Time-Frequency Synchronization, Channel Estimation and Equalization of DL Channels in 3GPP Long Term Evolution

Transcription

1 Time-Frequecy Sychroizatio, Chael Estimatio ad Equalizatio of DL Chaels i 3GPP Log Term Evolutio

2 Itroductio 3GPP LTE is a stadard for wireless data commuicatios techology ad a evolutio of the GSM/UMTS stadards. The goal of LTE was to icrease the capacity ad speed of wireless data etworks usig ew digital sigal processig ad modulatio techiques, special attetio has bee give i selectig techologies for LTE DL. Techologies such as orthogoal frequecy divisio multiplexig (OFDM) ad multiple iput, multiple output (MIMO), ca ehace the performace of the curret wireless commuicatio systems. The high data rates ad the high capacity ca be attaied by combiig the advatages of the two techologies. These techologies have bee selected for LTE DL ad UL trasmissio. The received sigal by user equipmet (UE) udergoes may distortios ad impairmets due to the chael respose, multipath delay, additive oise ad RF frot ed mismatches. The receiver had to compesate the effects ad retrieve the sigal trasmitted by the enodeb (LTE Base Statio). I order to aid the compesatio of distortios the DL sigals are trasmitted with pilot toes termed as referece sigals (RS). I additio to kow RS, the iheret cyclic properties of OFDM sigal ad the CP (cyclic prefix) are used achieve the sychroizatio i time ad frequecy so that the loss of orthogoality amog the subcarriers is restored. This project report aims at sychroizatio, chael estimatio ad equalizatio of PBC (physical broadcast chael) sigals of LTE. Sychroizatio techiques such as ML Estimatio, CP correlated techiques are discussed. Chael estimatio algorithms such as Least Squares (LS), Miimum Mea Square Error (MMSE) ad Equalizatio algorithms ZF ad MMSE, have bee derived. Fial equalized output was compared to with iitial trasmitted modulatio. All the simulatios are coducted usig 4G LTE test-bed from Mymo Wireless where RF sigals are captured over the wireless multipath propagatio medium ad suitable algorithms are used for the sychroizatio, chael estimatio ad equalizatio.

3 1. INTRODUCTION X 0 x 0 Iput Symbols Serial to Parallel IFFT Parallel to Serial ad add CP Add CP DAC RF X N-1 x N-1 Figure 1 Block diagram of a typical pilot-aided OFDM system A brief block diagram of the OFDM system is show i Figure 1. I a OFDM system, the available spectrum is divided ito multiple subcarriers which are orthogoal to each other. Each of these subcarriers is idepedetly modulated by a low rate QAM data stream. OFDM symbols are geerated from a stream of serial QAM symbols. The N parallel streams are treated as samples i frequecy domai, fially the N-poit time domai blocks are obtaied from the IFFT, which are subsequetly serialised to create a time domai sigal. OFDM has several beefits icludig its robustess agaist multipath fadig ad its efficiet receiver architecture. Data symbols are idepedetly modulated ad trasmitted over closely spaced orthogoal subcarriers. I LTE, modulatio codig schemes (MCS) 4QAM, 16QAM, ad 64QAM are sued for DL ad UL trasmissios. I the time domai, a guard iterval cyclic prefix (CP) is iserted prior to each OFDM symbol. As a fudametal priciple of LTE, the data chaels are shared chaels, i.e. for each trasmissio time iterval of 1 ms, a ew schedulig decisio is take for the assigmet of time-frequecy resources durig for DL ad UL. Trasmitter: A serial complex QAM samples is coverted to parallel data aliged as per the subcarrier idex umber for mappig oto the OFDM symbol subcarriers. See Figure 1. The IDFT block trasforms the frequecy domai data, X k, o the k th subcarrier ito time-domai samples x as x = IDFT{ X } ; 0,1,..., N 1, where N is total umber of subcarriers k Guard iterval is added as below to remove the ISI x = x, where N g, N 1,..., 1 ( N ) g N g = Number of cyclic prefix samples prefixed to OFDM symbol for copig with time-domai dispersio of the chael Parallel IFFT trasformed samples are coverted to serial data ad fed to DAC for upsamplig followed by RF upcoversio.

4 Chael: Due to the chael impulse respose h which is a multipath fadig chael ad The additive oise w which cotamiates the trasmitted sigal The received sigal becomes y x h w. Receiver: The receive data from the RF is fed to ADC. See Figure The sychroizatio is doe by the receiver to make it free from the sychroizatio errors such as symbol time offset, CFO ad samplig clock offset. The FFT is performed for extractig the data subcarriers oto which the QAM data was mapped followed by chael-estimatio by usig the referece symbols ad the QAM data is extracted by chael equalizatio. Y k FFT{ y }, k 0,1,..., N 1 Yk X k k I k Wk, k 0,1,..., N 1, where k is the chael respose, I k is the iter-carrier iterferece, Wk is the additive Gaussia oise. x 0 X 0 ADC Time-Frequecy Sychroizatio Remove CP Serial to Parallel FFT Parallel to Serial ad Decoder Output Symbols x N-1 X N-1 Figure OFDM receiver block diagram I this report we deal with the 3GPP LTE DL receiver processig which describes about LTE DL trasmissio scheme DL OFDMA (orthogoal frequecy divisio multiple access) Frame Structure DL data trasmissio: Physical cell-search usig primary ad secodary sychroizatio sigals combied with time ad frequecy sychroizatio Time-sychroizatio followed by carrier frequecy offset (CFO) estimatio ad compesatio of OFDM symbols Chael Estimatio: DL referece sigals used for chael estimatio, chael iterpolatio ad equalizatio

