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Computer and Communication Engineering: First International Conference, ICCCE 2018, Guayaquil, Ecuador, October 25–27, 2018, Proceedings Miguel BottoTobar
Advances in Information and Communication Networks: Proceedings of the 2018 Future of Information and Communication Conference (FICC), Vol. 1 Kohei Arai
Notation: A isaset, |A| isthecardinalityofset A.lower-case a isascalar, a isavector, A isamatrix. AT , AH denotethetransposeandHermitianof matrix A
3SystemModel
Weconsideramm-waveMIMOdownlinksystemwithuniformlineararrays (ULAs)conformedby Nt transmitterantennasintheUEand Nr receiverantennasintheeNB,asshowinFig. 1.Weconsiderthatboththetransmitterandthe receiverhaveonlyoneRFchain,hence,onlyanalogbeamforming/combining canbeapplied.
where L isthenumberofpaths, αl representsthecomplexpathgainofthe l -thpropagationpath, θl ∈ [ π/2,π/2]and φl ∈ [ π/2,π/2]denotetheAoA andAoDofthe L-thpathattransmitterandreceiver,respectively.Thevectors at ( )and ar ( )denotethearrayresponsevectorsfortransmittingandreceiving antennaarrays.Thearrayresponsevectorof ar (θl )isgivenby:
where λ isthetransmissionwavelengthand d istheantennaspacing.Furthermorethearrayresponsevectorin(5)hasaunitnormandthefactor √Nt Nr in (4)reflectsthisnormalization.Thearrayresponsevector at (φl ),canbewritten inasimilarfashion.
3.2Beam-CodebookDesign
DifferentcodebookmodelshavebeendesignedaccordingtothechannelpropertyforinstanceGrassmanniancodebooks,ortosatisfyanhybridarchitecture forexampleMulti-ResolutionhierarchicalcodebookInthisworkduetofullanalogousarchitecturewedenotethecodebooks F and Q atthetransmitter andreceiverrespectivelyas:
where Ur =[ur (θ k ),..., ur (θk )], Nr /2 ≥ k ≤ Nr /2,isamatrix Nr × Nr whichcarriesthereceiverresponsevectorinthevirtualdirectionsthatsatisfy θk =arcsin( 2k Nr ),likewise Ut =[ut (φ i ),..., ut (φi )], Nt /2 ≥ i ≤ Nt /2 isamatrix Nt × Nt thatcarriesthetransmitterresponsevectorinthevirtual directionsthatsatisfy φt =arcsin( 2i Nt ),consequently Ut and Ur areunitary discreteFouriertransform(DFT)matricesreflectingthefixedvirtualreceive andtransmitangles,and H6G ∈ CNr ×Nt isthevirtualchannelmatrixandits entriesrevealsthedesiredchannelparameters,virtualAoAs,AoDsandpath gain[14].Inaddition,typicalsub-6GhzMIMOsystemscarrywithlowernumberofantennasthanmm-wave,thisfactwillleadtobroadervirtualanglesin thelowfrequencychannelcomparedwiththehighfrequencychannel,asshown inFig. 2 severalmm-wavevirtualAoAsandAoDsoverlaptothoseatvirtual
sub-6Ghz,reducingthesearchingspacetothoseoverlappedmm-waveangles, thenthecandidatebeamlistprovidedbythespatialinformationfromthesub6Ghzchannel,isstoredintheset S .Atthispointthetaskisselectthepairof virtualanglesinthemm-wavevirtualrepresentationthatprovidehighergainin orderinthereceiverinordertoestimatethemm-wavechannel.
