Precoding trong Hệ thống thông tin di động

CHNG 4: HN CH DUNG LNG PHN HI DA VO BEM TRONGMULTI-USER MIMO

4.1. Gii thiu chng:Bn cnh nhng hnh thc phn chia bit nh: thi gian, tn s v m trong

truyn thng khng dy, gn y phn chia theo khng gian c xem nh l mtchiu hng mi nng cao hiu nng ca h thng, c bit l trong truynmultiuser (MU). Trong a truy cp phn chia theo khng gian (SDMA), vic s dngnhiu anten mng cho php trm gc (BS) truyn ti ng thi nhiu lung d liu nvi nhiu ngi dng (user) khc nhau bng cch khai thc chiu tn hiu mi ny.Trong s cc k thut truyn MU, DPC (dirty paper coding) c bit n nh mtchin lc m ha MU ti u, khi hiu sut t c l dung lng gii hn caknh truyn MU. Tuy nhin, hiu sut ti u i km vi s tr gi cho phc tp lnv tnh thc t khng cao khi c mt lng ln user hot ng. Nh l mt k thuttuyn tnh c phc tp thp hn dng thay th, BD (block-diagonalization)precoding l mt xut m ha MU ti u c th thc hin c.

Trong cc ti liu vi hu ht cc k thut tin m ha (precoding) bit ugi thit cc ng MU downlink l ng nht v bt bin theo thi gian (user khngdi chuyn) trong sut mt n v d liu truyn kh ln block/burst (block-fading).Tuy nhin trong mng MU vi cc node mng c tc di chuyn nhanh (v d nhngi dng trn t, tu la hay tu cao tc trong h thng LTE(long-termevolution) ), kt qu l CIR (chanel impulse respone) lun lun thay i theo thi gianlm cho CIR tr thnh mt tp hp cc thng s rt ln. iu ny gy ra mt lng tiqu ln cho knh phn hi thng tin trng thi knh truyn (CSI feedback) trong qutrnh x l precoding v chn la (scheduling) user khi xem knh truyn lun thay i BS v lm ny sinh cc vn v knh CSI feedback b li thi. khc phc vn ny, trong knh MIMO downlink vi nhng user khng ng nht (mi u cui ding khc nhau c s anten thu khc nhau v cng sut nhiu khc nhau) , phngphp hn ch dung lng phn hi da vo BEM (basis expansion model) c xut. BEM c dng nh mt kiu mu tham s xp x bt kp s thay i theothi gian ca knh truyn v gim s lng thng s knh truyn. c bit hn gim lng thng tin phn hi, vector cc h s BEM hun luyn s c lng tbng thut ton LBG (Linde-Buzo-Gray) v lu vo codebook nh l mt tp hpcha mt lng ln cc h s BEM tham chiu, c bit trc c bn pht ln bnthu. V th, thay v phn hi mt lng ln cc thng s knh truyn ta ch cn gi vBS a ch ca cc h s BEM tng ng trong codebook qua knh feedback.

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4.2. Xy dng h thng:4.2.1. Tn hiu pht:

Xt knh downlink MU-MIMO LTE khng ng nht vi BS c trang b Ntanten pht, vi cc u cui khc nhau c s lng anten thu khc nhau v t s tnhiu trn nhiu (SNR) khc nhau, iu ch ghp knh phn chia theo tn s trc giao(OFDM) vi N im FFT c dng trong knh truyn downlink a sng mang. Saukhi IFFT v chn tin t vng (CP), tn hiu pht bng tn c s ca symbol OFDMth m c pht ti anten th p c th c vit nh sau:

xn,m(p) = exp ( ) (1)

Vi n {-Ng,,0,,N-1}, Ng l chiu di CP,X k,m(p) l sng mang con th k c tin m ha.4.2.2. p ng knh:

Vi mi cp anten pht th p ti BS v anten thu th ru ca user th u (c Ruanten thu), li knh th l l hl,n,m(ru,p) vi n, m ln lt l ch s thi gian v symbolOFDM. Trong knh downlink c xt, BEM c dung bt kp s thay i theothi gian ca knh truyn. Vi s tr gip ca BEM, li knh thay i theo thigian th l gia anten pht th p v anten th ru ca user th u ti khe thi gian th n vsymbol OFDM th m c biu din nh sau:

, (2)

Tc user c gi s l khng i trong M symbol OFDM(trong khungtruyn LTE).

L : s ng Phading ca knh truyn.:l gi tr ca hm c s th q c dng trong BEM.

: l nhng h s BEM.

Q : l s hm c s c dng trong BEM.

: c to ra u tin bi thut ton Jakes, sau c xp x bi

DSP-BEM, dng nh mt s kt hp tuyn tnh ca Q hm c s.

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4.2.3. Tn hiu thu:Sau khi loi b CP, mu thu th n trong symbol OFDM th m ti anten thu th

ru ca user th u c biu din:

n=0,.,N-1; (3)

Vi zn,m l nhiu Gausian cng thm vo vi phng sai u2 ta user th u. Gis nhng u cui khc nhau c c nhng cng sut nhiu khc nhau trong hthng ang xt.