5 . LTE DL Trasmissio Scheme I the followig sectios the LTE DL receiver processig for 0Mz badwidth is described. The TDD (Type- frame structure) mode of trasmissio, as show i Figure 3, is cosidered..1 OFDMA parameterizatio DL ad UL trasmissios are orgaized ito radio frames (also called as system frame umber (SFN)) with Tf 30700Ts 10 ms frame duratio, where T s is the samplig time iterval. Each frame (SFN) cosists of 10 subframes, each subframe is of legth T 3070T 1ms, each subframe cosists of two slots, each slot is of legth slot s Tslot 15360Ts 0.5ms. Each slot cosists of 7 OFDM symbols where the 1 st OFDM symbol has a legth of 08 samples (FFT legth CP legth 160), d to 7 th OFDM symbols have each of legth 19 samples (FFT legth CP legth 144). The supported UL-DL cofiguratios are listed i Table below where, for each subframe i a radio frame, D deotes the subframe is reserved for DL trasmissios, U deotes the subframe is reserved for UL trasmissios ad S deotes a special subframe with the three fields DwPTS, GP ad UpPTS. The legth of DwPTS ad UpPTS is give by Table of special subframe below, subject to the total legth of DwPTS, GP ad UpPTS beig equal to 3070 T s 1ms. Each subframe i is defied as two slots, i ad i 1 of legth T slot 15360T s 0.5 ms i each subframe. UL-DL cofiguratios with both 5 ms ad 10 ms DL-to-UL switch-poit periodicity are supported, see Table 1, Table ad Table 3. I case of 5 ms DL-to-UL switch-poit periodicity, the special subframe exists i both half-frames. I case of 10 ms DL-to-UL switch-poit periodicity, the special subframe exists i the first half-frame oly. Two cyclic prefix legths are possible, depedig o the delay dispersio characteristics of the cell. The loger cyclic prefix (16.67µs) should the target multi-cell broadcast MBMS (Multimedia Broadcast Multicast Services) ad very-large-cell scearios, for istace, for rural ad low data rate applicatios at a price of badwidth efficiecy. The umber of OFDM symbols per slot depeds o the size of this cyclic prefix, which is cofigured by the upper layers. PSS is always trasmitted i the 3rd OFDM symbol of DwPTS (subframes #1 ad #6) SSS is always trasmitted i the last OFDM symbol i slots 1 ad 11 (subframe #0 ad subframe #5) PDCC (Physical Dowlik Cotrol Chael) i DwPTS (subframes #1 ad #6) may spa 1 or OFDM symbols Data is trasmitted after the cotrol regio as i other DL subframes I DwPTS the cell specific RS patters are the same as i other DL subframes The referece sigal REs i GP are muted SRS(Soudig Referece Sigal) is trasmitted o UpPTS

6 Figure 3 Frame structure type used with TDD (for 5 ms switch-poit periodicity) Seve UL-DL cofiguratios with either 5 ms or 10 ms DL to- UL switch-poit periodicity are supported. I case of 5 ms switch-poit periodicity, the special subframe exists i both half-frames. I case of 10 ms switch-poit periodicity the special subframe exists i the first half frame oly. Subframes 0 ad 5 ad DwPTS are always reserved for DL trasmissio. UpPTS ad the subframe immediately followig the special subframe are always reserved for UL trasmissio. Table 1 Cofiguratio of special subframe (legths of DwPTS/GP/UpPTS i Samples)

7 Special subframe cofiguratio Normal cyclic prefix Exteded cyclic prefix DwPTS GP UpPTS DwPTS GP UpPTS Ts 1936 Ts 7680 T s 0480 Ts Ts 195 Ts Ts Ts Ts Ts Ts Ts 8768 Ts 0480 Ts 7680 Ts 6576 Ts 19 T s 3040 Ts 510 Ts 4384 Ts 5600 Ts 560 Ts 19 Ts 7680 Ts 1790 Ts Ts 0480 T s 510 Ts 6576 Ts 3040 Ts 560 Ts 560 T s 510 T s 4384 T s 4384 T s 19 Ts Table Cofiguratio of special subframe (legths of DwPTS/GP/UpPTS i OFDM Symbols) Special subframe Normal cyclic prefix Exteded cyclic prefix cofiguratio DwPTS GP UpPTS DwPTS GP UpPTS 0 3 TOFDM 10 TOFDM 3 T OFDM 8 TOFDM 1 9 TOFDM 4 TOFDM 8 TOFDM 3 TOFDM 10 TOFDM 3 TOFDM 9 TOFDM TOFDM 1 T OFDM 3 11 TOFDM TOFDM 10 TOFDM 1 TOFDM 4 1 TOFDM 1 TOFDM 3 TOFDM 7 TOFDM 5 3 TOFDM 9 TOFDM 8 T OFDM TOFDM 6 9 TOFDM 3 TOFDM 9 TOFDM 1 TOFDM T OFDM TOFDM TOFDM TOFDM 8 11 TOFDM 1 T OFDM T OFDM UL-DL cofiguratio Table 3 UL-DL cofiguratios DL-to-UL Switch-poit periodicity Subframe umber ms D S U U U D S U U U 1 5 ms D S U U D D S U U D 5 ms D S U D D D S U D D 3 10 ms D S U U U D D D D D 4 10 ms D S U U D D D D D D 5 10 ms D S U D D D D D D D 6 5 ms D S U U U D S U U D.1.1 Resource Grid Trasmitted sigal i each slot is described by a resource grid of subcarriers ad available OFDM symbols, see Figure 4. Each elemet i the resource grid is called a resource elemet (RE) ad each resource elemet correspods to oe complex-valued modulatio symbol (subcarrier). The REs have a costat spacig of f sc = 15 kz. I both DL ad UL, a basic

8 schedulig uit is deoted by a resource block (RB). A RB is defied as 1 cosecutive REs (180 kz) i the frequecydomai i oe subframe. The umber of resource blocks for differet LTE badwidths is give i Table 3. The umber of OFDM symbols per subframe is 14 for ormal cyclic prefix ad 1 for exteded cyclic prefix. Each OFDM symbol is appeded with a cyclic prefix (CP), compare. Each subframe has slots (eve ad odd), therefore, a slot cosists of 7 OFDM symbols for ormal CP ad 6 OFDM symbols for exteded CP. Each OFDM symbol cosists of IFFT part ad the CP part which is prefixed to IFFT part, see Table 4 for CP ad umber of samples for the 0Mz trasmissio badwidth. Note that the subcarrier spacig of 15 Kz ad the IFFT legth (048) remai same irrespective of the ormal CP or exteded CP, oly the legth of cyclic prefix chages, see Table 5. Figure 4 shows the placemet of OFDM symbols, REs ad the correspodig badwidths. REs of 1 st OFDM symbol REs of d OFDM symbol REs of 14 th OFDM symbol RE 047 Frequecy Subcarriers RE 100 RE 1199 RE 1198 RE 1197 RE RE1 RE0 Zero subcarriers (guard bad) 100x15Kz =18Mz Tx BW 1 RB = 1 REs = 180Kz 15Kz LTE BW =0Mz 048x15Kz =30.7Mz OFDM Symbols Time Slot-0 (0.5ms) 7 OFDM symbols 1 Subframe (1 TTI = 1ms) Slot-1 (0.5ms) 7 OFDM symbols = Data subcarrier or o-zero subcarrier = No-data subcarrier or Zero subcarrier Figure 4 DL Resource Grid of oe subframe with ormal CP Table 4

