Journal ofScience & Technology 101 (2014) 111-117 The Correlation Properities of Spatial and Onering Channel Model Based on SFBC MIMO - OFDM System Nga Nguyen', Bach Tran, Van Due Nguyen Hanoi University ofScience and Technology No I, Dai Co Viet Str., Hai Ba Trung, Ha Not Vie! Nam Abstract inthispaper, we investigate the influence of spatial correlation properties of channel models Thechannel is modelled based on the spatial channel model (SCl^^) approach, proposed by the 3"' Generation Partnership Project (3GPP) organization or One-nng scattenng model We also study the performance of spatial channel coding techniques such as space time block coding (STBCj and space-frequency block coding (SFBC) on the multiple-input multiple-output orthogonal frequency division multiplexing (MUvfOOFDM) system, based on long term evolution (LTE) downlink standard The simulation results show that the SFBC coding scheme has better pertormance than STBC when the same antenna element spacing is used Especially, when the antenna spaces of the transmitter and receiver antenna are changed, pertormance of the system is better with increased spacing between antennas at base station (BS) than at the mobile station (MS) side Keywords; MIMO - OFDM, SCM, STBC, V-BLAST, SFBC, LTE downlink channel Introduction Combining of the two technologies, MIMO and OFDM (MIMO- OFDM), the interference and attenuation are mitigated by using diversity methods which produce replicas of the transmitted signal over time, frequency or space domain meanwhile wireless communication system has achieved a high symbol data rate for wideband mobile networks Any channel model must have a set of parameters that permit to calculate the conelative affection of the antenna in both transmitter and receiver In [1,2] authors investigate the generalized formula for spatial conelation and present it in a good approximation with three different angular energy disfributions The 4G-LTE cellular network uses the MIMO-OFDM technology for the downlink channel as in [3,4] The UMTS and LTE for Cellular Network Planning are in [5-7] The [8,9] from which the conelation properties between antenna elements affecting the quality of MIMO-OFDM system are evaluated, is designed for multiple antenna systems ConelaHon properties depend on the antenna distance and the value of angle on the cluster of scatters In practice the sub-channels are correlated to each other in both time and space domains [10,11] • Corresponding Aulhor Tel: (+84) 989,145,909 Email due,nguyenvanl@husl,edu.vn The geometrical one-ring scattering model for MIMO- OFDM system in [12] is implemented with HYPERLAN/2 standard The extended One-ring for frequency selective channel with vehicular A (EVA) - ITU model performance of transmit diversity algonthm for MIMO-OFDM systems in case of perfect CSI is in [13] In this paper, we study the conelation properties of LTE charmels based on the SCM as described in [14,15] From that SCM is compared to the extended One-ring to reveal the better performance of SCM Besides, we use space time codes for frequency selective LTE channels such as STBC and SFBC [16,17] to estimate die symbol enor rate (SER) ratio The remainder of this paper has the following structure Section bnefly introduces spatial conelation properties of the SCM with LTE channels based on AoA and AoD angles Sections compares the conelation properties of SCM and One-ring based on LTE standard Section studies the structure of MIMO-OFDM systems with LTE down link channels Next, section explains coding methods and provides performances of STBC and SFBC coding in MIMO-OFDM systems under perfect CSI Last but not least, simulation result evaluation and conclusions are in Section and 7, respectively, Mimo Channel Modelling and Paremeters