Consideringtheset S iscarryingthebunchofpossiblesarrivalanddeparture virtualangles θp and φr respectively,where θp ,p =1, 2,...,P ; P<Nr and φr ,r =1, 2,...,Nt ; R<Nt decreasingthesearchingspaceandtrainingoverhead to P × R.Thenusingthesetofarrivalvirtualanglestoconstructthecombiner atthereceiveri.e. Q =[q1 (θ1 ), q2 (θ2 ),..., qP (θP )].Thedeparturevirtualangles arefeedbacktothetransmitterinordertobuilditsbeamformer F,wherelog 2 P bitsareneeded,thatcouldbesentusingthesub-6Ghzchannel.Thenewreceived signalinmm-wavesystemsis
Afteravectorizationstep:
where y = vec(Y), h = vec(H),and v = vec(V).Thelargestabsolutevalue entryin(15)determinesthebestbeam-pair,thatistosay iopt =argmax |[y]i |, willmatchthebestpairofAoAandAoD. Lengthofsignalx 510152025303540
Fig.3. Complexpathgainestimationforatypicalvalue.
4.2PathGainEstimation
AtthispointtheAoAsandAoDsfordifferentpathshavebeenestimatedby the qˆ i and fˆ i vectors,thereforethefinalstepistoestimatethenonzerovalues entriesofthechannel,tosimplifytheanalysis,weassumeasinglepathchannel, thenre-writingEq.(3)withavectortrainingsymbolsuchthat x ∈ C1×s ,the receivedsignalis:
WeapplythelinearLSestimatortocalculatethecomplexpathvalueassociated tothegivenAoAandAoD,givenby z =(xx H ) 1 xy H
where z = √ρqH ˆ i Hfˆ i , thatcarriesthepathgainestimation.Aboutthevector trainingsymbollengththeFig. 3 showsthevariabilityofthepathgainestimated αl accordingtothesignallength,wecanobservethereisaconvergencewitha lengthfurtherthan20.
AdditionallywefocusonanalyzetheratebetweentheeNBandanUEin downlinktransmission.Thentherate R isaffectedbychangingthechannel coherencetimeduetoMSvelocity,as
wheretheprelog-factortakesaccountthetrainingoverheadnecessarytoestimatesthechannel,here To = λBo 2vo , λ,Bo ,vo ,aremm-wavecarrierwavelength, bandwidthandmobilestationspeedrespectively,additionally Tτ isthenumber of P × R trainingblocksneededtoestimatethechannel.
Anothermetricchoosedtoevaluatetheperformanceoftheproposedmethod isthecomputationalcomplexitycomparedwithFastChannelEstimation(FCE) methoddescribedin[16].Thecomplexitycostisgivenby O (Nr Nt L + Nr L) countingthebeamandgainselection,bytheotherhandtheFCEcomputational complexityis O (Nr T + LNt T + LT ).
onsubchannel l , Hi,l isthemassiveMIMOchannelbetweentheMMWSC i and theUEonthe l -thsubchannel, qi,l isthecombiningvectorintheUEpointing toMMWSC i onsubchannel l and IS denotesthepowerinterferencesufferedby anUEfromneighboringMMWSCs,as
Theterm IS cansignificantlyreducetheratesachieved.Specifically,dependingonthesignaltonoiseandinterferenceratio(SNIR)feedbackfromtheUE, theMMWCscandecidetoformcooperativegroupscalledcoalitions,inorder toovercometheinterferencebetweenneighboringcellsandthehandoffmanagement.Underthiscoalitionalgameapproach,theMMWCsaremodeledasplayers thataccessthespectrum,avoidingcoalitionsamongthembyjointlyscheduling theirtransmissions,westatethefollowingdefinitionforacoalition:
Definition1. Acoalition S ⊆N isanon emptysubsetof N inwhichplayers insidethesetaccessthespectrumviaacoordinatedmanner.
Thereforeweconsiderthatifacoalition S isformed,thetransmissionsinside S aremanagedbyalocalschedulerasin[20],usingTimeDivisionmultipleaccess (TDMA)mode,suchthatthesubchannelsaresplitintimeslotsallocatedfor everyMMWSC.AsaresultnomorethanoneMMWSCwillaccesstheevery channelineachtimeslot,mitigatingtheinterferenceinsidethecoalition S Althoughcoordinationcanhelptoincreasethechannelratebydecreasing theinterference,italsoincursinacoordinationcost.Hereweconsiderthiscoordinationcostintermsoftransmitpower.Thus,thepowerspentbyaMMWSC i toreachthefarthestMMWSC ˆ j inacoalition S is ρˆ j,i .Thenthepowercost neededtoformacoalition S is:
Inaddition,wedefineamaximumtolerablepowercost ρlim foreverycoalition S asin[21].Byconsideringthecoalitioncostinthiswaywetakeaccountthe spatialdistributionoftheMMSCsandthecoalitionsize.
