SINGLE CARRIER BLOCK TRANSMISSION WITHOUT GUARD INTERVAL

Transcription

1 SINGLE CARRIER BLOCK TRANSMISSION WITHOUT GUARD INTERVAL Kazunori Hayahi Hideaki Sakai Graduate School of Informatic, Kyoto Univerity Kyoto, JAPAN ABSTRACT Thi paper propoe a imple detection cheme for a ingle carrier block tranmiion (SCBT) without guard interval (GI) Although the SCBT without the GI can ignificantly increae bandwidth efficiency, the received ignal uffer from interblock interference (IBI) and interymbol interference (ISI), which cannot be effectively equalized by a frequency domain equalizer (FDE) In the propoed cheme, the IBI i cancelled by uing a previouly detected ignal Moreover, taking advantage of the temporal localization of the difference of the ISI component between the received ignal with and without CP, we change the channel matrix from Toeplitz tructure into a circulant matrix in order to utilize the conventional FDE Computer imulation reult how that the propoed cheme can outperform a linear MMSE equalizer with lower computational complexity I INTRODUCTION A block tranmiion cheme uing cyclic prefix (CP) a a guard interval (GI), uch a orthogonal frequency diviion multiplexing (OFDM)1], digital multitone (DMT)2] and ingle carrier block tranmiion with CP (SCCP)3]5], ha been drawing much attention due to the high performance in frequency elective fading channel with a imple receiver tructure uing frequency domain equalizer (FDE) However, the CP ytem have obtained both of the good performance and the implicity at the expene of the bandwidth efficiency If no GI i employed in the block tranmiion, the received ignal uffer from interblock interference (IBI), and the FDE cannot effectively equalize interymbol interference (ISI) becaue the channel matrix i no more a circulant matrix, although we can expect ignificant increae in the bandwidth efficiency So far, ome invetigation on the CP free block tranmiion have been made, however, they are mainly for multicarrier ytem and employ complex tructure of the receiver, uch a temporal domain equalizer In thi paper, we propoe a imple detection cheme for the SCBT ytem without the GI A blockbyblock detection like the SCCP ytem i employed in the propoed cheme, therefore, we can utilize a previouly detected ignal block for the IBI cancellation Moreover, taking advantage of the temporal localization of the difference of the ISI component between the received ignal with and without CP8], we generate a replica of the difference ignal, which enable u to ue a conventional FDE by changing the channel matrix from Toeplitz tructure into the circulant matrix Computer imulation reult how that the propoed cheme can outperform a linear minimum meanquareerror (MMSE) equalizer while the propoed cheme require lower computational complexity II SIGNAL MODELING Let denote the nth tranmitted information ignal block of ize M 1 a (n) = 0 (n),, (n)] T We do not employ any GI between the tranmitted ignal block Denoting a channel impule repone a {h 0,,h L },thenth received ignal block i given by =H 0 (n)h 1 (n 1) n(n), (1) where n(n) i a channel noie vector, H 0 and H 1 denote M M channel matrice defined a h H 0 = h L 0, (2) h L h h L h 1 H 1 = hl (3) If we have the GI with ufficient length, H 0 become a circulant matrix and H 1 become a zero matrix Therefore, no IBI remain in the received ignal block and the FDE can equalize the ISI effectively However, in our cenario, H 0 and H 1 are no longer a circulant matrix and a zero matrix, repectively Defining matrice C, C ISI and C IBI a h h L h 1 hl C = h L 0, (4) h L h 0 C ISI = H 1, (5) C IBI = H 1, (6) /06/$2000 c 2006 IEEE

