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Embed Size px x x x x AbstractEnd-to-end learning of communications systems isa fascinating novel concept that has so far only been validatedby simulations for block-based transmissions.

It allows learningof transmitter and receiver implementations as deep neuralnetworks NNs that are optimized for an arbitrary differentiableend-to-end performance metric, e. In this paper, we demonstrate that over-the-air transmissionsare possible: We build, train, and run a complete communica-tions system solely composed of NNs using unsynchronized off-the-shelf software-defined radios SDRs and open-source deeplearning DL software libraries.

We extend the existing ideastowards continuous data transmission which eases their currentrestriction to short block lengths but also entails the issue ofreceiver synchronization. We overcome this problem by intro-ducing a frame synchronization module based on another NN.

Acomparison of the BLER performance of the learned systemwith that of a practical baseline shows competitive performanceclose to 1 dB, even without extensive hyperparameter tuning.

Weidentify several practical challenges of training such a systemover actual channels, in particular the missing channel gradient,and propose a two-step learning procedure based on the idea oftransfer learning that circumvents this issue. The fundamental problem of communication is that ofreproducing at one point either exactly or approximately amessage selected at another point [1] or, in other words, reli-ably transmitting a message from a source to a destination overa channel by the use of a transmitter and a receiver.

In order tocome close to the theoretically optimal solution to this problemin practice, transmitter and receiver were subsequently dividedinto several processing blocks, each responsible for a specificsub-task, e. Although such an implementation is known to besub-optimal [2], it has the advantage that each component canbe individually analyzed and optimized, leading to the veryefficient and stable systems that are available today.

The idea of deep learning DL communications systems[3], [4], on the contrary, goes back to the original definitionof the communication problem and seeks to optimize trans-mitter and receiver jointly without any artificially introducedblock structure. Although todays systems have been intenselyoptimized over the last decades and it seems difficult tocompete with them performance-wise, we are attracted bythe conceptual simplicity of a communications system thatcan learn to communicate over any type of channel without.

Dorner, S. Cammerer, and S. Themain contribution of this work is to demonstrate the practicalpotential and viability of such a system by developing aprototype consisting of two software-defined radios SDRs that learn to communicate over an actual wireless channel. To do so, we extend the ideas of [3], [4] to continuousdata transmission, which requires dealing with synchronizationissues and inter-symbol interference ISI.

This turns out to bea crucial step for over-the-air transmissions. Somewhat to oursurprise, our implementation comes close to the performanceof a well-designed conventional system. The fields of machine learning ML and, in particular,DL have seen very rapid growth during the last years; theirapplications extend now towards almost every industry andresearch domain [5], [6], [7].

Although researchers havetried to address communications-related problems with MLin the past see [8], [9], [10] and references therein , it didnot have any fundamental impact on the way we designand implement communications systems.

The main reasonfor this is that extremely accurate and versatile system andchannel models have been developed that enable algorithmdesign grounded in information theory, statistics, and signalprocessing, with reliable performance guarantees. Anotherreason is that, only since very recently, powerful DL softwarelibraries e. These are key for training and inference of complex DLmodels needed for real-time signal processing applications. Thanks to these developments, several research groups haverecently started investigations into DL applications in commu-nications and signal processing using state-of-the-art tools andhardware.

The concept of learningan end-to-end communications system by interpreting it asan autoencoder [26, Ch. Although a theoretically very appealing concept, it isnot implementable in practice without modifications as thegradient of the channel is unknown at training time.

The rest of this article is structured as follows: Section IIdescribes the basic autoencoder concept and explains thechallenges related to a hardware implementation. Section IIIcontains a detailed description of our implementation, in-cluding two-phase training, channel modeling, and necessaryextensions for continuous transmissions.

Section IV presentsperformance results for a stochastic channel model as well asfor over-the-air transmissions. Section V concludes the paper.

Notations: Boldface letters and upper-case letters denotecolumn vectors and matrices, respectively. The ith element ofvector x is denoted xi. The notation x. For a vector x, arg max x denotes theindex starting from 1 of the element with the largest absolutevalue. The operator cs [x]i denotes the circular shift of x byi steps. We consider a communications system consisting of atransmitter, a channel, and a receiver, as shown in Fig. To do so, itis allowed to transmit n complex baseband symbols, i.

At thereceiver side, a noisy and possibly distorted version y Cnof x can be observed. The task of the receiver is to producethe estimate s of the original message s. Note that, for now, an idealizedcommunications system was assumed with perfect timing andboth carrier-phase and frequency synchronization. As explained in [4], the communications system describedabove can be interpreted as an autoencoder [26, Ch.

Thisis schematically shown in Fig. An autoencoder describesa deep neural network NN that is trained to reconstruct theinput at the output.

As the information must pass each layer,. The trainable transmitter part of the autoencoder consists ofan embedding1 followed by a feedforward NN or multilayerperceptron MLP. Its 2n-dimensional output is cast to an n-dimensional complex-valued vector by considering one half asthe real part and the other half as the imaginary part see [4]. Finally, a normalization layer ensures that the power constrainton the output x is met. The channel can be implemented asa set of layers with probabilistic and deterministic behavior,e.

Additionally, any other channeleffect can be integrated, such as a tapped delay line TDL channel, carrier frequency offset CFO , as well as timing andphase offset. The receiver consists of atransformation from complex to real values by concatenatingreal and imaginary parts of the channel output , followed by afeedfoward NN whose last layer has a softmax activation see [26].

Its output b 0, 1 M is a probability vectorthat assigns a probability to each of the possible messages. The estimate s of s corresponds to the index of the largestelement of b. Throughout this work, we use feedforward NNswith dense layers and rectified linear unit ReLU activations,except for the last. See Full Reader. M , respectively. We want to emphasize a few important differences with re- Download Report. View Download 1 Category Documents. Although todays systems have been intenselyoptimized over the last decades and it seems difficult tocompete with them performance-wise, we are attracted bythe conceptual simplicity of a communications system thatcan learn to communicate over any type of channel without S.

Background The fields of machine learning ML and, in particular,DL have seen very rapid growth during the last years; theirapplications extend now towards almost every industry andresearch domain [5], [6], [7]. The autoencoder concept As explained in [4], the communications system describedabove can be interpreted as an autoencoder [26, Ch.

As the information must pass each layer, the network needs to find a robust representation of the inputmessage at every layer. Profi Hub F1 - Procentec?? HILFE -. Baudrate 8. Varicode Ascii8,… Documents. Recycle or discard the

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