Beam Pattern Scanning (BPS) versus Space-Time Block Coding (STBC) and Space-Time Trellis Coding (STTC)

It. J. Commuicatios, Network ad System Scieces, 2009, 6, 469-479 doi:10.4236/ijcs.2009.26051 Published Olie September 2009 (http://www.scirp.org/joural/ijcs/). 469 Beam Patter Scaig (BPS) versus Space-Time Block Codig (STBC) ad Space-Time Trellis Codig (STTC) Peh Keog TEH, Seyed (Reza) ZEKAVAT Departmet of Electrical ad Computer Egieerig, Michiga Techology Uiversity, Houghto, Michiga, USA Email: {rezaz, pteh}@mtu.edu Received April 2, 2009; revised Jue 10, 2009; accepted July 22, 2009 ABSTRACT I this paper, Beam Patter Scaig (BPS), a trasmit diversity techique, is compared with two well kow trasmit diversity techiques, space-time block codig (STBC) ad space-time trellis codig (STTC). I BPS (also called beam patter oscillatio), cotrolled time varyig weight vectors are applied to the atea array elemets mouted at the base statio (BS). This creates a small movemet i the atea array patter directed toward the desired user. I rich scatterig eviromets, this small beam patter movemet creates a artificial fast fadig chael. The receiver is desiged to exploit time diversity beefits of the fast fadig chael. Via the applicatio of simple combiig techiques, BPS improves the probability-of-error performace ad etwork capacity with miimal cost ad complexity. I this work, to highlight the potetial of the BPS, we compare BPS ad Space-Time Codig (i.e., STBC ad STTC) schemes. The comparisos are i terms of their complexity, system physical dimesio, etwork capacity, probability-of-error performace, ad spectrum efficiecy. It is show that BPS leads to higher etwork capacity ad performace with a smaller atea dimesio ad complexity with miimal loss i spectrum efficiecy. This idetifies BPS as a promisig scheme for future wireless commuicatios with smart ateas. Keywords: Atea Array, Beam Patter Sweepig, Trasmit Diversity, Space-Time Block Codes, ad Space-Time Trellis Codig. 1. Itroductio Trasmit diversity schemes use arrays of ateas at the trasmitter to create diversity at the receiver. Differet trasmit diversity techiques have bee itroduced to mitigate fadig effects i wireless commuicatios [1 5]. Examples are space-time block codig [1 3], space-time trellis codig [3 5], atea hoppig [6] ad delay diversity [6,7]. I Space-Time Block Codig (STBC), data is ecoded by a chael coder ad the ecoded data is split ito N uique streams, simultaeously trasmitted over N atea array elemets. At the receiver, the symbols are decoded usig a maximum likelihood decoder. This scheme combies the beefits of chael codig ad diversity trasmissio, providig BER performace gais. However, receiver complexity icreases as a fuctio of badwidth efficiecy [3] ad requires high umber of ateas to achieve high diversity orders. Moreover, atea elemets should be located far eough to achieve space diversity ad whe atea arrays at the base statio (BS) are used i this fashio, directioality beefits are o loger available [1 3]. This reduces the etwork capacity of wireless systems i terms of umber of users. I Space-Time Trellis Codig (STTC) iformatio symbols are ecoded by a uique space-time chael coder ad the ecoded iformatio symbols are split ito N uique streams, simultaeously trasmitted over N atea arrays elemets. At the receiver, after receivig a block of symbols deoted by frame (e.g., 130 symbols per frame), Viterbi algorithm is used to recover ad error-correctig the iformatio symbols i the frame [3 5]. This scheme combies the beefits of space diversity ad codig gai, providig a sigificat probability-of-error performace gai. However, the receiver complexity icreases expoetially as a fuctio of umber of trellis states (trasmit ateas); ad, i geeral, high order of trellis states (trasmit ateas) are required to achieve high diversity ad codig gai [8,9].