5.2MMWCsCooperationasaCoalitionalGame
ThemaingoalistodealwithinterferencefromneighboringMMWSCinthe bordercoverageareabyformingcoalitions,i.e.,usingcoalitionalgametheory [18],wedenoteas B thesetofallpartitions GN of N ,thisproblemcanbe modeledascoalitionalgameinpartitionformwithtransferableutilityas[19]:
Definition2. Acoalitionalgameinpartitionformwithtransferableutility (TU)isdefinedbythepair (N ,v ) where N isthesetofplayersinthegame, andavaluefunction v (S,GN ) assigningarealvaluetoeachcoalition S .
12P.Palaciosetal.
Wealsoassumethat v (∅)=0.Thus,thedefinitionaboveimposesadependence onthecoalitionalstructure N whenevaluatingthevalueof S ⊆N ,i.e.tothe players N\S aswell.BytheotherhandtheTUpropertyimpliesthatthetotal utilityrepresentedbyarealnumber,(inourcasethechannelrate)canbedivided inanymannerbetweenthecoalitionmembers.
Clearly,thecooperationmodelcanbestatedasagameinpartitionform wheretheMMWSCaretheplayers,sincethechannelrateofacoalitionis affectedbytheinterferencefromothersplayers,thusthereisadependence betweenthecoalitionandtheplayerswhichdonotbelongtothecoalition (coalitionalstructure).Thereforetheutilityachievedbythecoalition S can beexpressedintermsofthechannelrateas:
where αl i ∈ [0, 1]denotesthefractionoftimedurationduringwhichMMWSC i transmitsonthesubchannel l totheUE.Inthenon-cooperativescenario,i.e., FDDtransmissionmode,eachtransmissionoccupiesawholesubchannel,hence αl i =1.Inaddition I ˆ S denotestheco-tierinterferencesufferedbytheUEserved byMMWSC i onsubchannel l fromplayers j ∈N\S asfollows:
Thereforethankstotransmissionschedulingtheinterferencefromplayerswithin thecoalition S issuppressed,whileinter-coalitioninterferencestillremainand leadstoagameinpartitionform.Giventhepowercostandutilityfunctionfor anycoalition S ∈N ,wecandefinethevalueofanycoalition,i.e.,thetotal benefitas:
(S ,GN )= |S |U (S ,GN ) ifρS ≤ ρlim 0 otherwise, (24)
Thesub-6Ghzchannelworksat f6G =3GHzandmm-wavechannelat fmm =28GHz,bandwidth Bo =10MHzalikethanmm-wavecase,thedistance betweentheUEandeNBissetat50m,thepathlossexponentatsub-6Ghz isequalto2whileformm-wavehasbeensetto3.Theanglesofarrivaland departureforbothenvironmentsarelimitedat[ π 2 , π 2 ),theantennasnumberat sub-6Ghzandmm-wavewillbechangingaccordingtoeveryexperimentatthe UEandeNB,theinterantennaelementdistanceatbothcasesishalf-wavelength. Additionallythesignal-to-noiseratioissetas SNR = Po σ 2 o .
Toassesstheestimationerrorweexpressthemm-wavevirtualchannel Hvirt assparse[16],suchthat Hvirt = JT LNr Λ JLNt where Λ isan L × L diagonal matrixandthe L aretheentriesdifferentthanzeroof Hvirt ,thebinarymatrices JT LNr , JLNt are L × Nr and L × Nt selectionmatrices,generatedbykeeping L rowsof Nr × Nr and Nt × Nr identitymatricesrespectively.Thereforewecan computethemeansquareerrorasMSE= E { Hvirt Hvirt 2 F / Hvirt 2 F }.