of The SCM The scattenng channel modelling of 3GPP in [8] is shown in Fig, 1, The angular parameters are the following definitions as: Journal ofScience & Technology 101 (2014) 111-117 QBS is an angle between the BS-MS Ime of The given Eq (2), from that Ad, and A(/„ are sight (LOS) and the BS broadside; 9,ic is an angle the distances of transmitter and receiver antenna, between the BS-MS LOS and the MS broadside; 5„, respectively, t is the lime delay of the channel AoD is the angle of departure (AoD) of the n"" path When r = 0, the spatial cross conelation (n-1 A*); S„ AaA is the angle of arrival (AoA) of the «'* path (n=; N); &„„,.AOD IS offset of - m'* function (CCF) of wideband MIMO channel is given as follow; (m-1 M) subpath of the «'''path with respect to 5n AOD; K.m.AoA IS offset of- m'* (m=7 .M) subpath of ft'S (-"ã.m.AoA is the AoA for the m"' subpath of the n"' path at the MS with respect to the BS broadside, as in Eq, (1) Assume that the number of sub-paths per path M -^ 00 and the Power Delay Profile (PDP) has the same value in all paths, the CCF fiinction is as follow: P ; , t CAdJ = £[expO-fcAd„ cos(0„,^,,,,))] = ^exp{jkAd^cos{d„_^_^oA))-P'{en.mAoA)de (jkAd,cosie„,^,^,^))de =yoC^Ad„) Journal ofScience & Technology 101 (2014) 111-117 Table Parameterfor Sub-path AoD and AoA offsets Subpath # Offset for a deg AS at BS 1,2 3,4 5,6 7,8 9, 10 11, 12 13,14 15, 16 17, 18 19,20 degrees) ± 0,0894 ± 2826 ± 0.4984 ±0.7431 ± 1,0257 ± 3594 ± 7688 + 2,2961 + 3.0389 ±4.3101 («) Offset for a 35 deg AS at MS ^Fi,m,AoA (degrees) can see the CCF of MS when usmg Bessel function is in the middle of the others, the shape is similar so it is not have much differential than that showed by the Gaussian and Uniform distributions ± 1.5649 ± 4.9447 ± 8.7224 ± 13 0045 ± 17 9492 ± 23,7899 ± 30 9538 ±40 1824 ±53 1816 ± 75 4274 A A Fig Spatial conelation at the receiver Where Joi.) is expressed by Bessel fimction of the first kind order 0; P'(0n,m.4o/i) isprobability density fimction of expOfcAd„ cos(6„^n!,,4o,4))- 3.2 Correlation Properties of the AODs at the transmitter In case as m [8] the AoAs are Gaussian random variables: i5„,^o^ ;; (0 UAOA), « ^ U -^N As m equation (5) we have pl^l (.^d^) - the cross conelation function with the antenna distance of MS equal to zero (Ad-u^ = 0) Where (T„^o^ = , ( e;tp(-0.2175|10/o5ioCPn)l)), In Suburban Macro environment in [8], ^n.m.AoD is the AoD for them'''sub path ofthen"'path at the BS with respect to the BS broadside, as in Eq P^ is the relative power of the «th path (D- So the CCF when usmg Gaussian distribution: Psj^j C^t^u) = ^ [ e x p O f c A d u COs{eMs + S„_AaA + ^n.mAoA))] ' (§) In case as in [12], S^^AOA 'S a function of Uniform distribution U(0,2n) Pt^uli^dj = e[expO'fcAd^cos(0n,m,^„^))] = E[exp(jkAd, cos(9„s + KAOA + K.^.AOA))] (9) Where: As in [8] the AoDs are Gaussian random variables S„.AoD'~^(0,0^„o')'"^^' >N- a^s ^ 10^^s'^+'''i^x~i7(0,l); So the CCF when using Gaussian distribuhon: p'sluli^d,) kn / 1\ kn ( 1\ n ""•"»''= M l" - j + ''"•"•= S I" - J + M Where e „ j is assumed as constant and A„.^_AOA is in Table [8], The fimction above is called generahzed MEDS (GMEDS*) as in [12], where k e {\, 1, 3, 4; denotes the number of quadrants of the cluster of scatters on the ring When choosing A = 4, we have GMEDS4 So die CCF when using Uniform disfribution depends on the Uniform distribution of GMEDS., d.a.AoAWhen the MS antenna spacing is changed, the conelation graph is in Fig,2 from which ^^.AOA have Gaussian distribution Uniform disfribution and the reference model (the Bessel functionya(/fAdu)), We and XdX, respectively In theory, SCM have much parameter for each environment so the curve of the SCM is not as clear and idealized as Onering Fig, 6a, Spatial C C F p j ; ; ( A d = 