9 Chael Badwidth (MZ) Trasmissio Badwidth (N RB ) Table 5 Cofiguratio OFDM CP CP duratio Symbols Normal CP; Δf=15 kz for 1st symbol 144 for others 5. μs for first symbol 4.7 μs for other symbols Exteded CP;Δf=15 kz μs. DL data trasmissio The DL schedulig or UL grats allocatio is doe by enodeb i terms of RBs, i.e. oe UE ca be allocated iteger multiple of RBs for uplik or dowlik trasmissios. The RB allocatios ca be cotiguous or distributed. The DL schedulig or UL grats by enodeb to a UE is doe o a subframe basis, that is 1 ms duratio. The allocatio of RBs by the enodeb to a UE for DL or UL is depedet o a umber of factors such as the radio lik quality measured i terms of chael quality idicator (CQI), RI (rak idicator) ad PMI (precodig matrix idicator) ad sigal to iterferece ad oise ratio (SINR). The DL ad UL the trasmissios are split ito 3 categories, e.g. sychroizatio, cotrol ad data chaels. The list of DL chaels are give below. Sychroizatio Sigals/Chaels o Primary, Secodary Sychroizatio Sigals (PSS, SSS) ad Referece Sigals (RS) o Physical Broadcast Chael, PBC. The chaels oce detected ca be used for time-frequecy sychroizatio apart from the sychroizatio of system frame umber beig trasmitted by enodeb. Cotrol Chaels o Physical Cotrol Format Idicator Chael, PCFIC. o Physical ybrid ARQ Idicator Chael, PIC o Physical DL Cotrol Chael, PDCC Data Chaels o Physical DL Shared Chael, PDSC o Physical Multicast Chael, PMC PSS ad SSS are used for estimatig the Sector ID (NSID) ad Group ID (NGID) respectively, where [NSID + 3xNGID]. I the case of TDD PSS is trasmitted o 6 subcarriers withi 7 reserved subcarriers aroud DC subcarrier i the last OFDM symbol of subframe-0 ad subframe-5 of every Frame (10ms). Similarly SSS is trasmitted o 6

10 subcarriers withi 7 reserved subcarriers aroud DC subcarrier i the 3rd OFDM symbol of subframe-1 ad subframe-6 of every Frame. The RS sigals are differet for each cell-id ad their positioig i the frequecy-domai is depedet o the cell-id, their positioig i time-domai is depedet o the umber of ateas. For example, as show i Figure 5 ad Figure 6 for 1x1, x1, x ad 4x4 the RS occupy the selective REs oly i the 1st OFDM symbol of each slot, for 4x4 MIMO the first OFDM symbols are occupied. The RS deoted by, R 1, R ad R 3 show i Figure 5 ad Figure 6. The UE estimates the Chael Impulse Respose (CIR) from each trasmittig atea, therefore, whe a RS is trasmitted from oe atea port, the other atea ports i the cell are idle (ull), see the colour codig i the Figure 5 ad Figure 6. The CIR estimates for REs that do ot carry the RS are computed via time-frequecy iterpolatio. The DL referece sigal structure is importat for chael estimatio, it may be observed that there are RSs per slot i the time domai 4 RSs per slot which results i a total of 8 per RB. The required spacig i the time domai betwee the referece symbols ca be obtaied by cosiderig the maximum Doppler spread (highest speed) to be supported, for example maximum mobile speed to be supported is ~500Kmph. Cosider the RF carrier frequecy is.1 Gz. Doppler shift f d fcv / c =.1Gz x 500 x x = 975 z Accordig to Nyquist samplig theorem miimum samplig frequecy eeded to recostruct 1 sigal is Tc 0. 5 ms. Therefore, referece symbols per slot are eeded i the time f d domai i order to estimate the chael correctly.

11 Figure 5 Mappig of DL referece sigals (ormal cyclic prefix)

12 Oe atea port l 0 l 5 l 0 l 5 Resource elemet (k,l) R 1 R 1 Two atea ports R 1 R 1 R 1 R 1 Not used for trasmissio o this atea port Referece symbols o this atea port R 1 R 1 l 0 l 5 l 0 l 5 l 0 l 5 l 0 l 5 R 1 R 1 R R 3 Four atea ports R 1 R 1 R 1 R 1 R R R 3 R 3 R 1 R 1 R R 3 l 0 l 5 l 0 l 5 l 0 l 5 l 0 l 5 l 0 l 5l 0 l 5 l 0 l 5 l 0 l 5 eve-umbered slots odd-umbered slots eve-umbered slots odd-umbered slots eve-umbered slots odd-umbered slots eve-umbered slots odd-umbered slots Atea port 0 Atea port 1 Atea port Atea port 3 Figure 6 Mappig of DL referece sigals (Exteded cyclic prefix) I the followig sectios we focus maily o achievig the time-frequecy sychroizatio, chael estimatio ad equalizatio for retrievig the Master Iformatio Block (MIB) iformatio from PBC usig the LTE Test-bed show i Figure 1. The receiver sigal processig chai described for PBC i the followig sectios remais same for cotrol ad data chaels except that the modulatio codig scheme (MCS) for PBC is QAM-4 whereas for data chaels like PDSC it ca be QAM-4 or QAM-16 or QAM-64, the selectio of MCS is decided by enodeb based o the chael quality. 3. Cell Search ad Sychroizatio We cosider the TDD UL-DL Cofiguratio Idex 1 for the discussio i the followig sectios. The positio of the PSS, SSS ad PBC for TDD is show i Figure 7. The Figure 8 shows the sequece of processig steps for PSS, SSS ad the PBC. 3.1 Primary Sychroizatio Sigal (PSS) Upo the UE power-o or while UE searchig for a eighbourig cell iformatio it first looks for the PSS ad estimates the slot boudary (with ambiguity i subframe umber) ad the sector-id (N SID ). Sice PSS is trasmitted twice i each Frame ad both the trasmissios are idetical there is a ambiguity o the boudary whether start of Frame or middle of Frame.