Sau khi bin i FFT ti user, tng ng vi sng mang con th k trong symbolOFDM th m ti anten th ru ca user th u tn hiu thu c xc nh:

, (4)

l nhiu lin sng mang (ICI)

l

tn s knh truyn (CFR)

l nhiu ti bn thu min tn s

Trong mng MU ang xt,vi s lng user bt k, precoding v schedulingc thc hin trn mi sng mang con trong mi symbol OFDM ca mt khungLTE. Biu din cng thc (4) mt cch n gin di dng ma trn :

Yu = Hu X + Zu ; (5)

Vi

Gi s rng BS c cng sut pht trung bnh b hn ch tr( ) P

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Vi = E[XXH].

Trong (5) nhiu lin sng mang(ICI) b b qua v n l thnh phn c cng sutnh.Trong h LTE c thit lp,cng sut PICI b gii hn bi:

PICI 2 (6)Vi fd l tn s Doppler ca knh,v l tc u cui,vn tc nh sng c=3.108

m/s,fc l tn s sng mang, Ts l chu k ly mu ca h thng v s2 = E(| |2).

V d: H thng LTE vi fc =2 GHz,fs=1/Ts=1,92 MHz,v=400 km/h,kt quPICI 4.910-7 s2. Xem nh mt thnh phn nhiu thp c th b qua.

4.3. H thng truyn MU-MIMO hn ch dung lng feedback da vo BEM:4.3.1. Hn ch dung lng feedback da vo BEM:

Trong thit k hn ch feedback gi s vic c lng cc h s BEM cthit lp ti cc user , ta chia n ra lm Q/V phn tngng vi LBG codebook G ( gim phc tp ca codebook ngun) nh sau:

(7)

Vi ,

x = {1,,Q/V} v V l chiu di ca mi vector con.Trong LBG codebook ngun, ng vi mi ng fading l, thut tan

LBG(dng 105 vector hun luyn BEM) c dng to ra trc codebook sau:

(8)

Vi , l=0,L-1 v B l s bit nh phn biu dinv tr cho mt codevector trong LBG codebook.

(9)

Tng ng vi mi tc di chuyn thu bao th ta s to ra mt codebooktheo thut ton LBG t nhng vector h s BEM hun luyn tng ng vi tc .

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Vi mi u cui di ng khc nhau vi nhng tc bit trc, LBGcodebook G s c trin khai vi tc gn nht vi nhng tc bit trc .

Nhng thc t tc cc user rt kh xc nh mt cch chnh xc. Ngoi radung lng trong my thu ca cc thit b u cui cng khng m bo c vic lutr mt lng ln cc LBG codebook G c to ra trc tng ng vi nhng tc khc nhau. V vy lun tn ti chnh lch gia tc thc s ca mobile v tc sdng to ra codebook ti cc u cui di ng.

S dng mt LBG codebook G vi mt tc cho trc, qu trnh khi phccc vector h s BEM c thc hin nh sau:

Tm ra xp x tt nht ca cc vector con h s BEM c lng c trongcodebook bn thu.

(10)

Sau a ch ca h s BEM trong codebook c gi v BS qua knhfeedback khng li. Da vo a ch bit, BS c th xc nh c vector contng ng ca h s BEM trong codebook vi cng tc nh sau:

(11)

vi (12)

v (13)

x = 1,,Q/V v l = 0,,L-1.

T nhng phin bn lng t c, ma trn p ng tn s knh truynCFR ng vi user th u c th c xc nh ti BS nh sau:

(14)

v (15)

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Cc hm c s bit c BS ln user.

Nh ch ra cng thc (15), p ng knh ng vi mi sng mang con trongmi OFDM symbol trong khe thi gian LTE hin ti c th c xc nh t phin bn

ca h s BEM . Nh cp trc , nhng h s BEM xem nh c c lng hon ho bng thut ton c lng knh da vo BEM bit dngtn hiu pilot trong khe thi gian LTE trc.

Sau khi c c thng tin feedback ti BS, u c xem nh p ng knhhon ho (perfect CSI) v c s dng trong qu trnh x l BD precoding vscheduling, c trnh by mc tip theo.4.3.2. Block-Diagonalization Precoding:

Vi phin bn lng t CSI u c, ta dng n tin m ha dng d liupht cho cc user nhm loi b nhiu lin user (IUI). v

Vi tp user la chn U, tn hiu truyn ti BS lX = (16)

S dng cng thc (5) v (16), tn hiu thu ca user th u trong tp user cla chn c biu din di dng vector nh sau:

(17)

loi b thnh phn nhiu gia cc user IUI, trong (17),th ma trn BD precoding Wu phi tha mn c iu kin zero-forcing sau:

Hu Wu = 0 ; u # u , 1 u,uU. (18)Bng cch s dng BEM trong vic hn ch lng thng tin phn hi, BS ch

c phin bn lng t CSI trong (14) v do ma trn BD-precoding Wu sc xc nh bi nhng {u}u=1U xem nh l nhng CSI hon ho vy .