0.5A,AdJ Fig 7a Spatial CCF ^/^^^(Adj = O.Ad^) MIMO - OFDM for LTE downlink channel The MIMO-OFDM system for LTE downlink chatmelisin [14] In [13], the serial input stream is combined to a vector of data X{k)= {Xi(k) Xifk), XN(k)} where A' IS the number of data symbols transmitted / received in a block, and k is the sequence number of data vector or in time slot k The received data symbol on «'* subcamer can be represented as [14]: Vu(k) - SLiHusCf k)Xu(k) + Nu(k) (17) where s: s"' fransmit antenna at the time slot k, «, u"' received antenna at the time slot k H„ (f, k) is the time variant charmel transfer function of the «'* subcarrier when receiving the A'* data symbol Nu (k) is the discrete Fourier transforms of the independent Gaussian noise random variable Thereby, (.)" designates the Hermittan transpose operator The received symbol obtained by the zero-forcing ZF equahzer given by [14] X„ = (,H^H^y^H}^Y„) (18) Fig 6b Spatial CCF ( j j ; ; (Ad„, Ad, = WX) Fig 7b.: i I C C F p g : ; ( A d „ A d „ = 0) Journal ofScience & Technology 101 (2014) 111-117 applied to LTE downlink channel based on SCM [8] and [9], The OFDM system parameters are presented in Table Coding for MEMO - OFDM System 6.1 Space time block code (STBC) In [17] STBC is applied with two consecutive OFDM symbols in the 2*2 MIMO system Table Parameters of MIMO -OFDM system 6.2 Space frequency blocit code (SFBC) r^, = 2 '^ffT=512 MHz QAM 64 Simulation results obtained by the SFBC and the STBC for an MIMO - OFDM system over the SCM channel and One-ring channel are shown in Figures 10 and 11, Based on the investigated spatial correlation function of the channel in previous section, we can see that the system has higher diversity gain when the distances between antenna elements are larger, especially in BS side The optimum factors of the distance of antenna elemenls for BS and MS is \0X and 1/2X as the 3"'GPP citatioD, SFBC scheme in [16], an adaptation in frequency domain, is used in LTE downlink channel, SFBC can realize full space diversity and avoid the disadvantages of STBC which are the changing of time of channel and delay spread - caused by the neighbour OFDM subcamers in OFDM symbol Therefore, the matnx of fransmitted symbol, channel coefficient and received symbol are respectively calculated as following as in [14], The input sequence SFBC before going to the fransmission channel is distributed in frequency and space domain is as in Fig.9 Fig 10, In One-nng model, we have compared two block coding When SNR = 16dB with Ad,=10X; Adu^O 5X, calculated SER of SFBC is 0,055 but of STBC IS 0,1066; other case with Ad,r lOA and Ad,=IOl, SER of SFBC is 0.0473 but of STBC is 1044 From SNR = 8dB, it seems that the more the SNR is, the smaller the SER of SFBC is System Performance Evaluation In die simulation results, we evaluate the SER performance of the 2J:2-MIMO-OFDM system T,n, Value ^ = 300 Parameters Number of subcarrier Length of GI Number of IFFT Bandwidth Modulation The matrix of transmitted symbol, channel coefficient and received symbol are relatively sequence as m [14] The input sequence STBC before going to Ihe transmission channel is distributed in time and space domain is as in Fig.8 •' \.,„ "(I) \x(2k) J'(« ^M 1 rpt-«| -x.(z* \xt2k-l} , Space Fig STBC encoder with MIMO ] [^ I JGW I xj^kT] ••• I x^ic) I x;, Fig SFBC encoder with MIMO CompaiUiDn in Onenug LIE " > * ô ằ ô " ã = '' SFBC-Sgjfts 10, \^>^-M2 SFBC Sg5ra,=10 S ^ l = ' ETBC6B5,>.=10 &^^M2- 10 and 6^), = STBC5B^=10.S,^. * « » « " • = '''' SFBC- Sgjfts 10, \^>^-M2 SFBC Sg5ra,=10 S ^ l = ''... Spatial C C F p j ; ; ( A d = 0.5A,AdJ Fig 7a Spatial CCF ^/^^^(Adj = O.Ad^) MIMO - OFDM for LTE downlink channel The MIMO- OFDM system for LTE downlink chatmelisin [14] In [13], the serial input stream