Background and description of research

0757-EX-CN-2017 Text Documents

DeepSig Inc.

2017-10-19ELS_199885

Executive Summary DeepSig is developing a suite of revolutionary capabilities leveraging deep learning based signal processing techniques to adapt and excel under a range of difficult operating conditions, mission requirements, and impairment effects. These capabilities offer the potential of significant performance improvements to existing communications systems. Our work so far has been in simulation and lab environments, and we are preparing to move to the next stage of our research – operating in real-world environments. Our application for an FCC experimental license is in support of this research effort. Technical Background: Autoencoders for Communications Systems DeepSig principals have developed a fundamentally new approach to the design and adaption of radio communications at the physical layer protocols based on the use of deep learning and a construct called the ‘channel autoencoder’. The autoencoder allows the physical layer transmitter and receiver to take the form of mostly unconstrained mappings in a series of efficient parametric linear algebra operations. Using deep learning, we are able to derive a solution to the full communications system design problem by seeking to minimize bit error rate (reconstruction loss). This may be done over a wide variety of channels and impairment models in order to obtain more optimally tailored solutions. By learning physical layer information encoding, decoding, and representation solutions in this end-to-end way, tailored waveforms may achieve novel and unprecedented performance under difficult channel conditions. Below we illustrate the ability of such a system to achieve capacity curves on par with conventional radio modulation and coding methods under a relatively simplistic Gaussian channel. 5 Figure 2: A communications system over an AWGN channel represented as an autoencoder. The input s is encoded as a one-hot Figure vector, the output is a probability 3 The Fundamental distribution over all possibleAutoencoder Approach messages from which the most likely is picked as output ŝ. non-linearly compress and reconstruct the input. In our case, any prior knowledge an encoder and decoder function that the purpose of the autoencoder is different. It seeks to learn together achieve the same performance as the Hamming (7,4) representations x of the messages s that are robust with code with MLD. The layout of the autoencoder is provided respect to the channel impairments mapping x to y (i.e., noise, in Table IV. Although a single layer can represent the same fading, distortion, etc.), so that theDeepsig Inc.message transmitted Proprietary Sensitive can mapping Information from message index to corresponding transmit vector, be recovered with small probability of error. In other words, our experiments have shown that SGD converges to a better while most autoencoders remove redundancy from input data global solution using two transmit layers instead of one. This for compression, this autoencoder (the “ channel autoencoder” ) increased dimension parameter search space may actually help often adds redundancy, learning an intermediate representation to reduce likelihood of convergence to sub-optimal minima by