t c (18), ta c th biu din n di mt dng khc:

vi u=1,,U. (19)

t c zero-forcing trong (18), Wu phi l null space ca ma trn vimt iu kin cn Nt u (s anten pht phi ln hn hoc bng tng s anten

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thu ca cc user c la chn). tm ra null space ca ma trn ta phn hy(SVD) n nh sau:

(20)

Vi u l bao gm nu = ct u tin ca thnh phn phn hy th3 ca ma trn v u l nhng ct cn li (Nt-nu), u

Nh trnh by ,ta c:

u = 0 (21)

Vi uH u = I. Nh vy u l ngim tha mn phng trnh (18). Nhng ta schn ma trn BD-precoding ng vi user th u nh sau:

Wu = PuRu (22)

Vi l ma trn bt k tha mn iu kin hn ch tng cng sut vPu c to thnh t Ru ct ca ma trn u.

Pu = u (:,Nt - nu Ru + 1 : Nt - nu), (23)Vi nu = u.

Sau khi BD-precoding thnh phn nhiu cc user b loi b (inter-user-interference), tn hiu thu user th u l:

Yu = Hu PuRusu + Zu. (24)

By gi ta i xc nh Cu = RuRuH l mt ma trn positive semidifinite.Vi phin bn lng t CSI c sn ti BS, tc user th u c th c xcnh trong qu trnh tnh ton precoding/scheduling ti BS nh sau:

(25)

Vi ma trn =E[XXH] = uCuPuH(v E[susuH]=IRu). iu kin v cngsut tr( ) P . Suy ra (Cu) P (v tnh cht tr(ABC) = tr(BCA)).

Ma trn Cu c th c xc nh sao cho maiximize tc h thng

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Tng ng vi vic minimize - . Nh vy Cu l ngim ca h phng trnh sau:

Minimize -

Tha (Cu) P

Cu 0, u = 1,,U. (26)

Vi kiu h phng trnh trn ta c th gii quyt n mt cch hiu qu bngcch s dng iu hin ti u KKT (Karush-Kuhn-Tucker). n gin ha vic tnhton, ta t Du = u Pu xem nh l hiu ng knh ca user th u sau khi precoding. Tac 1/ u2 DuDuH = uEuuH vi Eu l ma trn ng cho cha cc gi tr (eu,1,, )v uuH = I. Suy ra u2Du-1Du-H = uEu-1uH. Nh trnh by trong [1], Cu c xcnh bng cng thc sau:

(27)

Vi (x)+ =max(x,0).Water-level c xc nh bi:

(28)

Nh vy vi tp user c la chn, qu trnh BD-precoding c gng clng i thnh phn nhiu gia cc user v maximize tc h thng. Nh cp trn, tnh kh thi ca vic hn ch feedback da vo BEM s c kim tra trongmng MU vi s lng user kch hot trng h thng ty . c bit vi vic s dngknh hn ch feedback ny, qu trnh precoding v scheduling u c x l ti BS.i hi mt qu trnh x l phc tp trong vic maximize tc h thng. Ta s xemxt mt cch chi tit k thut scheduling mc tip theo.4.3.3. Greedy Scheduling :

Trong k thut precoding, mc ch ca vic scheduling l tm ra tp nhnguser trong tt c nhng user ang kch hot trong h thng nhm maximize tc hthng. C mt cch thc n gin trong vic chn la ra tp user l tm kim y

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(x l tt c user) nhng iu s to ra phc tp qu ln v tnh thc thi khngcao khi s lng user qu ln. trnh nhc im trn Greedy Scheduling c xemnh l mt gii php thay th. Sau khi BD precoding cho tng user trong tp user S,tng tc BD(S) c th c xc nh ti BS nh sau:

(29)

vi Pu v Cu ln lt c xc nh (23)v (27).Chi tit qu trnh thc hin Greedy Scheduling vi Ua user ang kch hot trong

h thng c trnh by theo nhng bc sau:1) Khi u: A0 ={1,2,,Ua} l tp ch s ca cc user ang kch hot. S0={ }

l tp user c la chn ban u rng. v=0 tng ng vi s lng user c la chn. R0 = 0 l tc cu h thng.

2) Vng lp: Xc nh u* l ch s ca user c chn trong vng lp hin ti, u* c xc

nh nh sauu* = arg max { BD (Sv {u*})}, u Av (30)

max = BD (Sv {u*}) (31)

v = v+1 Nu max Rv-1 nhy ti bc 3, khng th thc hin cc bc sau:- Rv = max- Sv = (Sv-1 {u*}) (thm mt user vo tp user c chn)- Av = Av-1\{u*} (loi b i mt user trong vng lp tm kim sau) Quay tr li bc 2.3) Dng qu trnh la chn user:Vi tp S user c chn,tc thc s ca h thng l:

(32)

4.4. M phng v kt qu:Tin hnh m phng h thng vi cc thng s sau:

- S knh pha dinh tng ng mi cp anten pht vi anten thu L=5.- Tc ca user v=200km/h.

