Improved N-continuous OFDM for 5G Wireless Communications

Transcription

1 1 Improved N-contnuous OFDM for 5G Wreless Communcatons Peng We, Lln Dan, Yue Xao, We Xang, and Shaoqan L arxv: v1 [cs.it] 19 Jan 2016 Abstract N-contnuous orthogonal frequency dvson multplexng (NC-OFDM) s a promsng technque to obtan sgnfcant sdelobe suppresson for baseband OFDM sgnals, n future 5G wreless communcatons. However, the precoder of NC-OFDM usually causes severe nterference and hgh complexty. To reduce the nterference and complexty, ths paper proposes an mproved tme-doman N-contnuous OFDM (TD-NC-OFDM) by shortenng the smooth sgnal, whch s lnearly combned by rectangularly pulsed OFDM bass sgnals truncated by a smooth wndow. Furthermore, we obtan an asymptotc spectrum analyss of the TD-NC-OFDM sgnals by a closed-form expresson, calculate ts low complexty n OFDM transcever, and derve a closed-form expresson of the receved sgnal-to-nterference-plusnose rato (SINR). Smulaton results show that the proposed low-nterference TD-NC-OFDM can acheve smlar suppresson performance but ntroduce neglgble bt error rate (BER) degradaton and much lower computatonal complexty, compared to conventonal NC-OFDM. Index Terms Orthogonal frequency dvson multplexng (OFDM), sdelobe suppresson, N-contnuous OFDM (NC-OFDM). I. INTRODUCTION Orthogonal frequency dvson multplexng (OFDM) [1] has been one of the most popular multcarrer transmsson technques n future 5G wreless communcatons [2], [3] due to ts hgh-speed data transmsson and nherent robustness aganst the nter-symbol nterference (ISI). However, n rectangularly pulsed OFDM systems, the sgnal possesses a dscontnuous pulse edge and thus exhbts large spectral sdelobes. The authors are wth the school of Natonal Key Laboratory of Scence and Technology on Communcatons, Unversty of Electronc Scence and Technology of Chna, Chengdu, Chna (e-mal: wpwwwhttp@163.com; {llndan, xaoyue}@uestc.edu.cn). We Xang s wth the school of Mechancal and Electrcal Engneerng Faculty of Health, Engneerng and Scences, Unversty of Southern Queensland, Australa (e-mal: we.xang@usq.edu.au).

2 2 Thus, power leakage due to sdelobes, whch s also known as out-of-band power emsson, causes severe nterference to adjacent channels [6], especally n cogntve rado (CR) and carrer aggregaton (CA) combned 5G systems [4], [5]. For mprovng conventonal OFDM n out-of-band emsson, varous methods have been proposed for sdelobe suppresson [7 18]. The wndowng technque n [7] extends the guard nterval n the prce of a reducton n spectral effcency. Cancellaton carrers [8], [9] consume extra power and ncur a sgnalto-nose rato (SNR) loss wth hgh complexty. In the precodng methods [10 12], complcate decodng algorthms are requred to elmnate the nterference caused by the precoders. NC-OFDM technques [13 19] smooth the ampltudes and phases of the OFDM sgnal by makng the OFDM sgnal and ts frst N dervatves contnuous (so-called N-contnuous). Conventonal NC- OFDM [13] obtans the N-contnuous sgnal at the expense of hgh nterference. Amng at optmzng the frequency doman precoder n [13], Beek et al. proposed the memoryless scheme n [14] and the mproved scheme [15] nullng the spectrum at several chosen frequences. On the other hand, to enable low-complexty sgnal recovery n NC-OFDM, several approaches have been proposed [16 18]. However, smlar to the precodng technques, the exstng NC-OFDM technques need robust sgnal recovery algorthms for recepton. Among them, some methods degrade system performance, such as peak-toaverage-power rato (PAPR) growth n [14] and hgh complexty of transmtter n [16], [17]. In ths paper, to reduce the nterference of the NC-OFDM sgnals and obtan a low-complexty transcever, we propose a low-nterference tme-doman N-contnuous OFDM (TD-NC-OFDM) based on the conventonal TD-NC-OFDM [19]. A smooth sgnal s superposed n the front part of each OFDM symbol to acheve N-contnuous OFDM sgnal, ncludng smoothng both edges of the transmtted sgnal. The smooth sgnal s lnearly combned by the bass vectors n a bass set, whch s composed of the rectangularly pulsed OFDM bass sgnals truncated by a smooth wndow functon for an example. Furthermore, we gve rse to analyses of spectrum, complexty and sgnal-to-nterference-plus-nose rato (SINR) n the low-nterference TD-NC-OFDM. Among them, an asymptotc expresson of PSD of the TD- NC-OFDM sgnal s frst obtaned, where the sdelobes asymptotcally decay wthf N 2, when the frst N dervatves of the OFDM sgnal are all contnuous. Then, we compare the complexty among NC-OFDM, TD-NC-OFDM and ts low-nterference scheme, to show the complexty reducton of the proposed lownterference scheme. The closed-form expresson of the receved SINR of the low-nterference scheme s also calculated to show the slght SNR loss. Smulaton results show that the low-nterference scheme can acheve as notable sdelobe suppresson as NC-OFDM method [13] wth excellent bt error rate (BER) performance and low complexty. The remander of the paper s organzed as follows. In Secton 2, the OFDM sgnalng s brefly

