UPLINK DETECTION PERFORMANCE REGARDING BANDWIDTH-EFFICIENT BROADBAND TRANSMISSION IN A LARGE-SCALE MU-MIMO SYSTEM

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1 Uplin detection performance regarding band width-efficient broadband tranmiion in a large-cale MU-MIMO ytem UPLIK DCIO PFOMAC GADIG BADWID-FFICI BOADBAD ASMISSIO I A LAG-SCAL MU-MIMO SSM Paulo orre António Gumão colasuperior de ecnologia IntitutoPolitécnicodeCateloBranco paulotorre@ipcbpt Intituto Superior écnico Univeridade de Liboa gu@itutlpt Abtract - hi paper deal with Single Carrier/Frequency Domain qualization (SC/FD) for uplin tranmiion within a Multi-Uer (MU) Multi-Input Multi-Output (MIMO) ytem where the number of Bae Station (BS) antenna can be much larger than the number of tranmitter antenna ointly uing the ame time/frequency reource at Mobile erminal (M) Selected Quadrature Amplitude Modulation (QAM) cheme are aumed for tranmiion o that high bandwidth efficiencie are achievable In thi context we conider either a linear detection or a reduced-complexity iterative Deciion Feedbac (DF) detection evaluate the achievable performance in both cae and dicu them with the help of elected performance bound and emi-analytically evaluated error floor level From our performance reult we conclude that imple linear detection technique deigned to avoid the need of complex matrix inverion can lead to unacceptably high error floor level owever by combining the ue of uch imple linear detector with the appropriate interference cancellation procedure - within the iterative DF technique - a cloe approximation to the Single-Input Multi-Output (SIMO) Matched-Filter Bound (MFB) can be achieved after a few iteration even for 6-QAM cheme when the number of BS antenna i five time higher than the number of antenna ointly ued at the uer terminal Keyword: Broadband MU-MIMO ytem; maive MIMO; uplin; SC/FD; linear detection; iterative DF detection; performance evaluation bandwidth efficiency Introduction Cyclic-Prefix (CP)-aited bloc tranmiion cheme propoed and developed for broadband wirele ytem tae advantage of current low-cot flexible Fat Fourer ranform (FF)-baed ignal proceing technology with both Orthogonal Frequency Diviion Multiplexing (OFDM) and SC/FD [ ] Mixed air interface olution (for downlin and SC/FD for uplin []) are now widely accepted he development of MIMO technologie ha been crucial for the "ucce tory" of broadband wirele communication hrough patial multiplexing following and extending idea early preented in [] MIMO ytem are currently able to provide very high bandwidth efficiencie and a reliable radio tranmiion at data rate beyond Gigabit/ In the lat decade MU-MIMO ytem have been uccefully implemented and introduced in everal broadband communication tandard []; in uch "pace diviion mutiple acce" ytem the more antenna the BS i equipped with the more uer can ointly communicate in the ame time-frequency reource he adoption of MU-MIMO ytem with a very large number of antenna in the BS much larger than the number of M antenna in it cell wa propoed in [] hi "maive MIMO" approach wa hown to be recommendable [ 6 7]: imple linear proceing for MIMO detection/precoding (uplin/downlin) become quai-optimal; both MUI/MSI (Multi-Uer Interference/Multi-Stream Interference) effect and fat fading effect of multipath propagation tend to diappear; power and bandwidth efficiencie are ubtantially increaed hi paper deal with SC/FD for the uplin of a MU-MIMO ytem where a high bandwidth efficiency i intended through QAM tranmiion cheme (up to 6 bit/ymbol) and the BS i contrained to adopt lowcomplexity detection technique but can be equipped with a large number of receiver antenna not necearily much larger than the overall number of tranmitter antenna ointly uing the ame time/frequency reource at mobile terminal In thi context either a linear detection or a reducedcomplexity iterative DF detection are conidered a preented in ec : a to the linear detection alternative we include the optimum MMS (Minimum Mean Square rror) detection [8] a reduced-complexity MMS-type detection [9] and the quite imple MF (Matched Filter) detection; the iterative DF detection alternative which reort to oint cancellation of etimated MUI/MSI i an extenion of the iterative DF technique conidered by the author for -QAM tranmiion in [] and can alo be regarded a an he omanian eview Preciion Mechanic Optic & Mechatronic 6 Supplement to o 9