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S lng hm c s c s dng Q=18.- S khe thi LTE: 20.- S symbol trong mt khe thi gian: 7.- 128-point FFT.- Tn s ly mu: 1.92Mhz.- Tn s sng mang: 2Ghz.- Chiu di tin t vng: CP=10.- Phng sai nhiu: u2 =1.

4.4.1. Tc ca h thng khi thay i s lng user:S lng user thay i ln lt N_user=[4 10 20 30] vi s lng anten mi

user thay i tng ng [ones(1,N_user/2) 2*ones(1,N_user/2], s anten pht Nt=8.

Nhn xt: Tc user tng khi s lng user tng.4.4.2. Tc ca h thng khi s lng anten pht thay i:

S lng user khng i N_user=4, s lng anten thu ca mi user vn theoqut lut c, s lng anten pht thay i ln lt Nt=[2 4 6 8].

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Nhn xt: tc h thng tng khi s lng anten pht tng.4.4.3. BD-precoding:

Vi h thng Mutil-user MIMO n gin: s anten pht NT=4, s lng antenca mi user NR=2, s lng user =2, p ng xung h c to ra ngu nhin bi hmrand v xem nh bit bn pht. So snh BER ca trng hp s dng BD-precoding v khng s dng BD-precoding, iu ch M-QAM vi M khc nhau 2,4.

Nhn xt: s dng BD-precoding lm gim BER ng k. Trng hp M=2 cho BERtt hn M=4.

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4.5. Kt lun chng: chng ny ta i su tm hiu v cch hn ch dung lng feedback da

vo h s BEM.Tm hiu v phng php BD-precoding, phn b cng sut v xydng cch chn la user theo dung lng.M phng tc ca h thng khi ta thayi user , thay i anten pht v so snh 2 trng hp khc nhau khi c v khng sdng BD-precoding.

KT LUN V HNG PHT TRIN TI

TI LIU THAM KHO

[1] Nguyn L Hng,Mobile Communications[2] Yong Soo Cho,Jaek won Kim,Won Young Yang,Chung G.Kang.MIMO-OFDM Wireless Communication with Matlab[3] Nguyn L Hng,L Ngc Th,Loic Canonne-Velasquez Multiuser MIMODowlink Tranmission with BEM-Based Limited Feedback over Douby SelectiveChannels

PH LC****BD.m****

clear all;close all;N_trial = 50; % number of simulation trialsN_user = [4 10 20 30]; % number of available "homogeneous" users in the consideredLTE systemN_tx = 8; % number of transmit antennas at BS; N_rx: number of Rx antennas = 1 atthe current step.

L = 5; % number of resolvable multipaths < N_cp, could be considered as themaximum number of resolvable paths of all BS-to-user channelsPDP = exp(-[0:L-1]/4)/sum( exp(-[0:L-1]/4) );% Power Delay Profile in according toCOST 259, [L. M. Correia,

% "Wireless Flexible Personalised Communications",New York: Wiley 2001].v_offset = 20; % = 0 if users have perfect values of their speeds.v_kph =200;% speed of "homogeneous" users in km/hN_dps_base = 18; % number of DPS-BEM coefficents is used in the TV channelmodelingk_dimen = 2; % each BEM coefficient vector is divided into many segments with alength of k=2 before vector quantization.%======LTE downlink timing settings related to pre-defined DPS-bases/Codebook

%The below MAT-file contains the pre-defined LBG codebook to be used in thissimulation platform.loadCodebook_10bits_1E5trains_DPS_18Bases_200kph_fc2GHz_2LTEframes_normal_CP_128FFT;

achievable_rate = zeros(1,length(N_user)); % achievable rate of our proposed schemefor k=1:length(N_user)

N_rx = 2*ones(1,N_user(k))No = 1*ones(1,N_user(k)); % Noise variance in "hetergeneous" scenarios

for trial =1:N_trial % to obtain average values of capacity/ratedisp(['Current Trial = ', num2str(trial)]);

actual_speed = v_kph + v_offset*(2*rand-1); % due to imperfect knowledge of userspeeds

[BEM_coe_Rx,CIR_Rx,TI_CIR_Rx] =Zheng_DPS_CIR_Gen(N_user(k),N_rx,N_tx,L,PDP,actual_speed,N_dps_base,...

N_LTE_frame,N_slot,N_sym_slot,N_fft,Ns,1/fs,fc,pseudoInv_BEM_Base_ma);disp(['Channel Generation Completed, Current Trial = ', num2str(trial)]); % to

estimate the simulation time of each task

% Quantization of users' BEM coefficients (channel responses) for feedback to BaseStation.