Algorithm1. TheProposedMMWSCcooperationalgorithm
Step1:UEinterferencesensing
TheUEsensetheinterference UEint ,onceitoverpassathreshold Ithr ,theUE feedbacktheinformationtoitsattachedeNBinordertoinitiatethecooperation process,thus: if UEint ≥ Ithr then
Step2:CoalitionalGameStarts
Atthebeginningwhenplayersarenotcooperating GN = {1,..., N} = {S1 ,...,SN }
–Theresultingcoalitionisincludedintherecursivecore. until convergencetoastablepartitionintherecursivecore.
Stage3-Inner-coalitionscheduling:
–TheschedulinginformationisgatheredbyeachMMWSC i ∈ S fromits coalitionsmembers,andtransmittedwithinthecoalition S afterwards.
endif
Step3:HighSpeedmmWaveCommunications
–Andhighdataratetransmissionstarts.
Inordertoexploretheperformanceoftheproposedmethod,inthefirst simulationwesettheSub6-Ghzchannelwith16transmitterantennasand16 receiverantennas,intheotherandwesetthemm-wavechannelwith Nr = Nt = 64, Nr = Nt =32and Nr = Nt =16antennas,intheFig. 5 wecanseehowthe spectralefficiencychangeaccordingtodifferentSNRvaluesforeveryantenna array,asisexpectedunderthebeamcodebookdesign,increasingthenumberof antennasleadtoanincreasinginthebeam-resolution.
Forexhaustive-searchthisoccursduetothenumberof Nr × Nt blocksneeded forchannelestimation,herethetrainingtimeoccupiesmostofthechannel coherencetimeleavingnotimefordatasending,bytheotherhandunderthis methodthankstopriorspatialinformationobtainedfromsub-6Ghzthenumber ofbeamcandidatesdecrease,suchthat P Nr and R Nr thereforetheblocks fortrainingarehighlyreduced,leavingmoretimefordatatransmission.
Thelastexperimenttakesaccountthesystemcomplexitybetweentherefined CEmethodandFCEdetailedat[17]intermoftheircomputationtime,the complexitycostare O (Nr T + LNt T + LT )and O (Nr Nt L + Nr L)respectively. AllsimulationsareconductedatMatlabR2015abytheIntelCorei5CPU,in Fig. 6(a)the Nr issetto16,while Nt isincreasing,theninFig. 6(b)theNt isset to16and Nt ischanging.Forthesakeoffairnesswecomparativebothmethod
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“I think she refers to some legend,” answered Gertrude. Chee had always been interesting; her personality was felt, even when she was her usual, reserved little self; to-day, all embarrassment cast away, she was fascinating.
“We don’t know about it, Birdie; can’t you tell us?”
“I forgot you didn’t know,” replied Chee. Then as if in penitence, she added, “I’ll close the door again, if you’d rather, Cousin Gertrude.”
“No, leave it open. The storm is going around us. It will be pleasanter soon. Now tell us what you meant by ‘Grandfather.’”
So Chee began,—the rain dripping from the roof, and the fresh, purified air blowing in at the wide-swung door,—“Why, as I said, Thunder is our grandfather. He has three boys. That loud, sharp sound that hurt Cousin Gertrude’s ears was the baby; he is cross and cruel. But grandfather will never allow him to harm us. Grandfather lets him kill animals sometimes.
“His other sons are kind, gentle boys; they never do any harm, but cool the air instead, and make the earth fresh again. Thunder that just threatens and mutters is grandfather’s voice.”
“What about lightning?” asked Cousin Herman, with a twinkle in his eye. “Is that kind and good?”
Chee laughed. “Lightning? She’s—well, she’s his wife.” They all laughed at her answer, and Mr. Farrar mischievously glanced at Gertrude. Chee noticed that she blushed, but took courage and added, “There’s an old story about grandfather; would you like to hear it?”
Of course they were only too glad to keep her talking, so, clasping her hands around one knee, she commenced the story—her low, dreamy voice fitting well with the tale.