3 3 ntroduced, the tradtonal NC-OFDM s revewed. Secton 3 proposes the low-nterference TD-NC-OFDM model, gves the lnear combnaton desgn of the smooth sgnal wth a new bass set, and descrbes the transmtter. In Secton 4, the effect of the low-nterference TD-NC-OFDM on sdelobe decayng and the receved SINR s analyzed as well as the computatonal complexty of the transcever. Fnally, Secton 5 draws concludng remarks. Notaton: Boldfaced lowercase and uppercase letters represent column vectors and matrces, respectvely. {A} m,n ndcates the element n the mth row and nth column of matrx A. The M M dentty matrx and M N zero matrx are denoted by I M and 0 M N, respectvely. represents the absolute value. The trace and expectaton of a matrx are represented by Tr{ } and E{ }, respectvely. A T, A, A H and A 1 denote the transposton, conjugate, conjugate transposton, and nverse of matrx A, respectvely. A. OFDM sgnalng II. SYSTEM ASPECTS AND N-CONTINUOUS OFDM In a baseband OFDM system, the nput bt stream of the th OFDM symbol s frst modulated onto an uncorrelated complex-valued data vector x = [x,k0,x,k1,...,x,kk 1 ] T drawn from a constellaton, such as phase-shft keyng (PSK) or quadrature ampltude modulaton (QAM). The complex-valued data vector s mapped onto K subcarrers wth the ndex set K = {k 0,k 1,...,k K 1 }. An OFDM sgnal s formed by summng all the K-modulated orthogonal subcarrers wth equal frequency spacng f = 1/T s, where T s s the OFDM symbol duraton. The th OFDM tme-doman symbol, assumng a normalzed rectangular tme-doman wndow R(t) [10], can be expressed as y (t) = K 1 r=0 x,kr e j2πkr ft, T cp t < T s (1) where T cp s the cyclc prefx (CP) duraton. Then, n the tme range of (,+ ), the transmtted OFDM sgnal s(t) can be wrtten as where T = T s +T cp. s(t) = + = y (t T). (2) After the OFDM sgnal s oversampled by a tme-doman samplng nterval T samp = T s /M, the dscrete-tme OFDM sgnal s expressed as y (m) = 1 M K 1 r=0 kr j2π x,kr e m M, (3) where m M = { M cp,...,0,...,m 1}, and M cp s the length of CP samples.