13 3. Secodary Sychroizatio Sigal (SSS) The Frame boudary ambiguity is resolved by the detectio of SSS as the trasmissio of SSS i first half of the Frame is differet from the secod half of the Frame. Detectio of the SSS gives Frame boudary timig estimatio ad the group-id (N GID ). 3.3 Cell-ID Estimatio The Cell ID is estimated by the formula (N SID + 3.N GID ). LTE uses a hierarchical cell-search procedure i which a LTE radio cell is idetified by a cell idetity. There are 504 available physical layer cell idetities which are divided ito 3 groups (0, 1, ) with each group havig 168 layer idetities (0, 1,,, 167). 3.4 Physical Broadcastig Chael (PBC) As additioal help durig cell search, a PBC is available which carries the MIB with basic physical layer iformatio like system badwidth, umber of trasmit ateas, ad system frame umber ad PIC (duratio exteded or ormal). A 4-bit MIB bit-patter is fed from higher layers to physical layer, the 4 bits plus the 16 bits CRC become 40 bits, the 40 bits are ecoded by 1/3 rate Covolutioal Ecoder which gives 10 bits output. The 10 bits are repeated for 16 times resultig ito a total umber of bits as 190 bits. The 190 bits are QAM-4 modulated resultig ito 960 QAM-4 samples. The 960 QAM-4 samples are divided ito 4 parts each part is of 40 QAM-4 samples. Each part (40 QAM samples) is mapped to 4 OFDM symbols of each Frame. The PBC is spread across 4 Frames (40 ms), i each Frame a part of the PBC is trasmitted withi 7 subcarriers of the 4 OFDM symbols cetred aroud DC. Note that the decodig of MIB iformatio from PBC is achieved by processig ay oe of the Frames. Oe TDD Frame SF0 SF1 SF SF3 SF4 SF5 SF6 SF7 SF8 SF PBC PSS SSS Figure 7 PSS ad SSS ad PBC sigals positioig w.r.t. OFDM symbols, subframes ad Frame for TDD mode.

14 PSS Slot Timig Idetificatio Sector ID (0,1,) Estimatio SSS Subframe 0 or Subframe 5 Detectio, Gp ID detectio, FDD / TDD Detectio, Normal or Exteded Detectio Geerate RS sigals Estimate CQI Parameters, RSRP, RSRQ Detect PBC, Estimate MIB Detect DCI parameters, Estimate SIB1 ad SIB Geerate PRAC for Uplik trasmissio Figure 8 DL sychroizatio ad PBC processig flow Successful executio of the cell search ad selectio procedure as well as acquirig iitial system iformatio is essetial for a UE before takig further steps to commuicate with the LTE etwork. Acquisitio of IQ samples ito DL receiver buffer ad the sequece of steps durig the cell-search procedure are show i Figure. Oce the cell-search is completed followed by the detectio of cell system iformatio the UE switches ito camp-o mode for acquirig the etwork idetifier to associate with the enodeb ad joi the etwork, Figure 9. Rx Buffer Read poiter o ffset calculator Read poiter Cellsearch Buffer Read oe subframe No T_frame Symbol time estimate PSS detect T_pss SSS detect PBC decode Yes Camp o yes s uccess? Figure 9 Sychroizatio ad cell iformatio acquisitio util the campig state of UE.

15 4. Sychroizatio OFDM offers may advatages i terms of robustess to ISI, multipath fadig, simple method of chael estimatio, equalizatio ad spectrum efficiecy. owever the beefits come oly if the orthogoality of the subcarriers i the OFDM symbol is preserved. The followig time ad frequecy sychroizatio is critical for achievig a good OFDM receiver desig. Sychroizatio error due to symbol time offset (SFO): Timig offset problem is due to the ukow OFDM symbol arrival time. Symbol arrival timig may be differet tha that of the trasmitted sequece due to multipath propagatio ad chael delay spread. It is ecessary that the FFT widows are accurately picked ad ISI is elimiated by discardig the CP. Sychroizatio error due to carrier frequecy offset (CFO): Frequecy offset arises primarily due to carrier frequecy mismatch betwee the trasmitter ad the receiver ad also as a result of Doppler shift due to mobility of trasmitter ad/or receiver. The impact of the CFO is the loss of orthogoality betwee subcarriers that results ito loss of data. It is ecessary that CFO is sufficietly accurately estimated, compesated ad tracked. The CFO may exceed the subcarrier spacig resultig ito iteger part of CFO (IFO) ad fractioal part of CFO (FFO). IFO ad FFO are both to be estimated usig differet techiques ad compesate the combied total CFO i the received OFDM symbol. Sychroisatio error due to sample clock frequecy (SCO) mismatch: It is also ecessary to maitai OFDM sychroizatio i terms of the samplig clocks betwee DAC of trasmitter ad ADC of receiver. If the clock sychroisatio is ot accurate, relative samplig rate will be faster or slower which results ito loss or additio of samples, the error ca be compesated by iterpolatig additioal sample or deletig the extra sample for maitaiig the orthogoal property of the OFDM symbol. I the report we look i to the estimatio of STO, CFO followed by SCO. We use the ML method of joit time ad CFO estimatio ad compesatio. 4.1 Time ad Frequecy Offset Estimatio i OFDM Systems usig ML method A symbol clock ad a frequecy offset estimates may be geerated at the receiver with the aid of pilot symbols kow to the receiver or by maximizig the average log-likelihood fuctio. ML estimatio uses the cyclic prefix precedig the OFDM symbols, thus reducig the eed for pilots.

16 y0 y1 s 0 s 1 IFFT x 0 X1 Parallel To Serial x Chael y Serial To Parallel ML Method of Joit Time- Frequecy CFO estimatio ad Compesa tio yk Yk+1 FFT zk zk+1 s N-Ng+1 XN-Ng+1 yn-ng+1 yn+k-1 zn+k-1 s N x N yn yn+k-1 zn+k-1 Figure 10 OFDM system, trasmittig subsequet blocks of N complex data Let s be QAM sigal which is mapped oto the subcarriers, followed by IFFT ad CP additio. The resultig OFDM sigal x is serially trasmitted as show i Figure 10. The trasmitted sigal udergoes the multipath propagatio before it arrives at receiver alog with additio of i.i.d. white Gaussia oise w. The first ucertaity is see as a delay i the chael impulse respose ( ) where is the iteger valued ukow arrival time of a symbol. The latter is the CFO which is modeled as a complex multiplicative distortio of the j / N received data i the time domai e, deotes the differece i the trasmitter ad receiver oscillators as a fractio of the itercarrier spacig ( N 1 i ormalized frequecy). Based o these two ucertaities ad the additive Gaussia oise the received sigal is writte as, r( ) s( ) e j k / N w( ) OFDM symbol has N NCP samples where the last N CP samples are placed i the startig of the symbol i the same order. So, whe we take a widow size of N CP i the startig ad the edig of the symbol the two widow sizes will be idetical. The ML estimatio uses the idetical ature of the two widows ad fids the timig ad frequecy offsets. Let us take the N N cosecutive samples of r (), ad that these samples cotai oe complete CP CP OFDM symbol of N NCP samples. The positio of this symbol withi the observed block of samples is ukow because the chael delay is ukow to the receiver. Apply the autocorrelatio of size N with a distace betwee the widows as N. The the autocorrelatio sum gets maximized oly whe the two widows match which idicates that is the startig sample of the OFDM symbol. Usig this property STO ca be determied. E * r ) r ( m) if m 0 ( s w e j s if m N