2 Uplin detection performance regarding band width-efficient broadband tranmiion in a large-cale MU-MIMO ytem extenion to the multi-input context of reducedcomplexity iterative receiver technique propoed by the author for ytem (ee [ ] and the reference therein) In thi paper we evaluate in detail the detection performance for the everal detection alternative (dicued with the help of elected performance bound a preented in ec ) for a range of value regarding the number of available BS receiver antenna A wide et of numerical performance reult and the main concluion of the paper are preented in ection and repectively MU-MIMO Uplin Sytem Model and Detection echnique SC/FD with QAM Scheme for Bloc ranmiion We conider here a CP-aited SC/FD bloc tranmiion within a MU-MIMO ytem with X antenna and X antenna; for example but not necearily one antenna per M We aume in the th X antenna a length- bloc [ ] of time-domain data ymbol in accordance with the correponding binary data bloc and the elected QAM contellation concerning m bit/ymbol under a Gray mapping rule A length- L CP long enough to cope with the time-diperive effect of multipath propagation i alo aumed By uing the frequency-domain verion of the timedomain data bloc given by S S S DF S ( ) we can decribe the frequency-domain tranmiion rule a follow for any ubchannel : antenna pair ( i i the DF of the Channel Impule epone (CI) h h h h where ( h i for n > L ( n ) egarding n a tatitical channel model - which encompae all poible channel realization - let u aume that * and h n h h n n for n n By alo auming for any ( i ) a contant hn P n () (of coure with h n for n > L ) the average bit energy regarding the th antenna at each antenna i given by where b P m( L () and Linear Detection echnique n An appropriate linear detector can be implemented by reorting to frequency-domain proceing After CP removal a DF operation lead to the required et ; of length- input to the frequency-domain detector ( given by ()); it wor for each a hown in Fig leading to a et ~ ; of length- output ~ ~ ~ ~ () () ( ) ( ) S () where () () ( ) S S S () ( ) S i the input vector () i the Gauian noie vector (i) ( i) and denote the channel matrix with entrie concerning a given channel realization and () () ( ) i the reulting frequency-domain output vector A to a given channel realization it hould be noted that the CF (Channel Frequency epone) concerning the Figure : Frequency-domain linear detection and iterative DF detection combining a linear detection and interference cancellation in the frequency domain 6 he omanian eview Preciion Mechanic Optic & Mechatronic 6 Supplement to o 9

3 Uplin detection performance regarding band width-efficient broadband tranmiion in a large-cale MU-MIMO ytem When poibly with either an MMS frequency-domain optimum linear detection or a reduced-complexity frequency-domain linear detection can be conidered In all cae the detection matrix for each ubchannel ( ) can be written a where ˆ D B () Ĥ i the conugate tranpoe of the etimated MU-MIMO channel matrix Ĥ and matrix poibly depending on ~ D A ˆ B i a elected Ĥ herefore at the output of the frequencydomain linear detector (ee Fig ) It hould be noted that the th component of Ĥ ( )* ( ) i given by ˆ i i ( ) : thi mean i that the Ĥ factor provide Maximum ati Combining (MC) procedure one per antenna all of them baed on an appropriate MF for each component of the length- received vector at ubchannel For an MMS detection -the optimum linear detection- we need to adopt B A where By defining G - and Gˆ ˆ ˆ - B can be written a a function of Ĝ and αˆ with both the tandard detection and the implified MMS-type detection reported above ince A Gˆ αˆ For a given channel realization and a given detection matrix D which depend