4 4 B. N-contnuous OFDM To mprove the contnuty of the tme-doman OFDM sgnal, the conventonal NC-OFDM [13] ntroduces a frequency-doman precoder to makng the OFDM sgnal and ts frst N dervatves contnuous. NC-OFDM follows that ȳ (t) = K 1 r=0 ȳ (n) x,kr e j2πkr ft, T cp t < T s (4) (t) = ȳ (n) 1 (t) t=ts, (5) t= Tcp where x,kr s the precoded symbol on the rth subcarrer, and ȳ (n) (t) s the nth-order dervatve of ȳ (t) wth n U N = {0,1,...,N}. Based on (4) and (5), the precodng process can be summarzed as x = x 0, = 0 x = (I K P)x +PΦ H x 1, > 0 wherei K s the dentty matrx,p = Φ H A H (AA H ) 1 AΦ,{A} n+1,r+1 = k n r,φ = dag(ejϕk0,e jϕk1,...,e jϕkk 1 ), and ϕ = 2πβ wth β = T cp /T s. Fgure 1 depcts the spectrally precoded NC-OFDM transmtter. The th frequency-doman data vectorx s frst precoded. The precoded data vector x = [ x,k0, x,k1,..., x,kk 1 ] T then undergoes the nverse fast Fourer transform (IFFT), and fnally the CP s added to generate the transmsson sgnal. (6) N-contnuous OFDM x Subcarrer mappng Precoder x IFFT AddCP x 1 Delay Fg. 1. Block dagram of the N-contnuous OFDM transmtter. III. PROPOSED LOW-INTERFERENCE SCHEME OF TD-NC-OFDM Conventonal TD-NC-OFDM [19] and Conventonal NC-OFDM [13] cause hgh nterference, whch s needed to be reduced by complcate sgnal recovery algorthms [13, 16, 18]. As show n Fgure 2 (a), the nterference term, defned as the smooth sgnal w (m), s located n the whole tme-doman n the conventonal TD-NC-OFDM as well as NC-OFDM. To elmnate the nterference and smplfy the

5 5 s( m) CP y ( ) 1 m y( m) CP M cp 0 M 1 Adjacent pont at M tme s( m) wm ( ) CP CP w ( ) 1 m w( m) (a) s( m) CP CP w ) 1 1 ( m w( ( m) wm ( ) 0 0 (b) Fg. 2. Conventonal and proposed ways of of addng the smooth sgnal n the tme doman: (a) Addton n the whole OFDM symbol; (b) Addton n the front of each OFDM symbol. recever, we truncate w (m) wth a wndow functon. As llustrated n n Fgure 2 (b), the truncated term w (m) only locates n the front secton of each OFDM symbol. To make the OFDM sgnal N-contnuous, w (m) should satsfy ȳ (m) = y (m)+ w (m), (7) (m) = y (n) 1 (m) m=m y (n) (m). m= Mcp m= Mcp (8) w (n) w (m) s the lnear combnaton of the frst N+1 bass vectors n a bass set Q, wrtten as N b,n n (m), m L w (m) = n=0, (9) 0, m M L where L = { M cp, M cp +1,..., M cp +L 1} ndcates the locaton of w (m) wth the length of L, and the bass set Q s gven by { } Q = qñ qñ = [ñ( M cp ), ñ( M T cp +1),..., ñ( M cp +L 1)],ñ U2N, (10) where U 2N = {0,1,...,2N}. In (9), the desgn of the bass sgnal ñ(m) and the calculaton of the coeffcents b,n b = [b,0,b,1,...,b,n ] T wll be specfed as follows.

