidirectional communication is device-initiated, and also to the more challenging case when it is base-station initiated, provides guidelines on the design of massive multiple-input multiple-output links that need to support sporadic ultra-reliable low-latency transmissions. Specifically, it allows us to determine the optimal amount of resources that need to be dedicated to the acquisition of channel state information

Short-Packet Transmission over a Bidirectional Massive MIMO link

We consider the transmission of short packets over a bidirectional communication link where multiple devices, e.g., sensors and actuators, exchange small-data payloads with a base station equipped with a large antenna array. Using results from finite-blocklength information theory, we characterize the minimum SNR required to achieve a target error probability for a fixed packet length and a fixed payload size. Our nonasymptotic analysis, which applies to the scenario in which the bidirectional communication is device-initiated, and also to the more challenging case when it is base-station initiated, provides guidelines on the design of massive multiple-input multiple-output links that need to support sporadic ultra-reliable low-latency transmissions. Specifically, it allows us to determine the optimal amount of resources that need to be dedicated to the acquisition of channel state information.Comment: 5 pages, presented at Asiloma

Peak-Age Violation Guarantees for the Transmission of Short Packets over Fading Channels

We investigate the probability that the peak age of information in a point-to-point communication system operating over a multiantenna wireless fading channel exceeds a predetermined value. The packets are scheduled according to a last-come first-serve policy with preemption in service, and are transmitted over the channel using a simple automatic repetition request protocol. We consider quadrature phase shift keying modulation, pilot-assisted transmission, maximum-likelihood channel estimation, and mismatched scaled nearest-neighbor decoding. Our analysis, which exploits nonasymptotic tools in information theory, allows one to determine, for a given information packet size, the physical layer parameters such as the SNR, the number of transmit and receive antennas, the amount of frequency diversity to exploit, and the number of pilot symbols, to ensure that the system operates below a target peak-age violation probability

URLLC with Massive MIMO: Analysis and Design at Finite Blocklength

The fast adoption of Massive MIMO for high-throughput communications was enabled by many research contributions mostly relying on infinite-blocklength information-theoretic bounds. This makes it hard to assess the suitability of Massive MIMO for ultra-reliable low-latency communications (URLLC) operating with short blocklength codes. This paper provides a rigorous framework for the characterization and numerical evaluation (using the saddlepoint approximation) of the error probability achievable in the uplink and downlink of Massive MIMO at finite blocklength. The framework encompasses imperfect channel state information, pilot contamination, spatially correlated channels, and arbitrary linear spatial processing. In line with previous results based on infinite-blocklength bounds, we prove that, with minimum mean-square error (MMSE) processing and spatially correlated channels, the error probability at finite blocklength goes to zero as the number $M$ of antennas grows to infinity, even under pilot contamination. On the other hand, numerical results for a practical URLLC network setup involving a base station with $M=100$ antennas, show that a target error probability of $10^{-5}$ can be achieved with MMSE processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. Maximum ratio processing does not suffice.Comment: 30 pages, 5 figure