on the etimated channel realization Ĥ the output of the frequencydomain detector i given by ~ D Γ S (7) where Γ D and D With SC/FD (time-domain data ymbol) an IDF (Invere Dicrete Fourier ranform) i required for ~ ~ ~ ~ each vector he nth ~ ( ~ ( ) component of the reulting length- IDF y vector can be written a ~ yn n ISI MUI/ MSI ' Gauian noie ~ * ( yn n with Γ herefore ~ can be written a ˆ A ˆ αˆ () ~ γs Γ γ S D (8) with αˆ denoting a diagonal matrix characterized by the etimated value of o By imply adopting I B (an identity matrix) we can trongly reduce the implementation complexity: ince D Bˆ ˆ thi i a MF detection When replacing the MMS detection by a imple MF detection however a ignificant performance degradation i unavoidable An intermediate detection olution - regarding both complexity and performance - i provided by the adoption of a implified MMS-type cheme which replace the exact inverion of A by an approximate inverion In thi context we conider a recommendation of [9] o a to obtain B A while avoiding a complex B I where diag A matrix inverion: A diaga diaga A i given by () and (6) diag A i a diagonal matrix - very eay to invert - which hare the main diagonal with A where γ i a diagonal entrie given by written a ~ ( γ i ( ( S D (i) (i) Γ matrix with ( ( γ Γ With ( γ ( S ( l (l Γ (l) (l) S ~ ( ) (9) the term in the right-hand ide of eq (9) are concerned repectively to ignal Inter-Symbol Interference (ISI) MUI/ISI and Gauian noie at ubchannel Low-Complexity Iterative DF Detection echnique A low-complexity iterative DF technique can be eaily devied having in mind eq (8) hi frequencydomain non-linear detection technique i depicted in Fig It combine the ue of a linear detector and for all iteration after the initial iteration (ie for p > ) a cancellation of reidual MUI - and reidual MSI when ome uer adopt everal X antenna for he omanian eview Preciion Mechanic Optic & Mechatronic 6 Supplement to o 9 7

4 Uplin detection performance regarding band width-efficient broadband tranmiion in a large-cale MU-MIMO ytem patial multiplexing purpoe - a well a reidual ISI; uch cancellation i baed on the etimated data bloc which i provided by the preceding iteration and fed bac to the frequency-domain detector he output of thi detector for iteration p i γˆ( p) Γˆ ( p) Sˆ ( p ) ~ ~ ' ( p) ( p) () ~ ~ ; p >( forp ' ( p) ( p) where Γ ˆ ( p) D ( p) ˆ - with D ( p ) denoting the detection matrix employed in iteration p - and the entrie ( of the diagonal matrix γ ˆ( p) are given by ˆ ( ) ˆ ( p ( p) Of coure p Sˆ ( ) ) ( p ) ˆ ( p ) ˆ ( p ) Sˆ ( ) ( DF he implementation of thi iterative DF technique i epecially imple when D ( p) ˆ for any p ie with a linear MF detector for all iteration; an intereting alternative which alo avoid a complex matrix inverion conit of adopting B ( p) I for p > (ie detection) and for p B ( p) a given by eq (6) It hould be noted that Γ ˆ ( p) D ( p) ˆ B ( p) ˆ ˆ B ( p) Gˆ : Γˆ ( p) Gˆ for the MF detector and Γ ˆ ( p) i a function of detector Ĝ and αˆ for the implified MMS-type On Achievable Detection Performance when Many BS Antenna are Available Bit rror ate (B) with Linear Detection egarding evaluation of linear detection performance by imulation a imple emi-analytical method i preented here combine imulated channel realization and analytical computation of B performance which are conditional on thoe channel realization In all cae the conditional B value are directly computed by reorting to a Signal-to-oie- Interference-plu-oie-atio (SI) under the realitic aumption that the interference ha a quai- Gauian nature hee ratio are imply derived in accordance with the channel realization ( ) Of coure for concluding the computation in each cae - involving random generation of a large number of channel realization and conditional computation - a complementary averaging operation over the et of channel realization i required When uing a linear detection technique (ec ) it i eay to conclude having in mind [] that the ignal-to-interference-plu-noie ratio concerning the th input of the MU-MIMO ytem i given by SI where l ( l l ( Γ i D P m ( i) b () ( l) ( ) Γ l l ( l For -QAM tranmiion m the reulting B - conditional on the channel realization { ; } - i given by B Q SI () where Q () i the Gauian error function) with SI a computed above For 6 -QAM tranmiion m the reulting B ( ) - can be obtained very accurately a follow (having in mind the Gray mapping rule): B B B () where B p p and B p p p p with n p n Q SI () For 6 -QAM tranmiion ( m ) an accurate approximation to B can alo be obtained (alo having in mind the Gray mapping rule): B B B B () where B p p p p 7 8 he omanian eview Preciion Mechanic Optic & Mechatronic 6 Supplement to o 9

5 Uplin detection performance regarding band width-efficient broadband tranmiion in a large-cale MU-MIMO ytem B and p p p p p p p p with B 7 p p p p p p p p p p p p p p p p n p n Q SI (6) When n > of coure p n p and p n p for high SI By uing M m( we get term (MUI/MSI ISI) herefore the SIMO/MFB bound i given by the appropriate f SI according to m with SI i i (9) ince with MF detection i By auming a LOS (Line-Of-Sight) ingle-path radio propagation for each i antenna pair -ie i ( ) P - we can obtain B SI Q m( M M (7) SI b P m( () Irreducible B Level under Low-Complexity Implementation Contraint When a low-complexity linear detection technique i adopted - uch a the detection or the implified MMS-type detection reported in ubection - an "error floor" effect i unavoidable he correponding Irreducible B i given by IB lim f l l ( l B lim f SI (8) where f SI i the appropriate function of SI according to m which i ued for computation of B a explained in Sub-Section and ( l a in () l SIMO Performance Bound and Maive MIMO effect he SI for emi-analytical computation of the SIMO/MFB (Matched Filter Bound) on detection performance can be eaily derived from () by conidering the Gauian noie and the "ueful" term at the MF detector output but not the two interference leading to the SIMO/AWG/MFB When both the MUI/ISI effect and the effect of multipath propagation (fading ISI) tend to diappear: conequently the performance for the MU- MIMO ayleigh fading channel become very cloe to thoe concerning a SIMO channel with ingle-path propagation for all X/X antenna pair he "maive MIMO" effect that can be explained when mean that i P to f * l) and leading l ( l b B SI with SI m( (ie cloely approximating the SIMO/AWG/MFB) umerical eult and Dicuion he et of performance reult which are preented here are concerned to SC/FD uplin bloc tranmiion uing QAM (up to 6 bit/ymbol) with 6 and L 6 in a MU-MIMO ayleigh fading channel with or Perfect channel etimation and power control are aumed he fading effect regarding the everal X/X antenna pair are uppoed to be uncorrelated with independent zero-mean complex Gauian h coefficient aumed to have variance n 6 ( P for n 6 ) n n n P n 6 he omanian eview Preciion Mechanic Optic & Mechatronic 6 Supplement to o 9 9

6 Uplin detection performance regarding band width-efficient broadband tranmiion in a large-cale MU-MIMO ytem Figure : IB performance curve concerning either MF detection (dahed line) or implified MMS-type detection (olid line) - when or - for -QAM (the bet) 6-QAM and 6-QAM (the wort) Fig how Irreducible B (IB) reult for a wide range of value of and the ame contellation ( 6 or 6-QAM) at all input of the MU-MIMO ytem hee performance curve have been obtained through the emi-analytical imulation approach preented in ec and confirmed by conventional Monte-Carlo imulation (quai-uperpoed dot) involving an error-counting procedure wo alternative low-complexity linear detection technique were conidered both avoiding complex matrix inverion: the MF detection and the implified MMStype detection a reported in ec hee reult clearly how that under both low-complexity detection technique unacceptably high error floor level (ay IB > are unavoidable if i not large enough; they become epecially high when a high bandwidth efficiency i intended - through an increaed ize of the QAM contellation - and/or the MF detection i adopted An excellent agreement of performance reult obtained by emi-analytical mean and by conventional