[index_set_Rx] =VQ_index_search(BEM_coe_Rx,k_dimen,L,N_tx,N_rx,N_user(k),codevectors); %index_set_Rx(seg,tap,tx_anten,user) to be sent to Base Station

clear BEM_coe_Rx;disp(['BEM Quantization Completed, Current Trial = ', num2str(trial)]); % to

estimate the simulation time of each task

[BEM_coe_BS] =BEM_coe_recover(index_set_Rx,codevectors,N_tx,N_rx,L,N_dps_base,k_dimen,N_user(k)); % recovered BEM coefficients at Base Station

[CFR_BS,CFR_Rx] =CFR_Gen(N_user(k),N_tx,N_rx,L,Ns,N_fft,CIR_Rx,BEM_coe_BS,BEM_Base_ma,N_sym_slot,N_slot,N_LTE_frame);

clear CIR_Rx BEM_coe_BS; % to reduce the used memory in PC % OR CAN USEBEM COEFFICIENTS TO RECOVER CFR_Rx TO AVOID THE USE OF CIR_Rx

disp(['CSI Recovery at BS Completed, Current Trial = ', num2str(trial)]); % toestimate the simulation time of each task

[TI_CFR_Rx] = TI_CFR_Gen(N_user(k),N_tx,N_rx,L,N_fft,TI_CIR_Rx); %assumed time-invariant CFR (perfect estimation) used for comparison

clear TI_CIR_Rx;% The below Greedy scheduling under assumption of time-invariant channels

ignore the ICI power

[total_rate] =Greedy_scheduler(Power,No,CFR_Rx,CFR_BS,N_fft,N_tx,N_rx,N_user(k),N_sym_slot,N_slot);

achievable_rate(k) = achievable_rate(k) + real( total_rate );disp(['TV-channel Scheduling completed, Current Trial = ',

num2str(trial)]); % to estimate the simulation time of each taskclear CFR_BS;

endachievable_rate(k) = achievable_rate(k)/N_trial/(N_sym_slot*N_slot)/N_fftend

figure(1)plot(N_user,achievable_rate,'-.k*','LineWidth',2);hold on;xlabel('Number of active users');ylabel('Sum-rate (bps/Hz)');legend('BD using BEM-based limited feedback');

****DPS_BEM_Gen****

function [BEM_Base_ma,pseudoInv_BEM_Base_ma] =DPS_BEM_Gen(v_kph,N_dps_base,fc,N_LTE_frame,N_slot,N_sym_slot,N_fft,N_cp,fs);

Ns = N_cp + N_fft; % OFDM symbol length after CP insertionTs = 1/fs; %the resulting sampling periodsam_index = 0:Ns*N_sym_slot*N_slot*N_LTE_frame - 1; % set of the time-domainsamples in N_LTE_frame framessam_time = sam_index*Ts; % time instants in N_LTE_frame frameslen_sam_index = length(sam_index);% number of all time-domain samples inN_LTE_frame frames

v_ms = v_kph*1000/3600; % speed in m/sc =3e8;%speed of light m/sv_Dmax = v_ms*fc*Ts/c; % Normalized one-sided Doppler bandwidth; actual mobilespeed can be a bit greater than the used value of v_ms herein.%-------------------------------------------------------------------------NW = v_Dmax*len_sam_index; % following description of dpss Matlab function,v_Dmax ---> W; len_sam_index --> N[E_ma,V_ma] = dpss(len_sam_index,NW,N_dps_base); % Put in a SEPERATE M-file to reduce simulation time !!!!

BEM_Base_ma = E_ma(1:len_sam_index,1:N_dps_base);pseudoInv_BEM_Base_ma = inv(BEM_Base_ma'*BEM_Base_ma)*BEM_Base_ma';% for pre-computation of pseudo matrix inversion in TV channel generation

****Zheng_DPS_CIR_Gen****

function [BEM_coe_Rx,CIR_Rx,TI_CIR_Rx] =Zheng_DPS_CIR_Gen(N_user,N_rx,N_tx,L,PDP,v_kph,N_dps_base,N_LTE_frame,N_slot,N_sym_slot,N_fft,Ns,Ts,fc,...

pseudoInv_BEM_Base_ma);M = 20; % number of sinusoid waves in Zheng model (extended Jakes model)len_sam_index = Ns*N_sym_slot*N_slot*N_LTE_frame;% number of all time-domain samples in N_LTE_frame frames where mobile user speed

% is assumed to be unchanged.sam_time = (0:len_sam_index - 1)*Ts; % time instants in N_LTE_frame frames (of asuperframe)v_ms = v_kph*1000/3600; % mobile user speed in m/sc =3e8; % speed of light in m/swd = 2*pi*v_ms*fc/c;BEM_coe_Rx = zeros(N_dps_base,L,N_tx,max(N_rx),N_user);CIR_Rx = zeros(L,N_fft,N_tx,max(N_rx),N_user,N_sym_slot*N_slot);TI_CIR_Rx = zeros(L,N_tx,max(N_rx),N_user);for user = 1:N_user

for rx_anten = 1:N_rx(user)for tx_anten = 1:N_tx

for tap = 1:Lalpha_n = ( 2*pi*[1:M].' - pi + pi*(2*rand-1) )/4/M; % M is the number of

sinusoid waves in Zheng model (extended Jakes model)Shi_n = pi*(2*rand(M,1)-1)*ones(1,len_sam_index);%PHI_ma = pi*(2*rand(M,1)-1)*ones(1,len_sam_index); % or PHI_ma =

pi*(2*rand-1)*ones(M,len_sam_index) !!! as used in Zheng paperPHI_ma = pi*(2*rand-1)*ones(M,len_sam_index); %