6 6 To guarantee the smoothness of w (m) and to obtan the N-contnuous sgnal, an example of desgnng ñ(m) s gven by ñ(m) = f (ñ) (m)g h (m), (11) for m L, and ñ(m) = 0 for m M L. In L, f (ñ) (m) = 1/M (j2π/m)ñ k r K kñre jϕkr kr j2π e M m, (12) and g h (m) s the rght half part of a baseband-equvalent wndow functon g(m). Thus, the dscontnuty at the adjacent pont between two consecutve OFDM symbols can be elmnated by w (m) from only a sngle sde of the adjacent pont. Under the constrant of g h (m), the nterference caused by w (m) can be lmted to the front secton of the OFDM symbol. In order to satsfy (9), g(m) should be consdered as a smooth and zero-edged wndow functon, such as a trangular, Hannng, or Blackman wndow functon. On the other hand, the lnear combnaton coeffcents b,n n (9) can be calculated as b = y 1(M) y ( M cp ), (13) P 1 x 1 P 2 x { } where P s a (N + 1) (N + 1) symmetrc matrx related to Q wth element P s n+1,v+1 (n+v) ( M cp ), and element{p 1 } n,r+1 = 1/M (j2πk r /M) n and element{p 2 } n,r+1 = 1/M (j2πk r /M) n e jϕkr for n 0. Fgure 3 shows the block dagram of the proposed low-nterference TD-NC-OFDM. Accordng to K and Q, the matrces Q = [q 0,q 1,...,q N ],, P 1, and P 2, can be calculated and stored n advance. Then, the data s frst mapped and transformed to the tme doman by the IFFT. Furthermore, the oversampled OFDM sgnal s appended by a CP. Fnally, under the ntalzaton of y 1 = 0, the smooth sgnal s added onto the OFDM sgnal constructed by M s OFDM symbols y to generate the followng transmt sgnal y ȳ = +Qb, 0 M s. (14) Qb, = M s +1 IV. ANALYSIS OF SPECTRUM AND COMPLEXITY A. Spectral Analyss Accordng to the defnton of PSD [12] and the relatonshp between spectral roll-off and contnuty [20], the PSD of the OFDM sgnal processed by the low-nterference scheme s acheved as follows. All the dervatves of the OFDM sgnal s(t) are known to exst except for around the two edges and on the ponts between adjacent OFDM symbols. Meanwhle, except for these non-dfferentable ponts, the

7 7 x Subcarrer mappng IFFT J y AddCP y w Calculate coordnate b Generate smooth sgnal P f Q f New bass set Fg. 3. Block dagram of the OFDM transmtter wth the proposed low-nterference TD-NC-OFDM. smooth sgnal also possesses dervatves of all orders, accordng to the exstence of all the dervatves of the bass functon n (m). Then, we assume that at non-dfferentable ponts, the frst N-1 dervatves of the smoothed OFDM sgnal s(t) are contnuous, and the Nth-order dervatve s (N) (t) has fnte ampltude dscontnuty. We also suppose that all the dervatves of s(t) approach zeroes, whch corresponds to (14). Frstly, based on [20], we can obtan F { s(t)} = 1 (j2πf) N 1 + s (N 1) (t)e j2πft dt. (15) Furthermore, snce s (N) (t) has fnte ampltude dscontnutes, by settng u = s (N 1) (t) and dv = e j2πft dt n the above expresson, we arrve at 1 F { s(t)} = s(n 1) (t)e j2πft (j2πf) N 1 j2πf = 1 (j2πf) N + t=+ t= + s (N) (t)e j2πft dt j2πf s (N) (t)e j2πft dt. (16) Because s (N) (t) has fnte ampltude dscontnutes at the adjacent ponts, from (2), s (N) (t) can be wrtten as s (N) (t) = + = ȳ (N) (t T). (17) It s nferred n (17) that the Nth dervatve ȳ (N) (t) can be assumed beng wndowed by the rectangular functon R(t). Therefore, based on the defnton of PSD, (16), and (17), the PSD of s(t) can be expressed