“Well, once, years and years ago,[2] there were two Indian homes. In each home there was a beautiful daughter; they were lovely, good friends, but they couldn’t see each other very often, for their wigwams were such a long ways apart. But one awful hot day, one of them asked her mother if she couldn’t go and see the other girl, and
her mother said ‘no,’ ’cause she was so pretty But the girl teased so hard she had to let her go.
“She hadn’t gone very far before a tall man came and walked beside her, and said such nice things to her she forgot all about where she was going, until she found right in front of them a big rock with a hole in it. The man said, ‘This is where I live. Won’t you come in?’
“She was afraid of the dark, so she wouldn’t go. But he coaxed, and finally she said she’d go in if he’d go first. So he went, but just the minute he got inside, he turned right into an ugly old Wi-will-mecq, and she was scared most to pieces.”
“May we ask what a ‘Wi-will-mecq’ is?” asked Mr. Farrar.
“‘I’VE SAVED YOU FROM THE GREAT WI-WILL-MECQ’”
“It’s a great, horrid worm, and the girl tried to run away from it, but just then an awful loud thundering was heard, and she didn’t know anything more until she opened her eyes in a great big room with an old man in it.
“He said, ‘I’m your grandfather. I’ve saved you from the great Wi-willmecq.’ Then he showed it to her, out-doors, all chopped up in a hundred little pieces. He told the girl she must give him a smoke when he asked for it, to show she was grateful. Then he sent her home safe and sound. Do you like that story?”
“Very much,” answered Cousin Herman. “But I can see from her face that Gertie is wondering how in the world the girl could give old Thunder a smoke.”
“The Indians used always to do that after grandfather was so good to one of their people. They build a fire out-doors every time grandfather calls for it, and put some tobacco in it; it goes up in the smoke, and so he gets it.[3] Now you see I couldn’t be afraid, could I?”
Cousin Gertrude patted Chee’s braids. Mr. Farrar whistled softly to himself. Chee noticed that neither answered her question.
“Well, anyway,” she exclaimed, her eyes flashing, “you can ask just as many people as you like, and every one will tell you that there never was an Indian or anything he owned killed in a thunder-storm. [4] My daddy asked lots of wise people, and none ever could tell of a single one.”
Mr. Farrar could no longer whistle, his lips were trying to smile. With a smothered “Ha, ha,” he hurried out to feed his horse.
Chee was very much displeased. She went to the open door, and leaning her head against the casement, looked over the freshened fields. Before long, Gertrude joined her. Drawing the little girl to her, she too stood watching the landscape.
“Birdie,” she asked, at length, then hesitated, as though loath to go on, “do you honestly believe that pretty little story?”
Chee turned her face toward her questioner, all resentment gone— that soft light in her eyes, only there when she was deeply moved.
“Cousin Gertrude, dear,” she answered, looking clearly into the other’s face, “don’t worry. I know what you mean. Yes, and no. For the time I was telling it I believed it. But now when you ask me, I know quite well that Our Father sends the thunder, just as He sends the rain when we need it. Daddy told me so. But anyway, I shouldn’t be afraid because it’s just the same. He won’t let anything hurt me. Daddy told me that, and I think I should know it, anyway. Sometimes when the breeze blows softly against my cheek, it tells me so, and if ever I forget, the stars at night tell me how wrong it is to fear Our Father who loves us so.”
Cousin Gertrude made no reply, she only held the little one closer. Chee was not a heathen, but she was certainly a strange child.
CHAPTER XIV.
EVENING came. Mr. Farrar drove Gertrude and Chee to the minister’s home, and then hurried to the hotel. Everything looked favorable; the city musicians had arrived, and the night promised to be perfect.
Gertrude was already dressed for the entertainment, but Chee still wore her pink gingham. “Come, Chee, you won’t have any more than time,” she urged, anxious to know the contents of a box Chee had brought. “Don’t you want some help?”
“I’ve tried it on before,” answered the little girl, as she tugged upstairs with her package.