TI_CIR_Rx(1:L,tx_anten,rx_anten,user) =CIR_Rx(1:L,1,tx_anten,rx_anten,user,1);

%assuming time-invariant CIR is equal to the CIR at the 1st sample in the 1stOFDM symbol

endend

endclear Shi_n PHI_ma fading_gain sam_time;

****VQ_index_search****

function [index_set] =VQ_index_search(BEM_coe,k,L,N_tx,N_rx,N_user,codevectors);len_codebook = length(codevectors(1,:,1));N_segment = length(BEM_coe(:,1,1,1,1))/k;index_set = zeros(N_segment,L,N_tx,max(N_rx),N_user);for user =1:N_user


for tap =1:L % number of resolvable multipathsfor seg = 1:N_segment % the segment index of parts in a BEM coefficient

vector;[min_va,index_set(seg,tap,tx_anten,rx_anten,user)]=...

min( sum( abs( BEM_coe([1:k]+k*(seg-1),tap,tx_anten,rx_anten,user)*ones(1,len_codebook) -...

codevectors([1:k]+k*(seg-1),1:len_codebook,tap) ).^2 ) );

endend

endend

end% Just for reference on matrix sizes. % %BEM_coe(1:N_dps_bases,tap,tx_anten,user); % codevectors(1+k*(seg-1):k*seg,1:2^FB_len,tap)

****BEM_coe_recover****

function [BEM_coe_BS] =BEM_coe_recover(index_set,codevectors,N_tx,N_rx,L,N_dps_base,k_dimen,N_user);%Just for reference on matrix sizes used.% codevectors(1+k*(seg-1):k*seg,1:2^FB_len,tap)% index_set(seg,tap,tx_anten,user)BEM_coe_BS = zeros(N_dps_base,L,N_tx,max(N_rx),N_user);for user =1:N_user

for rx_anten = 1:N_rx(user)for tx_anten =1:N_tx

for tap =1:Lfor seg = 1:N_dps_base/k_dimen

BEM_coe_BS([1:k_dimen]+k_dimen*(seg-1),tap,tx_anten,rx_anten,user)=...

codevectors([1:k_dimen]+k_dimen*(seg-1),index_set(seg,tap,tx_anten,rx_anten,user),tap);

endend

endend

end

****CFR_Gen****

function [CFR_BS,CFR_Rx] =CFR_Gen(N_user,N_tx,N_rx,L,Ns,N_fft,CIR_Rx,BEM_coe_BS,BEM_Base_ma,N_sym_slot,N_slot,N_LTE_frame);% CIR_Rx(1:L,1:N_fft,1:N_tx,1:N_rx,1:N_user,OFDM_sym): just for reference inmatrix sizesmax_N_rx = max(N_rx);CFR_BS = zeros(max_N_rx,N_tx,N_fft,N_user,N_sym_slot*N_slot); % causeproblem of Memory in case of large user poolCFR_Rx = zeros(max_N_rx,N_tx,N_fft,N_user,N_sym_slot*N_slot); % causeproblem of Memory in case of large user poolfor OFDM_sym = 1:N_sym_slot*N_slot % CP length =Ns-N_fft

sum_BEM_bases = sum( BEM_Base_ma(Ns*N_sym_slot*N_slot*(N_LTE_frame-1) + (OFDM_sym-1)*Ns + Ns-N_fft + [1:N_fft],:) );

for user = 1:N_userfor rx_anten = 1:N_rx(user)

for tx_anten = 1:N_txsum_CIR_Rx = sum(

CIR_Rx(:,1:N_fft,tx_anten,rx_anten,user,OFDM_sym).' );for kk = 1:N_fft %

BEM_coe(1:N_dps_bases,tap,tx_anten,user):)CFR_BS(rx_anten,tx_anten,kk,user,OFDM_sym) =...

sum_BEM_bases*(BEM_coe_BS(:,:,tx_anten,rx_anten,user)*exp(-j*2*pi*(kk-1)*[0:L-1]'/N_fft) )/N_fft;

% compute H(kk,kk); (kk-1) since subcarrierindex run from 0 to N_fft -1

CFR_Rx(rx_anten,tx_anten,kk,user,OFDM_sym) = sum_CIR_Rx*exp(-j*2*pi*(kk-1)*[0:L-1].'/N_fft )/N_fft;

endend % end of "for tx_anten = 1:N_tx"

endend

end

****TI_CFR_Gen****

function [TI_CFR_Rx] = TI_CFR_Gen(N_user,N_tx,N_rx,L,N_fft,TI_CIR_Rx);