8 8 as 1 Ψ(f)= lm U 2UT E F { U 1 = U } (t T) 2 (j2πf) N = lm ȳ (N) U 1 2UT E U 1 = U { F ȳ (N) } (t) (j2πf) N e j2πft 2. Eq. (18) ndcates that the spectrum of the TD-NC-OFDM sgnal s related to the expectaton of ȳ (N) (t) and f N. In ths paper, the conventonal Blackman wndow functon s used as an example, gven as g(t) = cos(2πρt)+0.08cos(4πρt) where ρ = 1/((2L 2)T samp ). By substtutng (9), (11), (12), and (14) nto (18), the PSD of the smoothed OFDM sgnal n low-nterference scheme s expressed by 1 Ψ(f) = lm 2UT E + 1 T U 1 = U e j2πft (j2πf) ( ) N N j2πkr x snc(f,kr r(1+β))e jπfr(1 β) N N b,n N n ( j2πkr T s n=0 n=0 1 = lm 2UT E + 1 T U 1 = U k r K N N b,n N n ( j2π T s n=0 n=0 where G n (f) s gven by k r K T s ) N n+n T cp+t p T cp ( n) gh dt (t)ej2πfrt/ts 2 e j2πft (ft s ) N kr N x,kr snc(f r (1+β))e jπfr(1 β) k r K ) n n kr N n+n G n (f) k r K 2 G n (f) = e j r 0.42 ( n) 0.5(2πρ) n cos(πµf r ) T p snc(µf r ) 1 (ρt s /f r ) 2 ( cos(π n/2) πρ sn(π n/2) ) jπf r /T s (πf r /T s ) 2 (18) (19) 0.08(4πρ) n ( sn(πµf r ) cos(π n/2) + 1 (2ρT s /f r ) 2 j2πρ sn(π n/2) ), πf r /T s (πf r /T s ) 2 where snc(x) sn(πx)/(πx), and r = πf r (T p 2T cp )/T s wth f r = k r T s f, T p = (L 1)T samp, and µ = T p /T s. Eq. (19) shows that the power spectral roll-off of the smoothed sgnal, whose frst N-1 dervatves are contnuous, decays wth f 2N 2. Moreover, G n (f) reveals that the sdelobe s affected by the length of g(t), so that a rapd sdelobe decayng can be acheved by ncreasng the length of g(t). Fgure 4

9 9 compares the theoretcal and smulaton results of the low-nterference scheme wth a wndow length of 144. It s shown that the smulaton results match well wth the theoretcal analyses Theory Smulaton PSD (db) N=0 N=1 N=2 N= Frequency (MHz) Fg. 4. PSD comparson between the analytcal and smulaton results for the TD-NC-OFDM sgnal n the low-nterference TD-NC-OFDM wth L=144. B. Complexty Comparson Frstly, we consder the complexty of the transmtter. In NC-OFDM, ts frequency-doman precoder requres 2K 2 complex multplcatons and 2K 2 complex addtons as ndcated n (6). In TD-NC-OFDM [19], 2NK + (N + 1)(2N + 1) complex multplcatons and 2NK + N(2N + 1) complex addtons are requred. However, for the generaton and overlappng of the smooth sgnal, M(N + 1) complex multplcatons and M(N + 1) complex addtons are needed. By shortenng the length of the smooth sgnal, the low-nterference scheme just requres L(N+1) complex multplcatons and L(N+1) complex addtons. At the same tme, the complexty of calculatng ts lnear combnaton coeffcents n (13) s 2NK +(N +1) 2 complex multplcatons and 2NK +N 2 +1 complex addtons. Secondly, the complexty of the recever s shown n Table I. For NC-OFDM, an teratve sgnal recovery algorthm [13] s used to elmnate the nterference. Due to the equvalence between NC-OFDM and TD- NC-OFDM, the sgnal recovery algorthm s also desred n TD-NC-OFDM wth dentcal complexty. In the low-nterference scheme, the recever s the same as n orgnal OFDM wthout extra sgnal recover processng.