2 ISI Cancellation (or Equalization) C IBI ~ (n1) z 1 Linear Equalizer F H C IBI ~ (n1) z 1 Figure 1: IBI cancellation Figure 2: Linear Equalizer we can rewrite the received ignal block a =C(n) C ISI (n)c IBI (n 1) n(n) (7) Frequency Domain Equalizer H D Γ D The third term in the right hand of (7) i the IBI component in the received ignal Alo, ince the received ignal of the SCBT ytem with the CP conit of only the firt and the fourth term, the econd term i a difference ISI component between the received ignal with and without the CP C IBI ~ (n1) z 1 Figure 3: FDE III PROPOSED IBI CANCELLATION Since the equalization and the detection are conducted in a blockbyblock manner in the propoed cheme, the IBI component C IBI (n 1) could be cancelled by uing the previouly detected data vector (n 1) In the propoed method, we cancel the IBI by ubtracting C IBI (n 1) from a hown in Fig1 After the IBI cancellation, the received ignal vector can be written a = C IBI (n 1), (8) (C C ISI )(n)n(n), (9) where become an equality when (n 1) = (n 1) IV PROPOSED ISI CANCELLATION In thi ection, we how propoed ISI cancellation (or equalization) method auming that the IBI component are completely cancelled, namely, =(C C ISI )(n)n(n), () = H 0 (n)n(n) (11) In the following, we firtly derive a linear MMSE equalizer, which will be a performance benchmark of the other method And then, we derive FDE weight for the SCBT ytem without the GI Finally, we decribe the detail of the propoed difference ignal cancellation method A Linear Equalization Denoting the output of the equalizer a ŝ(n), the linear MMSE equalizer can be obtained by minimizing E{tr(ŝ(n) (n))(ŝ(n) (n)) H ]}, where E{ } and tr ] denote enemble average and trace of the matrix, repectively By olving the minimization problem, the linear MMSE equalizer F H can be given by { F H = H H 0 H 0 H H 0 } 1 σ2 n σ 2 I M, (12) where n and denote the variance of the noie and the tranmitted ignal, repectively, and I M i an identity matrix of ize M M Note that the idea itelf of the linear equalizer i quite imple, however, it require high computational complexity due to the invere of the large (M M) matrix B 1tap FDE The channel matrix H 0 i no more a circulant, therefore, the 1tap FDE cannot perfectly equalize the ditorted received ignal even when the IBI i completely cancelled However, the FDE i till attractive becaue of the implicity of the implementation uing fat Fourier tranform (FFT) Fig3 how the configuration of the receiver uing the FDE The output of the FDE can be given by ŝ fde (n) =D H ΓD, (13) where Γ = diagγ 0,,γ ] i a diagonal matrix and γ m i given by (ee Appendix) γ m = g m,m = 1 M λ m gm,m λ m 2 λ m gm,m λ mg m,m i=0 g, m,i 2 σ2 n (14) l h L i e j 2π M m(m Ll i), (15) l=0 i=0 g m,n 2 = 1 M l h L i 2 e j 2π M n(l l ) (16) l=0 i=0 l =0

3 Tentative Deciion Generator ~ (n) Conventional FDE Tentative Deciion C ISI C IBI ~ (n1) z 1 Figure 4: FDE With Difference Signal Cancellation C FDE With Difference Signal Cancellation The propoed FDE require low computational complexity and can achieve better performance than the conventional FDE, however, it till uffer from performance degradation due to the nonecirculant channel matrix H 0 In order to achieve further improvement of the performance, we conider the difference ignal C ISI (n) cancellation uing tentative deciion (n) = 0 (n),, (n)] T a hown in Fig4 The main idea i that, by adding the replica of C ISI (n) to, we obtain a received ignal vector, which i ditorted only by the circulant matrix C in the ideal cae = C ISI (n), (17) C(n)n(n) (18) And then, the conventional FDE can efficiently equalize a ŝ cancel (n) =D H Γ cnv D, (19) where Γ cnv = diagγ0 cnv,,γ cnv ] i a diagonal matrix of the 1tap FDE If we employ the conventional MMSE FDE, the mth element of the equalizer i given by γ cnv m = λ m λ m 2 σ2 n, (20) where λ m i the mth diagonal element of Λ = DCD H A for the tentative deciion ued for the replica ignal generation, we utilize the tructure of C ISI Since C ISI ha nonzero element only in L column, C ISI (n) =C ISI (21) = C ISI F F T (n), (22) where = M L (n),, (n)] T = F T (n) and ] 0(M L) L F = (23) Therefore, only the correponding tentative deciion, which i defined in the ame way a, i required in order to generate the replica of C ISI (n) I L ] Propoed FDE F F T C H 1 (E E) E F F T r Figure 5: Tentative Deciion Generation Moreover, ince H 0 (n) C ( I M F F H ) (n) ( = H 0 (n) C (n) = H 0 we have ( r (n) def = C fde (n) ]) ~ (n) ], (24) ub fde (n) ]) ] H 0 ub, (25) (n) where fde (n) = ŝ fde (n) and ub fde (n) =FT fde(n) Here, denote detection operation Furthermore, defining ] 0(M L) L F r =, (26) I L and r ub (n) =F T r r (n), we finally have where r ub (n) E, (27) h 0 0 E = F T r H 0 F =, (28) h h 0 By olving (27), the tentative deciion for the replica generation can be given by = E 1 r ub (n) (29) The chematic diagram of the tentative deciion generation i howninfigure5 V COMPUTER SIMULATION In order to confirm the performance of the propoed method, computer imulation are conducted with the following ytem parameter; Mod/Demod cheme: QPSK, ymbol per block: M =64, channel order: L =4, channel model: 3path frequency elective Rayleigh fading channel A for the ytem to be evaluated, we conider following 4 ytem: the conventional MMSE FDE, the linear MMSE equalizer with the propoed IBI cancellation, the propoed FDE with the IBI cancellation, and the FDE with the IBI and the difference ignal