% TI_CIR_Rx(1:L,tx_antenn,user)TI_CFR_Rx = zeros(max(N_rx),N_tx,N_fft,N_user);for user = 1:N_user


for kk = 1:N_fftTI_CFR_Rx(rx_anten,tx_anten,kk,user) = exp( -j*2*pi*(kk-1)*[0:L-

1]/N_fft )* TI_CIR_Rx(1:L,tx_anten,rx_anten,user);end

endend

end

****Greedy_scheduler****

function [total_rate_frame] =Greedy_scheduler(Power,No,CFR_Rx,CFR_BS,N_fft,N_tx,N_rx,N_user,N_sym_slot,N_slot);% Just for reference on matrix sizes: TI_CFR_Rx(1:N_fft,tx_anten,user)total_rate_frame = 0;for OFDM_sym = 1:N_sym_slot*N_slot

for kk = 1:N_fft % perform (per-subcarrier) scheduling for each subcarrieruser_set = [1:N_user]; % set of available users in the considered LTE systemloop = 1; % just a variable refering to the number of selected users. As a result,

noted that the number of selected users = loop-1 N_tx % not sastify the constraint ofnumbers of Tx/Rx antennas

if loop ==1temp_sum_rate(uu) = log2( det( eye(N_rx(user_set(uu)))+

(Power/N_tx)*...

CFR_BS_temp_users*CFR_BS_temp_users'/No(temp_user_set) ) );else

temp_sum_rate(uu) = 0;end

else% if some temporarily selected users are too close in space the rank of the

matrix H will be < sum(N_rx(temp_user_set))if loop == 1 % corresponding to the 1st round of Greedy user selection

%no SVD required since there is only one user in the currentlyconsidered scenario

temp_sum_rate(uu) = log2( det( eye(N_rx(user_set(uu))) +(Power/N_tx)*...

CFR_BS_temp_users*CFR_BS_temp_users'/No(temp_user_set) ) );else % with Greedy user scheduling, selecting too-close users will reduce

the sum-rate of the system.U_v = zeros(max(N_rx),max(N_rx),length(temp_user_set));G_ma = zeros(max(N_rx),max(N_rx),length(temp_user_set));Lamda_vec = zeros(max(N_rx),length(temp_user_set));Lamda_seq = [];for user_index = 1:length(temp_user_set)

H_temp = CFR_BS_temp_users;H_temp( sign(user_index-1)*sum( N_rx(

temp_user_set(1:max(user_index-1,1)) ) ) +...

[1:N_rx(temp_user_set(user_index))],:) = [];[U_ma,S_ma,V_ma] = svd(H_temp);V_precoding = V_ma(1:N_tx,N_tx-

N_rx(temp_user_set(user_index))+1 : N_tx); % if rank(H_temp) =length(H_temp(:,1));

G_ma(1:N_rx(temp_user_set(user_index)),1:N_rx(temp_user_set(user_index)),user_index) =...

CFR_BS(1:N_rx(temp_user_set(user_index)),1:N_tx,kk,temp_user_set(user_index),OFDM_sym)*V_precoding;

%Consider different No at each user

% Should be carefull at Es_total for case of more than 1 user; Use thesamme Es_total, this is verify by hand-writing at page (*)

used_length = length(lamda_seq_sorted); % number of currentlyconsidered users for scheduling

check = 1;while (check)

water_level = lamda_seq_sorted(used_length); % water level = 1/mu;if sum( max(water_level - lamda_seq_sorted, 0) ) > Power

used_length = used_length - 1;else

check = 0;end

end%Calculate optimal water levelwater_level = ( Power +sum( lamda_seq_sorted(1:used_length) )

)/used_length;temp_sum_rate(uu) = 0;for user_index = 1:length(temp_user_set)

S_k =U_v(1:N_rx(temp_user_set(user_index)),1:N_rx(temp_user_set(user_index)),user_in-dex)*...

diag( max(water_level -1./Lamda_vec(1:N_rx(temp_user_set(user_index)),user_index),0) )*...

U_v(1:N_rx(temp_user_set(user_index)),1:N_rx(temp_user_set(user_index)),user_in-dex)';

temp_sum_rate(uu) = temp_sum_rate(uu) + log2( det(eye(N_rx(temp_user_set(user_index))) +...

G_ma(1:N_rx(temp_user_set(user_index)),1:N_rx(temp_user_set(user_index)),user_index)*...

S_k*...

G_ma(1:N_rx(temp_user_set(user_index)),1:N_rx(temp_user_set(user_index)),user_index)'/...