470 P. K. TEH ET AL. Moreover, similar to STBC, i STTC atea array elemets should be located far eough to achieve space diversity which reduces STTC etwork capacity i terms of umber of users. BPS has bee itroduced as a powerful trasmit diversity techique capable of ehacig both wireless etwork capacity ad probability-of-error performace with miimal cost [10 13]. I this scheme, atea elemets located at the distace of half a wavelegth form a atea array. These atea arrays are mouted at the BS. They are icorporated to create directioal beams steered toward the desired users. Time varyig phase shifts are applied to atea elemets to move the atea patter withi the symbol duratio T s. The atea patter starts from a poit i space at time zero, sweeps a area of space from time 0 to T s, ad returs back to its iitial positio after time T s, ad repeats similar sweepig agai. The beam patter movemet is small, e.g., i the order of 5% of half power beam width (HPBW). Simulatios i [10] has show that i rich scatterig eviromets, BPS leads to a time varyig chael with a small coherece time T c with respect to T s. This geerates a artificially created fast fadig chael leadig to a time diversity that ca be exploited at the receiver [10,11]. Hece, BPS leads to: a) high performace via time diversity, ad b) high etwork capacity (i terms of umber of users) via directioality iheret i BPS. Here, BPS is compared with STBC ad STTC schemes with their atea replaced by directioal atea arrays (without scaig) [9] i order to achieve directioality (i.e., Spatial Divisio Multiple Access (SDMA) beefit) available i BPS. The elemets of compariso are: 1) probability-of-error (bit-error-rate, BER, ad frame-error-rate, FER) performace, 2) etwork capacity, 3) system complexity (i terms of physical dimesio), ad 4) badwidth efficiecy. Figure 1. Space-time block codes system (N = 2) Table 1. STBC structure for (N=2). Atea 0 Atea 1 Time, t s 0 s 1 * * Time, t+t s s 1 s 0 The results cofirm that BPS scheme leads to higher etwork capacity ad BER/FER performace ad lower complexity. However, BPS techique relative spectral efficiecy is less tha STBC ad STTC, e.g., i the order of 5%. I other words, BPS techique offers higher quality-of-service ad etwork capacity with a miimal cost of spectrum efficiecy. This itroduces BPS as a powerful scheme for future geeratio of wireless commuicatios with smart atea arrays. Sectio 2 itroduces STBC, STTC ad BPS schemes. Sectio 3 compares their characteristics ad, Sectio 4 presets ad compares their capacity ad BER/FER performace simulatios. Sectio 5 cocludes the paper. 2. Itroductio of STBC, STTC ad BPS Techiques Here, we briefly itroduce the fudametals of the three techiques, STBC, STTC ad BPS. 2.1. STBC STBC is a trasmit diversity techique capable of creatig diversity at the receiver to improve the performace of commuicatios systems. STBC utilizes N trasmit ateas separated far apart to esure idepedet fades [1,2]. At a give symbol period, N sigals are trasmitted simultaeously from N ateas. The sigal trasmitted from each atea has a uique structure that allows the sigal to be combied ad recovered at the receiver. For simplicity i presetatio, we oly cosider STBC with 2 trasmit ateas (N = 2) (see Figure 1). We cosider s 0 ad s 1 two cosecutive sigals geerated at two cosecutive times t 0 ad t 1 = t 0 +T s, respectively. The sigal trasmitted from atea zero is deoted by s 0 ad the oe from atea oe is deoted by s 1. At the ext symbol period, the trasmitted sigal from * atea zero is s 1 ad the sigal trasmitted from * atea oe is s 0 where * is the complex cojugate operatio (see Table 1). The chael is deoted by h 0 for trasmit atea 0 ad h 1 for trasmit atea 1. The mai assumptio here is that the fadig is costat across two cosecutive symbols (i.e., over t ad t 1 = t +T s, t [0,T s ]); we ca represet the chael fadig for atea 0 ad 1 as: j0 0() 0( s ) 0 0 j1 1() 1( s ) 1 1 h t h t T h e h t h t T h e respectively, where T s is the symbol duratio, i, i, i {0,1} are the Rayleigh fadig gai ad phase, respectively. The received sigal at time t ad t + T s, correspods to (1)