Eight o’clock drew near. The street in front of the hall was filled with farmers’ vehicles and passing townsfolk. Inside was the important bustle of ushers rushing to and fro, and the sound of instruments being tuned.
As the moments passed, the throng grew dense. Fans seemed to sway the audience back and forth. At last the curtains rose—the house was packed.
The chorus of white-clad children lifted its voice. It was a good chorus—the finest of which Chesterfield had ever boasted. Sadie’s grandpa was satisfied. The village philosopher’s psychological chart was being revealed to him. Even the doctor was elated. Beside him, sat “Cit’zen P’liteness,” which coincidence might have been fortunate for the boy, who more than once, in extreme excitement, choked and nearly swallowed his gum.
The musicians did their best. The people demanded encore after encore. It grew late. The enthusiasm lulled. Little children slept in their parents’ arms; here and there a fretful one cried out.
A hush fell over the stage, and people waited uneasily; children became still more impatient; the very air grew intense. A young lady near the front was faint—it was the one with blue eyes and golden hair. Soon a soft step was heard. All eyes were again fastened on the stage.
A small, brown-faced girl stood near the centre. She was dressed in gay Indian clothes; her long black unbraided hair fell nearly to her knees; bright beads were twined about her neck and arms; bare ankles showed above wee moccasins. In one hand she carried a small red violin and a long bow.
The people were too much interested to applaud. All strove for a better view of the dark, flushed face before them.
Catching sight of the golden-haired young woman, the child’s lips parted in a smile. Caressingly she put the violin under her arm, and nodded encouragement. The white face of her friend banished, for a moment, her own timidity.
The audience took this act of recognition to themselves, shouting and clapping again and again. The small face grew frightened, but the sight of a certain purple poppy, nervously bobbing among the sea of heads, restored its bravery. The little maid tucked the instrument beneath her chin. The confusion ceased.
“IT WAS AS THOUGH ALL THE PLAINTIVE STORY OF A DYING RACE HAD BEEN STORED IN THAT LITTLE RED CASE”
With her eyes uplifted, as though listening, she drew the bow across the strings—first tremblingly, then lovingly, and, finally, triumphantly. Once only her eyes lowered, sought the purple poppy, and lifted again. With more and more feeling came the music. It was as though all the plaintive story of a dying race had been stored in that little red case. Their hardships and sorrows; their wild life of the woods, the lakes, and the prairies; their weird chants and incantations; their joys and pinings now sobbed, now sung at the touch of small brown fingers.
Not a person stirred; even the children grew intent; for a moment the fans were poised; breathlessly the people listened. The music ceased. Tears were on cheeks fair and seamed.
A man appeared before the platform. It was Mr. Green, the minister. “Our little townswoman has been requested to render, as a special favor, that beloved melody, ‘Nearer, My God, to Thee.’” He spoke with earnestness, and retired immediately.
A strange expression came over the small musician’s face, a look so reverent, so pure, that the audience leaned forward in their seats. With an upward, yearning glance the child began to play.
If before, the dazzling, fantastic garb of the player had blended with the dreamy legends of her tender music, not so now; none looked at the girl save unconsciously to watch her face. Each person felt alone in holy communion with the music which descended as from heaven itself to the depths of their souls.
These strains spoke not of the forest, nor of the sea. They rung out in condemnation; they plead with tender reproachfulness; they swept through each soul, causing it to vibrate the notes in very sympathy with themselves, but it was always “Thou and me,” to each heart the world was not.
The notes died away. A great sigh arose from the audience. The curtain fell, and quietly the concourse of people dissolved. There
was no crowding, no laughter; there was little talk. As from a temple the people passed slowly out.
“Was it the instrument? Who can tell?” The clergyman asked himself that question. Cousin Herman asked it. Many others queried over it. It may have been. Who can tell? Strangely enough, no one ventured to ask the little half-breed. Had they done so, she doubtless would have answered, in her reverent way, “It was not me. It was just Our Father,” surely adding, “and Daddy Joe’s fiddle.”
CHAPTER XV.