10 10 Assume that a complex addton s equvalent to two real addtons; a complex multplcaton to four real multplcatons plus two real addtons; and a real-complex multplcaton to two real multplcatons. The complexty comparson among NC-OFDM, TD-NC-OFDM and the low-nterference scheme s shown n Table I, where L R denotes the number of teratons n the sgnal recovery algorthm [13]. TABLE I COMPLEXITY COMPARISON AMONG NC-OFDM, TD-NC-OFDM AND ITS LOW-INTERFERENCE SCHEME Scheme Real multplcaton Real addton NC-OFDM Transmtter O(8K 2 ) O(8K 2 ) Recever O(16(N +1)KL R) O(16(N +1)KL R) TD-NC-OFDM Transmtter O(8NK + 4(N + 1)M) O(8NK + 4(N + 1)M) Recever O(16(N +1)KL R) O(16(N +1)KL R) Low-nterference scheme Transmtter O(8NK + 4(N + 1)L) O(8NK + 4(N + 1)L) Recever 0 0 M-pont IFFT/FFT O(2M log 2 M) O(2M log 2 M) The low-nterference scheme consderably suppresses the sdelobes shown n Fgure 4. Smultaneously, snce the length of the smooth sgnal L s often as short as the CP length or shorter n real systems, the low-nterference scheme s of lower transmtter complexty than NC-OFDM and the conventonal TD-NC- OFDM. Moreover, ts complexty s comparable to M-pont IFFT. On the other hand, the low-nterference scheme just requres the recever of orgnal OFDM, and avodng extra processng n NC-OFDM and TD-NC-OFDM recevers. C. SINR Analyss One dsadvantage of NC-OFDM s that the transmt sgnal s easly nterfered by the smooth sgnal. Thus, a measure s needed to evaluate the nterference n terms of the SNR loss. In ths secton, we nvestgate the SINR of NC-OFDM, and demonstrate the effectveness of the proposed low-nterference scheme n reducng the SNR loss, based on the analyss of the average power of the smooth sgnal. In a multpath channel wth tme-doman coeffcents h l n the lth path, the th receved tme-doman OFDM symbol r (t) s gven by r (t) = L l=1 h lȳ (t τ l)+n (t) (20) where τ l s the tme delay n the lth path, and n (t) s the AWGN nose wth mean zero and varance σn. 2

11 11 Becausex s uncorrelated,.e.,e { x x H } = IK ande { x 1 x H } = 0K K, we can obtane { x H x } = Tr { E { x x H }} = K. Thus, the average power of the OFDM symbol vector y s E { y H y } 1 = M 2E{ x H F ff H f x } { } = E x H x = K/M. (21) To mtgate the performance degradaton n conventonal TD-NC-OFDM, the proposed low-nterference scheme s analyzed by explorng the dstrbuton of w (l) n the multpath fadng channel. As llustrated n Fgure 5, dfferent channel paths wth varyng tme delays lead to varyng w (l). Wth the ncreased tme delay, the delayed tal of w (l) s prolonged and the nterference ncreases. The nterferences w (l) are composed of the delayed tals n all the paths, whose powers are much smaller than the conventonal TD-NC-OFDM and NC-OFDM Low-nterference scheme (theory), L=144 Low-nterference scheme (sm), L=144 Low-nterference scheme (theory), N=4, L=1000 Low-nterference scheme (sm), N=4, L=1000 TD-NC-OFDM (sm) NC-OFDM (sm) N=0, 2, 4 γ SINR (db) N=0 N=2 N= E b N 0 (db) Fg. 5. Gaussan nose. A tme-doman llustraton of the effect of the smooth sgnal on the multpath channel wthout power attenuaton and Thus, the average power of w (l) n the lth path s calculated by { ) } { { }} H E (h l w h l w = Tr E h l w H w h H l = E{ 2} h l Tr { E { w H }} w = 2 { M h l 2E 2} { ( ) } H Tr B 2B H 2 Q H l Q l where g l s the delayed tal of g n the lth path and = Q l g lq f. The dervaton of Tr { E { w H w }} s shown n Appendx A. Therefore, n all the paths, the average power of these delayed tals s expressed by L { ) } H (h l w h l w = 2 L { h l 2} { ( ) H M 2 Tr B 2B H 2 Q H l l=1 E l=1 E Q l (22) }. (23)