Monte Carlo imulation i alo obervedby comparing Fig and Fig ( and repectively) we can notice that the IB level i eentially determined by the ratio foreach QAM cheme and each linear detection technique; we can alo notice that the implified MMS-type detection outperform the MF detection when that ratio i abovea given threhold ( approximately equal to in all cae) Fig how performance - obtained through the emi-analytical method - with and 6 and or and (c) the ame QAM contellation and the ame at all ytem input and a linear detection technique: MF detection implified MMStype detection or true MMS detection (ee ubection ) For comparion we alo include the analytical SIMO/AWG/MFB with the quai-uperpoed dot denoting the SIMO/MFB emi-analytically obtained hee reult confirm thoe of Fig on the performance limitation of the low-complexity linear detection technique (deigned to avoid a complex matrix inverion) alo howing the good performance achievable through a linear ideal MMS detection (which require a complex matrix inverion) with a nice approximation to the SIMO/AWG/MFB (a gap below db even for 6- QAM and the lower )By comparing Fig ( and 6 ) and Fig ( and ) - concerning the ame ratio two time above the threhold - we cannotice that a expected the achievable B for very high ignal-tonoie ratio cloely approximate the correponding IB hown in Fig ; by comparing both figurewith Fig (c) - concerning - we can oberve the performance benefit of the higher ratio Fig how the imulated B performance - obtained through the conventional Monte Carlo method - with and 6 and or and (c) the ame QAM contellation and the ame ued at all ytem input and an iterative DF detection technique a decribed in ubection A implified MMStype detector i adopted for the firt iteration (ie B ( p) i given by eq (6) for p ) and an MF detector i adopted for the remaining iteration (ie B ( p) I for p > ) Similarly to Fig thi figure alo include analytical SIMO/AWG/MFB reult In the cloely related Fig alo concerning an iterative DF detection a decribed in ubection we adopted an MF detector for all iteration he omanian eview Preciion Mechanic Optic & Mechatronic 6 Supplement to o 9

7 Uplin detection performance regarding band width-efficient broadband tranmiion in a large-cale MU-MIMO ytem (c) Figure : B performance - when and 6 and or and (c) - concerning MF detection (blac dahed line) implified MMS-type detection (blac olid line) or true MMS detection (dot-dahed line) for -QAM (the bet) 6-QAM or 6-QAM (the wort) in all X antenna [SIMO/AWG/MFB reference performance (dotted line) are alo included] (c) Figure : B performance - when and 6 and or and (c) - concerning an iterative DF detection with a implified MMS-type detector for p and an MF detector for p > for -QAM (blac olid line) 6 -QAM (dahed line) or 6 -QAM (dot-dahed line) [SIMO/AWG/MFB reference performance (dotted line) are alo included] Figure and how that by combining the ue of the low-complexity linear detector with an interference cancellation procedure a depicted in Fig a cloe approximation to the SIMO/MFB (and the practically identical SIMO/AWG/MFB) can be achieved: after a few iteration the performance gap at B become negligible if required by uing the implified MMS-type detection - intead of the MF detection - in the firt iterationby comparing the ubfigure of Fig and Fig with the correponding ubfigure of Fig we can oberve that after a few iteration the lowcomplexity iterativedf detection can outperform the optimum (MMS) linear detection which i not able to achieve a negligible performance gap regarding the SIMO/AWG/MFB; in pite of aninitial iteration where the B performance - trongly contrained by the ratio - i very poor after everal iteration we he omanian eview Preciion Mechanic Optic & Mechatronic 6 Supplement to o 9