TIME has passed. Though Aunt Mean and Uncle Reuben still live at the Bend, years have left their traces. They rest now through the day in their armchairs. Their faces are happy—far happier than in the old hard-working days.
Aunt Mean’s strong-minded features soften as she talks to Reuben, through his ear-trumpet, of the long ago.
“You were always a good woman, Mean,” he answers, soothingly. How love forgets its hardships and recounts its joys.
“I wasn’t no heathen, brother, but I was only half converted until that night.”
“We was all revived,” gently replies Uncle Reuben, “even the minister. Bless his soul, he’s got his reward for goodness now.”
“Hush! she’s coming.”
Footsteps sound upon the stairs. A sweet, low voice mingles with the Irish brogue of Biddy in the kitchen.
Soon a slight, middle-aged woman, dressed in black, enters the room. Her face tells of grief borne patiently, of joy from a trustful heart. Mrs. Green brings an open letter.
“From the children?”
“Yes, auntie. The little ones are all well. Herman has promised them a trip to the farm at Easter. Gertrude’s cold is better. They enclosed a letter from Chee.”
And so together they sit in the lamplight, lingering over their weekly pleasure—the children’s letter.
Most old places have their ghost stories. The Whittakers’ at the Bend is not an exception. Long ago the incident happened, but to this day neither of the old people are fond of the attic. Even the creaking stairway brings to Aunt Mean’s mind sad strains of music.
“Of course it was my guilty conscience, but, that night when I got up with a cramp, and heard the same old tune that poor Joe played the day before he died, it seemed as though my bones was frozen stiff.
“If I’d only done as you done, Reuben, and gone straight to the minister’s, it would have saved me nights of agony. Lots of times I used to hear them sounds after all but me was sound asleep. But I never dared get up. I’d hide my head underneath the bedclothes, and pray the Lord if He would only forgive me my hardness against poor Joe and his child, I’d do anything in the world.
“Ah, them was hard days, and that was a strange night, when I see the child and the fiddle on the platform, and the hull thing come over me like a streak of lightning.”
“’Twas the Lord’s way, Mean, my girl, and we won’t find no fault.”
“No, Reuben, and though you ain’t the one to say it, in your heart you’re mighty glad I’m a different woman from them days. I say it myself, as oughtn’t to.”
“You’re not the only one, Mean. ’Twas all the Lord’s doin’s.”
And Chee? Few know her by that name, or even the story of her birth and childhood.
In a far-off city, surrounded by luxury that wealth may buy, amid flattery that fame may bring, a certain celebrated musician still hears the echo of a little child’s plaintive prayer: “And if Thou do, I’ll do something for Thee sometime, only I can’t think of anything now. Thy kingdom come. Amen.”
It is Sabbath Day As the twilight is falling over the streets of that faroff city, you may enter the wide doors of a great building.
Many people of different nationalities reverently tread its dim aisles. The turmoil of life is forgotten in the hush of this peacefulness.
While you wait, a strain of tender music breathes softly through the place. The sounds scarcely break the silence. Stillness itself is given a voice. The faces about you brighten. Bitter lines soften; bowed shoulders straighten.
For one glorified hour you listen. And when the last evangel note has trembled its message to every part of the vast room, even from the frescoed dome to the deepest places in the hearts of the listeners, you silently turn away.
People of different races, speaking different tongues,—each soul with its own burden, griefs, or sins,—have all been lifted nearer heaven by the same voice of lingering music.
Is it a wonder that no other instrument, however precious, can say to weary hearts, “He is sure to have heard; it will be all right pretty soon,” as Daddy Joe’s fiddle?
THE END.
FOOTNOTES:
[1] Culloo is a mythical bird so large as to hide the sun when he flies before it.
[2] An abbreviation of a familiar Indian legend.
[3] Mentioned by A. L. Alger in “Indian Tents.”
[4] Universally believed among Indians.
TRANSCRIBER’S NOTES:
Obvious typographical errors have been corrected. Inconsistencies in hyphenation have been standardized.
Archaic or variant spelling has been retained.
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