17 0 else. The log-likelihood fuctio for ad is the logarithm (, ) of the probability desity fuctio f ( r, ) of the N NCP received samples give the arrival time ad. Uder the assumptio that r() is a joitly Gaussia vector the the log-likelihood fuctio becomes Where (, ) ( ) cos( ( )) ( ), mncp 1 ( m) r( ) r( N) m 1 ( m) mncp 1 m [ r( ) r( N) ] * E[ r( ) r ( N)] s E[ r( ) ] E[ r( N) ] s w SNR SNR 1 From the joit time-frequecy ML of (, ), the estimates of ad (refer[7]) are obtaied as, arg max { ( ) ( )} ML ML 1 ( ) ( ML) The ML estimatio method above has the followig issues, first issue is computatioally very complex to do a -dimesioal search (time ad frequecy) over the complete block of every OFDM symbol, d issue is ambiguity i threshold settig for detectig the correlatio peak. The recommeded method is to first search i time domai for ormalized correlatio with a threshold settig 0. 9, where max( ) 1), that idicates the presece of the OFDM symbol ad the -dimesioal search aroud the threshold ca be iitiated. Aroud the 0.9 use the ML method of search for detectig the ˆ ML adˆ ML. Note that the method gives the estimate of fractioal CFO (FFO). After compesatig the FFO the residual CFO ca be estimated usig the RS sigals i frequecy domai ad will be compesated. 4. SCO Estimatio Samplig time differece due to the mismatch betwee DAC ad ADC clocks of trasmitter ad receiver respectively. Ts ( Tx) Ts ( Rx). T ( Rx) s I the case of 0, the separatio betwee two cosecutive estimatios is N NCP samples, that is, a estimatio is obtaied from every OFDM symbol. owever, if 0, the effect of the widow drift is directly traslated to the metrics, leadig the separatio

18 betwee correlatio peaks to be ( N N ) samples. The calculatio of the ML CP Estimatio by J. J. va de Beek[7] metrics provides a estimatio of the widow drift, by comparig the estimatio for the th symbol with the expected positio of the estimatio i the ideal case, that is = ). I order to avoid deviatios caused by istataeous degradatios o the calculated metrics, a filterig is required for trackig the variatios due to. For this reaso, it is cosidered a maximum deviatio of 1 sample betwee two cosecutive symbols. It is possible to have a estimatio of, by averagig the correctios performed over the symbol widow. This estimatio is obtaied by averagig the value of sig( over the umber of received symbols, the quotiet betwee this average ad the umber of received samples gives a estimatio of the stability of the samplig clocks. 5. CANNEL ESTIMATION Chael Estimatio provides iformatio about the chael delay spread i terms of the chael coefficiets. The delay spread ca be measured by takig the IFFT of the chael coefficiets which are obtaied o per-toe basis from the kowledge of received RS REs ad kow RS REs. This iformatio is the used by equalizers so that the fadig effect ad co-chael iterferece ca be removed ad the origial trasmitted sigal ca be restored. Chael Estimatio plays a importat role i a commuicatio receiver. I order to mitigate hostile chael effects o the received sigal, precise chael estimatio is required to provide iformatio for further processig of the received sigal. Chael Estimators ca be categorized ito two types: 1) No- Data-Aided (or Blid) ) Data-Aided No-Data-Aided: A No-Data-Aided or blid chael estimator estimates the chael resposes by statistics of the received sigals. No specialized referece (traiig) sigals are eeded ad the trasmissio efficiecy is retaied for systems usig this type of estimators. Sice the trasmitted sigals are ot kow to the receiver i this type, a large umber of data must be collected i order to obtai reliable estimatio. Data-Aided: Data-Aided chael estimators require kow referece sigals (RS) to be trasmitted. Chael estimatio ca be achieved by comparig the received ad trasmitted referece or pilot sigals. A sufficiet umber of such referece sigals must be iserted accordig to the degree of chael variatio, amely coherece time ad coherece badwidth of the chael uder estimatio. OFDM based commuicatio stadards, provide some forms of referece

19 sigals, amely preamble or pilot sigals. This paper will focus maily o the data-aided chael estimatio algorithms for OFDM commuicatios. 5.1 PILOT BASED CANNEL ESTIMATION The least-square (LS) ad miimum-mea-square-error (MMSE) techiques are widely used for chael estimatio whe traiig symbols are available. We assume that all subcarriers are orthogoal (i.e., ICI-free). The, the traiig symbols for N subcarriers ca be represeted by the followig diagoal matrix: X[0] 0 X 0 0 X[1] X[N -1] Where X[k] deotes a pilot toe at the k th subcarrier, with E{X[k]}=0 ad Var{X[k]}= k=0,1,,,n-1. Note that X is give by a diagoal matrix, sice we assume that all subcarriers are orthogoal. Give that the chael gai is [k] for each subcarrier k, the received traiig sigal Y[k] ca be represeted as Y Y[0] X[0] 0 0 [0] Z[0] Y[1] 0 X[1] [1] Z[1] 0 YN [ 1] 0 0 X[N-1] [N-1] Z[N-1] Where is a chael vector as = X+Z T =[[0],[1],,[N-1]] ad Z is a oise vector give as T Z=[Z[0],Z[1],,Z[N-1]] with E{Z[k]}=0 ad Var{Z[k]}= k=01,,.n-1. The Ĥ deotes the estimate of chael Least Square Estimatio The least-square (LS) chael estimatio method fids the chael estimate Ĥ i such a way that the followig cost fuctio is miimized: F()= ˆ Y-Xˆ ˆ =(Y-X) (Y-X) ˆ =(Y X )(Y-X) ˆ ˆ ˆ =(Y Y-Y X-X Y X Xˆ By settig the derivative of the fuctio with respect to Ĥ to zero, ˆ ˆ