12 12 Fnally, from (21)-(23), the receved SINR γ SINR s obtaned by L { E h l 2} E { y Hy } l=1 γ SINR = { σn L l=1 2 + ) } H E (h l w h l w = L l=1 E σ 2 n { h l 2}+ 2 L E l=1 K/M { h l 2} { ( Tr B 2B H 2 M E{ h l L l=1 2 2} ) HQ H l Q l }. (24) Low-nterference scheme (theory), L=144 Low-nterference scheme (sm), L=144 Low-nterference scheme (theory), N=4, L=1000 Low-nterference scheme (sm), N=4, L=1000 TD-NC-OFDM (sm) NC-OFDM (sm) N=0, 2, 4 γ SINR (db) N=0 N=2 N= E b N 0 (db) Fg. 6. SINR analyss and smulatons of the TD-NC-OFDM sgnals n the EVA fadng channel, where the sgnal s modulated by 16-QAM. Fgure 6 compares theoretcal analyss n (24) and the smulaton results n terms of the SINR. The smulated Raylegh channel employs the Extended Vehcular A (EVA) channel model [21], whose excess tap delay s [0, 30, 150, 310, 370, 710, 1090, 1730, 2510] ns wth relatve power [0, -1.5, -1.4, -3.6, -0.6, -9.1, -7, -12, -16.9] db. It s shown that the theoretcal analyss algns well wth the smulatons. It also reveals that the SNR loss s neglgble for the low-nterference scheme. Moreover, the low-nterference scheme has much better SINR than NC-OFDM and TD-NC-OFDM. In general, even f the length of w (l) s ncreased, there s no extra need for sgnal recovery, whch reduces the heavy computaton load n orgnal NC-OFDM.

13 13 V. NUMERICAL RESULTS Ths secton presents smulaton results to evaluate the PSD, complexty, and BER performance of NC-OFDM, TD-NC-OFDM and proposed low-nterference schemes. Smulatons are performed n a baseband-equvalent OFDM system wth 256 subcarrers mapped onto the subcarrer ndex set{ 128, 127,..., 127}. 16-QAM dgtal modulaton s employed wth a symbol perod T s = 1/15ms, tme-doman oversamplng nterval T samp = T s /2048 and CP duraton T cp = 144T samp. The PSD s evaluated by Welch s averaged perodogram method wth a 2048-sample Hannng wndow and 512-sample overlap after observng 105 symbols. To nvestgate the BER performance, the sgnal s transmtted through the Extended Vehcular A (EVA) channel model. Fgure 7 compares the PSD of NC-OFDM transmt sgnals wth dfferent N and dfferent L. As N ncreases, the sdelobe suppresson performance s further mproved n the three methods. Moreover, the low-nterference scheme can obtan as good sdelobe suppresson performance as the conventonal TD- NC-OFDM and NC-OFDM. Fgure 7 also shows that wth the ncrease of L, a steeper spectral roll-off can be obtaned n the low-nterference scheme. Wth a relatvely small L, the sdelobe suppresson of the low-nterference scheme can approach that of TD-NC-OFDM, such as N=2 and 3 wth L= Orgnal OFDM NC-OFDM TD-NC-OFDM Low-nterference scheme PSD (db) N=0 N=1 N=2 N=3-100 N=3, L=36 N=3, L= Frequency (MHz) Fg. 7. PSDs of the transmt sgnals of NC-OFDM, TD-NC-OFDM and ts low-nterference scheme wth varyng N and varyng L. Fgure 8 presents the BER performances of NC-OFDM, TD-NC-OFDM and ts low-nterference scheme wth varyng N and varyng L n the EVA channel. It s shown that the BER performance of the receved