9 The real benefit of such a system however, is not under the naïve whitened Gaussian channel assumption, but under a series of more realistic systematic impairments which may be modeled and mitigated through adaptivity more richly than thermal noise. Below we show the gains for such a system against a traditional Figure 8: BPSK maximum A radio receiver represented likelihood decoder as an RTN. The input y first runswith through a Hamming a parameter code estimation networkunder fading g (y ), has ! a known transform t(y , ! ) applied to generate the canonicalized signal y , and then is classified in the discriminati ve network conditions. g(y ) to produce the output ŝ. 100 1 Autoencoder Categorical cross-entropy loss Autoencoder + RTN 0.8 10− 1 Block error rate 0.6 10− 2 0.4 8 −3 10 Autoencoder (8,4) 0.2 DBPSK(8,7) MLE + Hamming(7,4) Autoencoder (8,4) + RTN 10− 4 0 0 5 10 15 20 0 20 40 60 80 100 E b/ N 0 [dB] Training epoch Figure 9: BLER versus E b/ N 0 for various communication Figure 10: Autoencoder training loss 4with and without RTN schemes over a channel with L = 3 Rayleigh fading taps Autoencoders with Multiple Antennas tion of single carrier modulation schemes based on sampled in both directions and transmission of the estimate may not After the encoding to mt complex valued transmit streams, Extending be needed. Thethe autoencoder scheme is illustrated in system to theamulti-antenna Figure 5 showing transmit block-code tensor case, we [batch of shape demonstrate size, m , 2, n] is that a similar construct to the role of convolutional layers in imparting translation radio frequency time-series data, i.e., IQ samples. This task has invariance where appropriate. This leads to a simpler search been accomplished for yearst through the approach of expert a full closed-loop system which can spacejointly learn ageneralization. method formed for transmission where theengineering third dimension has the real decision trees (single can learn binary to encode information andefficiently andover a MIMO Tochannel. We usedshow simulation results below for and improved feature and either analytic for compact CSI feedback, encoding, The autoencoder decoding and imaginery RTN as presented above canvalues. be easily simulate trees areMIMO widely propagation we in practice) use or trained discrimination methods the operating on a compact below. feature space, such as support amay 2x2be MIMO system. of information over the MIMO fading trained as shown channel. extended in Figureto4, effectively This to operate but the learned system directly deal with several rather on IQ samples problems •such network custom layers than enc:asLearned to model symbols pulse shaping, domain enumerated vector machines, random forests, or small feedforward NNs Encoder: s 7 ! x mapping to a compact CSI form timing-, of Hv isfrequency- and phase-offset• compensation. simply wholesale rnd: RandomThis mr ⇥mis [53]. Some recent methods take a step beyond this using t channel responseonHexpert feature maps, such as the spectral to the Fig.receiver where 16. Learned an estimated 2x2 Scheme anchannel exciting 1 bit CSI Random and promising response Channels. Ĥ mayareaFig. of 18. research that 2x2 we leave toCSI pattern recognition • Learned Scheme mul: Complex 2 bit matrix Random Channels. of x with H multiplication future investigations. Interesting applicati ons of this approach coherence function or ↵ -profile, combined with NN-based be obtained using either traditional estimation approaches or • norm: Normalize average power [54]. However, approaches to this point have not could also arise in optical communications dealing with highly classification NN-based regression. non-linear channel impairments that are • awg: Additive notoriously gaussian difficult to soughtnoiseto use N(0, σ ) learning on raw time-series data in the feature model and compensate for [52]. • dec: Learned Decoder:radio ! domain. r 7 ŝ This is however now the norm in computer vision which motivates our approach here. In terms of these basic operations, we can express the full As is widely done for image classification, we leverage a se- D. CNNs for classification tasks network f as follows for the open loop MIMO encoding case: ries of narrowing convolutional layers followed by dense/fully- Many signal processing functions within the physical layer connected layers and terminated with a dense softmax layer f (s, ✓) =tasks. can be learned as either regression or classification dec(awg(norm(mul(enc(s), σ))a VGG rnd())), to Here for our classifier (similar (2)architecture [55]). The we look at the well-known problem of modulation classifica- layout is provided in Table V and we refer to the source code and the for the closed-loop MIMO encoding case as: f (s, ✓) = (λH, dec(awg(norm(mul(enc(s, H), H)), σ)))(rnd()) (3) Using this formulation, forwards and backwards gradient passes can readily be computed on f (s, ✓). In the backwards Fig. 5.Fig.Deployment 17. LearnedScheme 2x2 Scheme 1-bit CSI for v-Bit CSIAll-Ones MIMO.Channel. pass, the awg function becomes the identify function (it is used Fig. 19. Learned 2x2 Scheme 2 bit CSI All-Ones Channel. only for forwards passes). While the normalization module enforces a constant average power, the noise deviation σ may a system can be readily partitioned into a real world distributed be easily baselines, adjusted of to determine at learned training“ codebooks” or test time to or over- simulate under- varying A. Optimization communications Process system in order to efficiently manage CSI levelsthe perform of methods SNR. which are widely used today for closed- Inrequirements. our optimization process, we represent s as a 2k valued loop MIMO systems. We have seen that discretized CSI with this scheme works integer of codeword indices which may be transmitted by the Additionally, the work I V. S needs I M ULtoATI ON RESULTS continue to evaluate per- incredibly well, learning very compact CSI encodings and system, eachseems actually encoding to helpk the bits. In the network, autoencoder converge we present more rapidly this formance on larger-scale MIMO arrangements such as 8x4 k In this section we train the autoencoder based learned as aand one-hot input to a better vector general of length solution 2 with bits). (given sufficient a single We have non- arrangements and massive MIMO, and to consider the case encoding model described above and evaluate the Bit Error zero observed value ofthat1 learned for thesolutions desiredoftencodeword, and the favor constant output of multi-tap delay spreads. The work has been conducted in modulus Rate (BER) performance over a range of SNRs and compare as apower soft-max classification at the receiver, but that task in some which they have learnedthe the time-domain rather than in the conventional long-symbol cases approximates the performance to and widely used baselines usedmayunder be different sub-optimal probability solutions of each codewhich word.splitInpower classification suchunevenly the MIMO/OFDM betweentasks, domain, so numerous connections channel conditions. Matlab is used to simulate the conventional two antennas a categorical even in the loss cross-entropy case function of no-CSI. (` C E ) may be readily drawn still in connecting these two domains optimally. MIMO systems for both spatial diversity and multiplexing. used for This work opensusing optimization up numerous gradientnew avenues descent network Finally, we will extend the MIMO described here in the for investiga- to select tion, many of which we hope to pursue in the nearDeepsig future. singleInc. Proprietary Keras with user Tensorflow case Sensitive to multi-userbackend Information is (MU-MIMO) used for the includes which DL autoencoder parameters. In this case ` C E is given by Among these, are combining Ĥ 7 ! Hv estimation with y 7 ! Multiple Access; i.e.,using implementation N transmitters to 1 receiver, and Broad- a GPU backend. Hv estimation, or in general allowing the channel estimation cast; We i.e. consider 1 transmitter to N receivers, comparisons to two channels. configurations; different Current −1 ’to support this system to be learned, and with schemes routines required |y |−1 forAlamouti these MIMO problems are known to have sub- diversity the 2x1 STBC intended to provide spatial ` Csome E (y, error ŷ) = rather than(ydirectly + (1 − i l og(pi )using yi )lfree error − pi ))of H.(1) optimal implementations due to complexity issues in current og(1values |y| based range extension and performance improvements, along Similar analysis have i =0 already been performed for conventional day systems such as the implementation of capacity-achieving

Description of Experiment We plan to exercise our ground-breaking approach to waveform design by testing it in a real-world environment – namely, downtown Arlington. We plan to have three fixed antenna locations, and several mobile stations. We also plan to conduct the experiments in a few different frequency bands so that we can evaluate the differences in the machine-learned models with different propagation characteristics. Due to the nature of our experiments, they do not need to be high power, and will not be for long durations. The below map shows the three fixed points we will use for our experiments, where the red pins indicate the locations as listed in our license application: Depending on the experiment, we may only use one or two of the fixed locations at a time. Also depending on the experiment, we plan to have up to four mobile transceivers operating between the East and West fixed locations. The goal of the experiments will be to evaluate the performance of our low-power machine-learned autoencoder-based communications systems in a harsh urban environment. Deepsig Inc. Proprietary Sensitive Information


Document Created: 2017-10-19 19:06:19
Document Modified: 2017-10-19 19:06:19
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