20 Implies F ˆ -(Y X) -X Y+( X X) X Xˆ Ĥ ˆ ˆ = -X Y-X Y+X X X X = -X Y X X = 0 ˆ ˆ X X = X Y 1 Ĥ = (X X) X Y 1 1 = X (X ) X Y 1 = X Y Therefore 1 Ĥ LS = X Y The mea-square error (MSE) of this LS chael estimate is give as: MSE E{ - ˆ } LS = E{(-) (-)} 1 1 = E{(-X Y) (-X Y)} 1 1 = E{(X Z) (X Z)} 1 1 = E{Z (X ) X Z)} 1 = E{Z (X X) Z)} = Z X ˆ ˆ The above mea-square equatio is iversly proportioal to the SNR, which implies that it may be subject to oise ehacemet especially whe the chael is i a deep ull MMSE Chael Estimatio The MMSE chael estimatio fids a better estimate i terms of a weighted matrix i such a way that the Mea Square Error is miimized whe compared to LS estimatio. The received sigal was give by Y=X+Z. We have see from the Least Square Estimatio, the estimated chael was give as Ĥ LS =X -1 Y. Let Ĥ LS =. Let us deote the MMSE Estimate of a chael as Ĥ obtaied by passig the through the weighted matrix W, i.e. Ĥ=W the actual chael beig. The error is give as e=- ˆ. The MSE of the chael estimate Ĥ is give as J() ˆ = E{ e }=E{ - ˆ }

21 Figure 11 MMSE chael estimatio The Orthogoality priciple states that the estimatio vector e=-ĥ is orthogoal to Ħ. Such that E{e }=E{(-) ˆ } ˆ =E{ - } =E{ -W } =E{ }-E{W } =E{ }-WE{ } =0 R WR 0 W=R (R ) 1 R E{ } 1 1 = E{X Y(X Y) } 1 1 = E{(+X Z)(+X Z) } 1 1 = E{(+X Z)( +Z (X ) )} = E{ +X Z +Z (X ) +X ZZ (X ) } 1 1 = E{ } E{X ZZ (X ) } R is the cross-correlatio matrix betwee the true chael ad temporary chael estimate vector i the frequecy domai. Usig the above equatio the MMSE chael estimate is give as Ĥ = W The elemets of the 1 = R (R ) Z 1 = R (R ) X R ad R i the above equatio are give as E{ h h } = E{ h h } = r [ k k ] r[ l l ] * * ' ' k, l ' ', ' ' k, l k l k, l f l

22 Where k ad l deote the subcarrier (frequecy) idex ad OFDM symbol (time) idex, respectively. I a expoetially-decreasig multipath PDP (Power Delay Profile), the Frequecy-domai correlatio rf [ k ] is give as 1 rf [ k] (1 j k f ) rms Where Δf =1/ T sub is the subcarrier spacig for the FFT iterval legth of T sub. Meawhile, for a fadig chael with the maximum Doppler frequecy fmax ad Jake s spectrum, the timedomai correlatio rl t[] is give as r[ l] J ( f lt ) t 0 max sym Where Tsym Tsub TG for guard iterval time of T G ad J 0 (x) is the first kid of 0th-order Bessel fuctio. Note that rt[0] Jt[0] 1, implyig that the time-domai correlatio for the same OFDM symbol is uity. 6. INTERPOLATION At the receiver, the chael complex gai at the pilot symbol positios ca be easily obtaied from the received sigal ad the kow pilot symbols. To estimate the chael for data symbols, the pilot subcarriers must be iterpolated. Iterpolatio is the applied to derive the estimatio of the chael kowledge at data symbol(o-pilot subcarriers) positios. There are may iterpolators such as Wieer filter, miimum mea-square error (MMSE), Liear iterpolatio, secod-order polyomial iterpolatio, splie, trasform domai iterpolatio ad low pass iterpolatio. Polyomial-based iterpolators have bee popular i the frequecy-domai iterpolatio algorithms eve though there are may better iterpolators due to their low implemetatio complexity. 6.1 Liear Iterpolatio Liear iterpolatio has bee proposed to estimate the frequecy-domai chael resposes at data subcarriers. For the k-th subcarrier to be iterpolated, let k/d = m+μ, where 0, ad m=[k/d], the largest iteger smaller tha k/d. The,the liear iterpolatio method obtais the chael respose at the k-th subcarrier as ˆ ˆ ˆ ˆ k D(m+ ) (1 )md (m+1)d The estimatio quality ca be improved by usig higher-order polyomials. owever, the implemetatio grows more complicated as the order icreases. A piecewise secod-order polyomial iterpolatio is as follows ˆ k ˆ D(m+ ) = C ˆ C ˆ C ˆ 0 md 1 (m+1)d (m+)d where

23 (1 )( ) C0 C ( ) C 1 (1 ) Other high-order polyomial-based iterpolators such as the piecewise parabolic iterpolator ad the cubic iterpolator take i four base poits for iterpolatio: ˆ ˆ k D(m+ ) = C ˆ C ˆ C ˆ C ˆ 1 (m-1)d 0 md 1 (m+1)d (m+)d I the piecewise parabolic iterpolator, the coefficiets are give by C 1 C 1 ( 1) 0 C ( 1) C 1 Usually, α is set to provide better iterpolatio quality. O the other had, the coefficiets of the cubic iterpolator are C C0 1 C C Shifted Raised-Cosie Iterpolatio Receiver performace will be poor if there is ucertaiity i the timig of the received sigal. I real time situatios, due to eergy leakage, their exist a pre-cursor as well as a post-cursor i the recostructed CIR. Their should be good time domai widow that ca preserve the major portio of the recostructed CIR ad, reject the aliased ad oisy compoets. Their may be eed to shift the time-domi widow right istead of ceterig at the origi due to multipath time delay. Shitig the widow i time domai is equivalet to rotatig the phase of the iterpolatio coefficiets i the frequecy domai. Where the CIR is strog the widow should be flat so that o distortio is iroduced, the two eds of the widow ca weigh smaller i order to supress the uwated compoets such as