14 14 sgnal s sgnfcantly degraded as N ncreases n NC-OFDM and TD-NC-OFDM. By contrast, the lownterference scheme causes slght BER performance degradaton. Compared to the BER performance of NC-OFDM and TD-NC-OFDM wth the hgh-complexty sgnal recovery [13], the ncreased length of the smooth sgnal just results n slght performance degradaton for the low SNR loss n the low-nterference scheme as mentoned n Secton 4.3. Meanwhle, the low-nterference scheme exhbts promsng sdelobe suppresson performance as shown n Fgure N=0 N=1 N=2 N= BER Orgnal OFDM NC-OFDM TD-NC-OFDM NC-OFDM wth sgnal recovery, N=3, L R =8 TD-NC-OFDM wth sgnal recovery, N=3, L R =8 Low-nterference scheme, N=3, L=144 Low-nterference scheme, N=3, L=500 Low-nterference scheme, N=3, L= E b N 0 (db) Fg. 8. BERs of NC-OFDM, TD-NC-OFDM and ts low-nterference scheme wth varyng N and varyng L n the EVA channel. VI. CONCLUSION In ths paper, a low-nterference TD-NC-OFDM was proposed to reduce the nterference and mplementaton complexty as opposed to the orgnal TD-NC-OFDM and NC-OFDM. By addng the smooth sgnal, the N-contnuous sgnal was obtaned by the low-nterference scheme. The smooth sgnal was desgned by the lnear combnaton of a bass set, whch s generated by rectangularly pulsed OFDM bass sgnals truncated by a smooth wndow. Furthermore, usng the contnuty crteron, a closed-form spectrum expresson was derved n the low-nterference TD-NC-OFDM, whch had more rapd decayng than [20]. Then the complexty of the low-nterference scheme was measured. The receved SINR s also measured by dervng the closed-form expresson. Smulaton results showed that the low-nterference scheme was capable of effectvely suppressng sdelobes as well as NC-OFDM and TD-NC-OFDM but

15 15 wth much better BER performance and much lower complexty. In ths sense, the low-nterference TD- NC-OFDM s a promsng alternatve to conventonal NC-OFDM n future cogntve rado and carrer aggregaton combned 5G systems. ACKNOWLEDGMENT Ths work was supported by the open research fund of Natonal Moble Communcatons Research Laboratory, Southeast Unversty (No. 2013D05). For ease of exposton, Eq. (13) s rewrtten as where P 1 and P 2 nclude a row of n = 0. APPENDIX: DERIVATION OF Tr { E { w H w }} b = (P 1 x 1 P 2 x ) (25) Accordng to the constructon of P 1 and P 2, Tr { E { w H }} w can be expressed as Tr { E { w H }} { }} w = Tr {E Qb b H QH { { ( ) }} H = Tr E Q P 1x 1 x H 1P H 1 Q H { { ( ) }} H +Tr E Q P 2x x H P H 2 Q H { = Tr P 1P H 1 ( ) H Q H Q} +Tr { P 2P H 2 ( ) Q} H Q.(26) H Then, we rewrte P 1 and P 2 as P 1 = 1/MB 2 andp 2 = 1/MB 2 Φ wth {B 2 } n+1,r+1 = (j2πk r /M) n. We obtan wth {B 1 } r+1,n+1 = (j2πk r /M) n e jϕkr. Accordng to (27), we arrve at Tr { E { w H }} 1 w = M 2Tr = 2 M 2Tr { B 2B H 2 { B 2B H 2 B 1 = Φ H B T 2, (27) ( ( ) H Q H Q} ) H Q H Q} + 1 { M 2Tr B 2ΦΦ H B H 2 ( ) H Q H Q}. (28)

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