4 BER Conventional MMSE FDE Propoed FDE IBI cncl 2] JM Cioffi, Aymmetric digital ubcriber line The CRC Handbook of Communication, ] H Sari, G Karam and I Jeanclaude Tranmiion technique for digital terretrial TV broadcating IEEE Commun Mag, vol33, pp0 9, Feb ] D Falconer et al Frequency domain equalization for inglecarrier broadband wirele ytem IEEE Commun Mag, vol40, pp58 66, Apr 2002 Linear MMSE Equalizer IBI cncl 3 Propoed FDE IBI and Diff Sig cncl E b /N 0 db] Figure 6: BER Performance cancellation Fig6 how the BER performance veru the ratio of the energy per bit to the noie power denity (E b /N 0 )of the above 4 ytem From the Figure, we can ee that the FDE with the IBI and the difference ignal cancellation cheme can achieve the bet performance among the 4 ytem, and amazingly enough, it can outperform the linear MMSE equalizer with the propoed IBI cancellation Thi could be explained by the exitence of a nonlinear proceing in the propoed difference ignal canceller, namely, the detection operation The nonlinear operation make it poible for the propoed ytem to outperform the optimum MMSE linear equalizer The reaon why the BER of the conventional MMSE FDE get worth a E b /N 0 increae i that the actual ignal to interference plu noie power ratio (SINR) come away from / n a E b /N 0 increae VI CONCLUSION We have propoed a imple detection cheme for the SCBT ytem without the GI Although the GI free block tranmiion can ignificantly increae the bandwidth efficiency, it uffer from the IBI and the ISI, which cannot be equalized with the conventional FDE In the propoed cheme, the IBI i cancelled by uing previouly detected data ignal A for the ISI, we have conidered three ISI cancellation or equalization cheme, namely, the linear MMSE equalizer, the 1tap FDE, and the FDE with the difference ignal cancellation Moreover, the BER performance of the propoed cheme are evaluated via computer imulation From the reult, we can ee that the propoed FDE with the IBI and the difference ignal cancellation can outperform the linear MMSE equalizer with lower computational complexity REFERENCES 1] S Hara and P Praad Overview of multicarrier CDMA IEEE Commun Mag, vol35, pp , Dec ] Z Wang and G B Giannaki Wirele multicarrier communication IEEE Signal Proceing Mag, vol17, pp29 48, May ] S Trautmann and N J Fliege Prefect equalization for DMT ytem without gurad interval IEEE Journal on Selected Area in Commun, vol 20, no 5, pp , June ] S Roy and C Li A ubpace blind channel etimation method for OFDM ytem without cyclic prefix IEEE Tran Wirele Commun, vol 1, no 4, pp , Oct ] K Hayahi and H Sakai A Subtractive interference cancellation cheme for ingle carrier block tranmiion with inufficient cyclic prefix Proc of WPMC2005, vol 1, pp 706 7, Sept 2005 A MMSE WEIGHTS OF 1TAP FDE FOR SCBT SYSTEM WITHOUT GI Since the received ignal vector can be rewritten a =D H ΛD(n) C ISI (n)n(n), (30) the FDE output can be given by ŝ fde (n) =D H ΓΛD(n) D H ΓDC ISI (n) D H ΓDn(n) (31) In order to derive the MMSE weight, we define a cot function J to be minimized a J = E { tr(ŝ(n) (n))(ŝ H (n) H (n))] } Ignoring the term tr I M ], which ha no element of Γ, J can be written a J =σ{trγλλ 2 H Γ H ] trγλdc H ISID H Γ H ] trγλ] trγdc ISI D H Λ H Γ H ] trγdc ISI C H ISID H Γ H ]trγdc ISI D H ] trλ H Γ H ]trdc H ISID H Γ H ]} σntrγγ 2 H ] (32) Moreover, defining a matrix a G = DC ISI D H, (33)

5 and the (m, n) element of G a g m,n (m, n =0,,M 1), we have J = ( λ m 2 γ m 2 γ m 2 λ m gm,m γ m λ m λ m γ m 2 g m,m γ m 2 i=0 g m,i 2 γ m g m,m λ mγ m g m,mγ m) n γ m 2 (34) The differentiation of J with repect to γ m i given by J γ m = { λm 2 γ m λ m gm,mγ m λ mg m,m γ m } γ m g m,i 2 λ m gm,m σnγ 2 m (35) i=0 By olving J γ =0, we obtain the MMSE weight (14) a m γ m = where and λ m gm,m λ m 2 λ m gm,m λ mg m,m i=0 g, m,i 2 σ2 n (36) g m,m = 1 M g m,n 2 = 1 M l=0 i=0 l h L i e j 2π M m(m Ll i), (37) l h L i 2 e j 2π M n(l l ) (38) l=0 i=0 l =0