24 oisy ad aliasig effect. So, smoother weightig i the time domai etails faster fall-off i the frequecy domai iterpolatio coefficiets. Splie iterpolator i which raised cosie fuctio is used as the frequecy domai iterpolatio coefficiets, satifies the above requiremets. Ml Ml si( ) cos( ) j dl N W l, R, C N * N * e Ml Ml 1 4 ( ) N N β is the roll-off factor, which decides the excess width of the widow s mai lobe. d cotrols the positio of the widow shifted to the right. 6.3 Two-Dimesioal MMSE Iterpolatio The time-varyig chael frequecy respose is a wide sese statioary D radom process. To get a perfect recostructio is hardly possible because of radom oise ad CIR. Amog the liear iterpolators, D MMSE iterpolator is the optimum i terms of the miimum mea-squared error criterio. Sice i the practical sceario the Referec( or pilot ) sigals are iserted i two dimesioally, so there is a eed to do the iterpolatio i both dimesioal(time ad frequcy. D MMSE iterpolator ca smooth the oise i the chael estimates for the pilot subcarrier; filter estimates o pilots; geerate the the CIR for data subcarriers iside the grid; ad predict the chael respose for data subcarriers outside the pilot grid. Two 1D MMSE iterpolatios also achieve the performace early equal to D MMSE iterpolator but with little bit reductio i the complexity tha D MMSE. But high complexity i the usage of MMSE iterpolator prevets their applicatio i practical OFDM receivers. 7. EQUALIZATION Chael Estimatio provides iformatio about distortio of the trasmissio sigal whe it propagates through the chael. This iformatio is the used by equalizers so that the fadig effect ad/or co-chael iterferece ca be removed ad the origial trasmitted sigal ca be restored. Oce chael estimates at data subcarriers are derived, the receiver performs equalizatio to compesate for sigal distortio. 7.1 Oe-Tap Equalizer OFDM systems are favoured over sigle-carrier modulatios i that the simple oe-tap frequecy-domai equalizer(fde) ca equalize OFDM sigals that go through frequecyselective fadig chaels. I chaels whose impulse resposes remai costat withi oe OFDM symbol period, the received sigal at each subcarrier takes the form of Z X + N i,k i,k i,k i,k Oe-Tap Equalizers restore the trasmitted sigal by Xi,k Gi,kZi,k : G i,k, the equalizer coefficiet at the k th subcarrier durig the i th symbol.

25 7.1.1 Zero-Forcig Equalizer Regardless of oise, the Zero-Forcig Equalizer simply uses the iverse of the chael respose ( G i,k 1 i,k ) ad forces the frequecy-selective-faded sigals back to flat faded oes. owever it may result i oise ehacemet i the subcarriers that suffer deep fadig. Cosider the oise-free MIMO System that ca be iterpreted as a liear system of M R - equatios(m R received sigals) with M T ukows(m T i/p symbols). y x Where dimesios are as follows: y M *1; R = M *M ; x= M T*1; I the ZF approach, this system is iverted to fid the ukow i/p symbols The ZF receiver is a M T * M R matrix deoted as F. such that: Fy x (or) F=I The ZF receiver iverse the MIMO chael matrix. R The existece of the chael iversio is subjected to some coditios o the chael. 3 cases ca be distiguished. does t have full colum rak (e.g. whe M T > M R ). There are o uique solutios for the i/p symbols. A ZF receiver caot be defied. is a square ad ivertible. There exists a sigle ZF receiver F ZF = -1. is tall(m T <or= M R ) ad has full colum rak. The system is over determied. That mea several receivers exit satisfyig F=I. 1 Those receivers ca be writte as (C ) C, where C is a M T *M R matrix with full colum rak. Whe there is o additive oise, ay of those receivers ca be applied to recover the i/p symbols. Whe there is oise, a error will be made o the estimatio of the symbols, the error depeds o the coefficiets of the receiver. So appropriate ZF receiver to be selected. MMSE-ZF Receiver: ZF receiver that miimizes the mea squared estimatio error. Assume the chael has full colum rak, their may exist may receivers that ca elimiate the ISI. Let the ZF receiver be F; F=I O/P of F is: x = Fy = x+f Estimatio Error: x-x = F Applyig MMSE to the estimated error. T

26 E x-x E F = E{(F) (F)} = E{ F F} = E{trF F } = tre{f F } = trf F The ZF receiver miimisig the MSE is uique. MMSE-ZF receiver or ZF equalizer is equal to F ZF ( ) MMSE-Receiver The purpose of the MMSE receiver is to miimize the average estimatio error o the trasmitted symbols. The average is take over the trasmitted symbols ad the oise: the MSE is x, E x-x.eve though the ZF receiver also miimizes the output MSE but the costrait of complete ISI elimiatio. Let the iputs, outputs, oise ad chael be defied as T y = [y y y y ] ; 0 1 (R-1) T x = [x 0 x 1 x x (T-1) ] ; T = [ 0 1 (R-1) ] ; ad is R*T matrix The output of a receiver F is of the form Fy ad the vector of errors is x-x = Fx+F-x = (F-I)x+F Applyig the MMSE coditio: E{ x-x } = E{ (F-I)x+F } = E{ ((F-I)x+F) ((F-I)x+F) } = E{(X (F-I) + F )((F-I)x+F)} = E{(X (F-I) (F-I)x)}+E{ F F} = P tr((f-i) (F-I)) + tr(f F) X = P tr(( F -I)(F-I)) + tr(f F) X X = P tr(( F F- F -F I) + tr(f F) Differetiatig the above equatio w.r.t F ad equatig it zero gives the MMSE receiver.

27 E P X ( F + F --) + (F F ) F = P (F +F - - ) + (F F) X X = P (F - ) + F = 0 P (F - ) + F 0 X X P F + F P F( + I) F ( + I) P X 1 X Derivatio for F F by usig a * matrix for F ad *1 for : F F F F * * * * F F 1 F 1 F F F * * F11 F1 F11F1 F1F 1 1 * * F F F F F F * * 1 = * * 1( F11 F 1 ) (F1F11 FF 1) 1(F11F1 F1F ) ( F1 F ) * * * * = 1 ( F11 F 1 ) 1 (F1F11 FF 1) 1(F11F1 F1F ) ( F1 F ) * * * * E F F = E ( F F ) (F F F F ) (F F F F ) ( F F ) = F F F F = tr(f F) 8. Project summary Processig of received data received through 4G LTE Test-Bed (amed as MW1000), ad retrievig back the trasmitted sigal at PBC slots. The processig of the LTE data was doe which was trasmitted ad received i MW1000 test bed through (i) wired chael ad (ii) wireless chael. The data trasmissio ad receivig was doe i real time ad the testbed which cosists the enodeb ad UE. Ad their specificatios meet the LTE stadards. The TDD frame structure of Normal cyclic prefix type is take for the project ad a Uplik- DL cofiguratio of Type 1. I the test-bed simulatio cases the chael is assumed to

28 remai costat for 1 ms, ad it is eough to iterpolate the chael i frequecy domai ad takig it as the costat for the symbols ear to the actual estimated symbols. LTE Test-Bed Specificatios: MW1000-3GPP LTE enodeb ad UE Test-bed with reprogrammable capability i C ad Liux OS with RF frot ed itegratio 3GPP LTE - Release 9 RF carrier frequecy -.4 Gz The samplig frequecy Mz, Trasmissio Badwidth 0Mz Number of Resource Blocks 100 FFT/IFFT size IQ Samples - 16 bit I, 16 bit Q Cyclic Prefix - Normal Duplexig Mode - TDD (UL-DL Cofig Idex-1) Trasmissio Mode - (Trasmit Diversity) Trasmissio Medium - RF, Wireless The MW1000 Test Bed The etire setup of the test bed is as show below. Figure 1 Mymo s 3GPP LTE x MIMO Test-bed (MW1000)