8 Uplin detection performance regarding band width-efficient broadband tranmiion in a large-cale MU-MIMO ytem can practically achieve an ideal(interference-free and fading-free) B performance eentially determined by - regardle of - for each QAM cheme provided that [ven when uing the (extremely imple) MF detector in all iteration the ideal B performance can be practically achieved even for 6-QAM cheme when ] Fig 6 how the imulated B performance - when and - concerning the iterative DF technique with an MF detector for all iteration in a pecific cae where different QAM ymbol are imultaneouly tranmitted through the tranmitter antenna: 6-QAM for with e and equal to ± ±± ±7; 6-QAM for m n 6 with e and n n equal to m n ± ±; -QAM for with e and m n equal to ± Clearly the SIMO/AWG/MFB performance concerning the adopted can be practically achieved for all QAM cheme - in thi realitic context where different QAM cheme coexit - in pite of auming the extremely imple detector for all iteration n (c) Figure : Similar to Fig but auming an MF detector for all iteration Figure 6: B performance - when and - concerning an iterative DF detection with an MF detector for all iteration for -QAM (olid line) 6 -QAM (dahed line) or 6 -QAM (dotdahed line) repectively in 8 and X antenna [SIMO/AWG/MFB reference performance (dotted line) are alo included] Concluion hi paper wa dedicated to uplin detection iue concerning a MU-MIMO ytem where QAM-baed (up to 6 bit/ymbol) SC/FD tranmiion cheme are adopted and a large number of BS antenna i available poibly much larger than the correponding number of tranmitter antenna at mobile terminal In thi context we conidered everal detection technique and evaluated in detail the reulting performance - dicued with the help of elected performance bound - for a range of value regarding the number of BS receiver antenna From our performance reult our main concluion i that imple linear detection technique deigned to avoid the need of complex matrix inverion can lead to unacceptably high error floor level owever by combining the ue of uch imple linear detector with he omanian eview Preciion Mechanic Optic & Mechatronic 6 Supplement to o 9

9 Uplin detection performance regarding band width-efficient broadband tranmiion in a large-cale MU-MIMO ytem an interference cancellation procedure - within a lowcomplexity iterative DF technique - a cloe approximation to the SIMO/MFB performance can be achieved even for 6-QAM cheme after a few iteration when the number of BS antenna i five time higher than the number of antenna ointly ued at the uer terminal 6 eference [] A Gumao Dini JConceicao and teve Comparion of wo Modulation Choice for Broadband Wirele Communication In Vehicular echnology Conference VC Spring oyo It volume page vol may [] AGumao Dini and teve On Frequency-Domain qualization and Diverity Combining for Broadband Wirele Communication I ranaction on Communication (7): 9 July [] GFochini Layered Space-ime Architecture for Wirele Communication in a Fading nvironment when Uing Multi-element Antenna Bell Lab echnology Journal vol () 996 [] Gebert et al Shifting the MIMO Paradigm Signal Proceing Magazine I ():6 6 Sept 7 [] L Marzetta on-cooperative Cellular Wirele with Unlimited umber of Bae Station Antenna Wirele Communication I ranaction on 9():9 6 ovember [6] ueetal Scaling Up MIMO: Opportunitie and Challenge with Very Large Array Signal Proceing Magazine I (): 6 Jan [7] Joydi StenBrin and MDebbah Maive MIMO in the UL/DL of Cellular etwor: ow Many Antenna Do We eed? SelArea in Comm I Journal on ():6 7 Feb [8] amhi Kim uung Lee and yuncheol Par Performance Analyi of MIMO Sytem with Linear MMS eceiver Wirele Comm I ranon 7():7 78 ov 8 [9] Wuetal Approximate matrix in verion or highthrough put data detection in the large-cale mimo uplin In Circuit and Sytem (ISCAS) I Int Symp on page 8May [] Porre LCharrua and AGumaoOn Detection Iue in the SC- baed Uplin of a MU-MIMO Sytem with a Large umber of BS Antenna I Vehicular echnology Conf VC Sep [] Antonio Gumao Paulo orre ui Dini and elon teve A Cla of Iterative FD echnique for educed-cp SC-Baed Bloc ranmiion In urbo Code elated opic (UBO CODIG) 6 th Intern Symp on page 6April6 [] AGumao Porre Dini and teve A urbo FD echnique for educed-cpsc-baed Bloc ranmiion Sytem Comm I ran on ():6 Jan7 he omanian eview Preciion Mechanic Optic & Mechatronic 6 Supplement to o 9