No(temp_user_set(user_index)) ) );end

end % of "if loop ==1"end % checking to see if adding one more user will sastify

sum(N_rx(temp_user_set))

keep_searching = 0; % Stop Greedy user selection due to a decrease in thesystem sum-rate.

elseselected_user_set = [selected_user_set user_set(index_max)];% selected_users(loop) = user_set(index_max);CFR_BS_chosen_users =

[CFR_BS_chosen_users;CFR_BS(1:N_rx(user_set(index_max)),1:N_tx,kk,user_set(index_max),OFDM_sym)];

user_set(index_max) = 0; % just a way to ignore the currently selected userin later consideration/user selection.

user_set = sort(user_set,'descend');% a way to ignore the currently selecteduser in later greedy user selection.

loop = loop+1; % number of selected users (add ONE new selected user) =loop-1

endend % end of the entire schdeduling process.% Compute the achievable system sum-rate with the above set of selected users% Repeat the BD precoding for the above set of selected usersif length(selected_user_set) == 1 % corresponding to the 1st round of Greedy user

selection%no SVD required since there is only one user in the currently considered

scenarioactual_sum_rate=log2( det( eye(N_rx(selected_user_set(1))) +

(Power/N_tx)*...

CFR_Rx(1:N_rx(selected_user_set(1)),1:N_tx,kk,selected_user_set(1),OFDM_sym)*...

CFR_Rx(1:N_rx(selected_user_set(1)),1:N_tx,kk,selected_user_set(1),OFDM_sym)'/...

No(selected_user_set(1)) ) );else % with Greedy user scheduling, selecting too-close users will reduce the

sum-rate of the system.U_v = zeros(max(N_rx),max(N_rx),length(selected_user_set));G_ma = zeros(max(N_rx),max(N_rx),length(selected_user_set));Lamda_vec = zeros(max(N_rx),length(selected_user_set));Lamda_seq = [];V_precoding = zeros(N_tx,max(N_rx),length(selected_user_set));for user_index = 1:length(selected_user_set)

H_temp = CFR_BS_chosen_users;H_temp( sign(user_index-1)*sum( N_rx(

selected_user_set(1:max(user_index-1,1)) ) ) +...[1:N_rx(selected_user_set(user_index))],:)

= [];[U_ma,S_ma,V_ma] = svd(H_temp);

V_precoding(1:N_tx,1:N_rx(selected_user_set(user_index)),user_index) =...V_ma(1:N_tx,N_tx -

N_rx(selected_user_set(user_index))+ 1 : N_tx); % if rank(H_temp) =length(H_temp(:,1));

G_ma(1:N_rx(selected_user_set(user_index)),1:N_rx(selected_user_set(user_index)),user_index) =...

CFR_BS(1:N_rx(selected_user_set(user_index)),1:N_tx,kk,selected_user_set(user_in-dex),OFDM_sym)*...

V_precoding(1:N_tx,1:N_rx(selected_user_set(user_index)),user_index);%Consider different No at each user

%Calculate optimal water levelwater_level = ( Power +sum( lamda_seq_sorted(1:used_length) )

)/used_length;Cov_I_Sig = zeros(N_tx,N_tx); % Covariance matrix of interference + signal

of interestS_k = zeros(max(N_rx),max(N_rx),length(selected_user_set));for user_index = 1:length(selected_user_set)

S_k(1:N_rx(selected_user_set(user_index)),1:N_rx(selected_user_set(user_index)),user_index) =...

U_v(1:N_rx(selected_user_set(user_index)),1:N_rx(selected_user_set(user_index)),user_index)*...

diag( max(water_level -1./Lamda_vec(1:N_rx(selected_user_set(user_index)),user_index),0) )*...

U_v(1:N_rx(selected_user_set(user_index)),1:N_rx(selected_user_set(user_index)),user_index)';

Cov_I_Sig = Cov_I_Sig +V_precoding(1:N_tx,1:N_rx(selected_user_set(user_index)),user_index)*...

S_k(1:N_rx(selected_user_set(user_index)),1:N_rx(selected_user_set(user_index)),user_index)*...

V_precoding(1:N_tx,1:N_rx(selected_user_set(user_index)),user_index)';endactual_sum_rate = 0;for user_index = 1:length(selected_user_set)

actual_sum_rate = actual_sum_rate +...log2( det(

No(selected_user_set(user_index))*eye(N_rx(selected_user_set(user_index))) +...

CFR_Rx(1:N_rx(selected_user_set(user_index)),1:N_tx,kk,selected_user_set(user_in-dex),OFDM_sym)*...

Cov_I_Sig*...

CFR_Rx(1:N_rx(selected_user_set(user_index)),1:N_tx,kk,selected_user_set(user_in-dex),OFDM_sym)' )/...

det(No(selected_user_set(user_index))*eye(N_rx(selected_user_set(user_index))) +...

CFR_Rx(1:N_rx(selected_user_set(user_index)),1:N_tx,kk,selected_user_set(user_in-dex),OFDM_sym)*...

( Cov_I_Sig -...

V_precoding(1:N_tx,1:N_rx(selected_user_set(user_index)),user_index)*...

S_k(1:N_rx(selected_user_set(user_index)),1:N_rx(selected_user_set(user_index)),user_index)*...

V_precoding(1:N_tx,1:N_rx(selected_user_set(user_index)),user_index)' )*...

CFR_Rx(1:N_rx(selected_user_set(user_index)),1:N_tx,kk,selected_user_set(user_in-dex),OFDM_sym)' ) );

endendtotal_rate_frame = total_rate_frame + actual_sum_rate;

endend

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