29 Descriptio of the above set up: It is first of its kid for buildig ad validatig the LTE basebad ad protocol desigs rapidly i a real-time eviromet. The uiqueess of the test-bed is that the desigers ca desig ad implemet ad verify the algorithms, system desig ad Phy ad protocol stack layers. The test-bech eables the desig team to quickly build the complete system models i ANSI C ad Liux OS platform ad for validatig the algorithms performace i real RF eviromet. The 3GPP LTE UE ad enodeb layers are seamlessly itegrated, ad the basebad at IQ samplig rate 30.7Mz is iterfaced with RF-Mixed-Sigal card for operatio at desired ISM RF bad or LTE Bad-37, 38 or 7. The desig test-bech is built with a flexibility to access ad modify ay part of the sigal processig or bit rate processig fuctioal blocks of LTE UE or enodeb writte i ANSI C source code. The test-bed ca be cofigured to radiate ad capture the RF sigals i a free-space multipath propagatio eviromet or directly coectig enodeb ad UE RF ports through SMA cables ad RF atteuators to avoid the free-space radiatio. The TDD trasmitted sigal of UL-DL Cofiguratio Idex 1 for 1 SFN is show i Figure x 10 5 Figure 13 LTE TDD Oe Frame (10ms) Time Domai Sigal Captured from Test-Bed Processig of the received Data:

30 The DL received IQ sigal is captured for multiple frames (each frame 10ms) at 30.7 Mz samplig rate. The cell search by PSS ad SSS followed by time-frequecy sychroizatio is performed. The approximate sigal widow of PBC i slot-1 of subframe 0 is processed for demostratig the time-frequecy sychroizatio, chael estimatio ad equalizatio results. Retrievig the PBC data The received data by UE has udergoe may distortios due to the chael respose, multipath delay, additive oise etc The receiver had to compesate all the effects ad retrieve the origial sigal back i.e. trasmitted by the enodeb. The effects that the sigal ad their affect was discussed above. Processig of the data ivolves o Sychroizatio o Extractig the PBC slots o Chael Estimatio o Iterpolatio o Equalizatio These processes are described above ad the brief otes about the steps followed i the project are: For sychroizatio the widow start positio was take few samples before to avoid ecroachmet ito the ISI part of the ext symbol. The few samples take before add upto symbol offset which will be corrected durig the equalizatio. Frequecy sychroizatio was doe at multiple stages (i time domai ad frequecy domai) to get a effective compesatio. For chael estimatio the LS (least squares) estimatio algorithm was used eve though the MMSE estimator was the optimum because of the complexity ivolved i the usage of MMSE i real time. The assumptio is that the chael is quasi-statioary for 1ms (oe subframe). It is eough to estimate the chael i OFDM symbol-1 ad symbol-5 (where RS sigals are preset) ad iterpolate i frequecy domai. The equalizatio was doe usig the zero forcig equalizer. The project results are as show below: The received OFDM IQ frequecy domai sigals with CFO ucorrected ad uequalized is show i Figure 14.

31 Quadrature Scatter plot I-Phase Figure 14 Received usychroized ad uequalized IQ data The above show is the received sigal IQ data of the symbol which cotais PBC, the actual trasmitted data is 4QAM data. We ca see the distortio caused by the chael dispersio ad the CFO. Figure 15 below shows the time ad frequecy plots durig the ML Estimatio of Time ad Frequecy offsets.

32 6 ML Estimatio of time offset ML Estimatio of frequecy offset Figure 15 ML Estimatio of Time ad Frequecy offset The above plot shows the ML Estimatio of the Time ad Frequecy Offsets. The peak positio i the time offset idicates the start positio of the OFDM symbol. Ad the correspodig positio i below subplot idicates Frequecy offset for that etire symbol. Uequalized PBC IQ data after Time ad frequecy sychroizatio compesatio is plotted i Figure 16.

33 Figure 16 Extracted compesated but Uequalized PBC IQ data This plot i Figure 17 idicates the PBC data after sychroizatio i time ad frequecy ad post equalizatio. The coarse ad fie timig sychroiatio, the iteger CFO, coarse ad fie sychroizatio are estimated ad compesated before equalizatio. The restored PBC costellatio is a 4QAM ad as show i Figure 17.

34 Figure 17 Timig ad CFO compesated ad MMSE Equalized PBC 4QAM costellatio 9. CONCLUSION: The retrievig of the PBC data from a received distorted sigal was doe. Ad the required results were obtaied 10. REFERENCES Durig the project executio the followig Refereces are [1] 3GPP, TS V9.0 ad TS 36.1 V9.0 [] Tzi-Dar Chiueh ad Pei-Yu Tsai, OFDM Basebad Receiver Desig for Wireless Commuicatios, Joh Wiley ad Sos 007 [3] Tim Brow, Elisabeth De Carvalho ad Persefoi Kyritsi, Practical Guide to the MIMO Radio Chael with MATLAB Examples, WILEY 01 [4] Yog Soo Cho, Jaekwo Kim, Wo Youg Yag ad Chug-Gu Kag, MIMO-OFDM Wireless Commuicatios with MATLAB, WILEY 010

35 [5] J. J. va de Beek, M. Sadell, P.O.Borjesso. ML Estimatio of Time ad Frequecy Offset i OFDM Systems,IEEE Tras. Sigal Processig, vol. 45, o. 7, pp July [6] E. del Castillo-Sachez, F.J. Lopez-Martiez, E. Martos-Naya, J.T. Etrambasaguas, Joit Time, Frequecy ad Samplig Clock Sychroizatio for OFDM-based systems Wireless Commuicatios ad Networkig Coferece, 009, WCNC 009,IEEE [7] Rohde ad Schwarz, UMTS Log Term Evolutio (LTE) Techology Itroductio C.Gesser MA111_E [8] YE(Geoffery) LI ad Gordo Stuber, Orthogoal Frequecy Divisio Multiplexig for Wireless Commuicatios, Spriger 006 [9] Erik Dahlma, Stefa Parkvall ad Per Bemig, 3G Evolutio SPA ad LTE for Mobile Broadbad, Academic Press, 008