BEAM PATTERN SCANNING (BPS) VERSUS SPACE-TIME BLOCK CODING (STBC) AND SPACE-TIME TRELLIS CODING (STTC) 471 rt () hs 0 0hs 1 1t rt ( Ts ) hs hs * * 0 1 1 0 t Ts respectively. Here, t ad t T s are complex radom variables represetig receiver oise ad iterferece at time t ad t + T s, respectively. I the STBC receiver, Maximal Ratio Combiig (MRC) leads to a estimatio of s 0 ad s 1, correspodig to: * * sˆ 0 hr 0 t hr 1 tts (3) * * sˆ hrhr 1 1 t 0 tts respectively (ote: r t =r(t)). Substitutig (1) ad (2) ito (3), we obtai 2 2 * * sˆ 0 0 1 s0 h0t h 1 tts (4) 2 2 * * sˆ 1 0 1 s1h0t Th s 1t I other word, a maximum likelihood receiver leads to the removal of the s 1 ad s 0 depedet terms i ŝ 0 ad ŝ 1, respectively. This geerates a high probability-of-error performace at the receiver. 2.2. STTC Techique STTC is a trasmit diversity techique that combies space diversity ad codig gai to improve the performace of commuicatio systems [3,5,8]. STTC utilizes N trasmit ateas separated far apart to esure idepedet chaels. At a give symbol period, N sigals are trasmitted simultaeously from N ateas. The sigal trasmitted from each atea has a uique structure with iheret error-correctio capability to allow sigal to be recovered ad corrected at the receiver [8]. I this paper, we oly cosider the simulatio sceario preseted i [3], that is /4-QPSK, 4-states, 2 b/s/hz STTC (hereafter, deoted as STTC-QPSK) that utilizes two trasmit ateas ad oe receive atea. The trellis structure of STTC-QPSK is show i Figure 2(a) ad the costellatio mappig i Figure 2(b). I STTC-QPSK, iformatio symbols are ecoded usig a chael coder by mappig iput symbols to a vector of output (codewords) based o a trellis structure (Figure 2(a)). Here, iformatio symbols are ecoded based o the curret state of the ecoder ad the curret iformatio symbols. Thus, the ecoded codewords are correlated i time. At the left of the trellis structure (Figure 2(a)) are the STTC codewords (s 1,s 2 ), s 1,s 2 {0,1,2,3}. I Figure 2(a), there are four emergig braches from each trellis state, because there are four possible QPSK symbols, amely {0,1,2,3}. For example, cosider the space time trellis coder that starts at state (q 1,q 2 ) = (0,0) (represeted by (2) 00). Whe the iformatio symbol is 10, the coder trasitio from state 00 to 10 produces the output code-words (s 1,s 2 ) of (0,2). Whe the ext iformatio symbol is 11, the coder trasitio from state 10 to 11 produces the output codeword (2,3). The chael coder cotiues to chage from its curret state to a ew state based o the icomig iformatio symbols. Based o the desig, the chael coder resets to state 0 after completig the codig of a frame (e.g., 130 symbols). The output code-words of the ecoder is the mapped ito a /4-QPSK costellatio (Figure 2(b)). The mappig results i two iformatio symbols. Each iformatio symbol is the trasmitted o each atea simultaeously. Through this ecodig scheme, redudacy is itroduced ito the system but at the same time, the symbols are trasmitted over two ateas. Therefore, codig redudacy does ot impact the throughput. I order to achieve SDMA to improve etwork capacity, each STTC-QPSK atea elemet is replaced with oe atea array [9] to geerate two static beams directed toward the desired users (Figure 3). The chael is deoted by h 0 for trasmit atea 0 ad h 1 for trasmit atea 1. We represet the chael fadig for atea i, i {0,1} as: i h () t h e j (5) i i i respectively, where i, i, i {0,1} are the Rayleigh fadig gai ad phase, respectively. The received sigal at time t ca be modeled as rt () hs() t hs() t t () (6) 0 0 1 1 where s i (t) is the trasmitted symbol ad (t) is the complex radom variable represetig receiver oise at time t. The receiver is desiged usig Viterbi algorithm. The brach metric for a trasitio labeled q 1 (t) q 2 (t) correspods to [3] P i1 2 rt () q() t (7) i i where P is the umber of trasmit atea. Viterbi algorithm is used to compute the path with the lowest accumulated metric [3]. 2.3. BPS BPS is a ew trasmit diversity techique utilizig a atea array to support directioality ad trasmit diversity via carefully cotrolled time varyig phase shifts applied to each atea elemet. This creates a slight motio of the beam patter directed toward the desired users [10]. Beam patter movemet creates a artificial fast fadig eviromet that leads to time diversity exploitable by the BPS receiver [11]. Beam patter move-

472 P. K. TEH ET AL. Figure 2. (a) STTC-QPSK trellis structure, ad (b) Costellatio mappig usig gray code Figure 3. STTC far located atea elemets are replaced by atea arrays to support SDMA. patter that esures: 1) costat large scale fadig over T s, ad 2) the geeratio of L idepedet fades withi each T s. 1) Achievig costat large-scale fadig: I order to esure costat large-scale fadig over each symbol period T s, the mobile must remai withi the atea array s HPBW at all times. This correspods to Figure 4. Atea array structure. met is created by applyig time varyig phase (t) to the elemets of atea array (see Figure 4). I BPS, the beam patter sweeps a area of space withi T s (symbol duratio) ad returs to its iitial positio ad starts movig agai. Properly selectig the phase offset (t) leads to a movemet of atea beam d Ts, 0 1 (8) dt where is the HPBW, φ is the azimuth agle, dφ / dt is the rate of atea patter movemet, ad T s (dφ / dt) is the amout of atea patter movemet withi T s. The received atea patter amplitude is esured to remai withi the HPBW for the etire symbol duratio, T s, usig the cotrol parameter, 0 < < 1. 2) Achievig L idepedet fades withi each T s : Usig (8), the phase offset applied to the atea array is

BEAM PATTERN SCANNING (BPS) VERSUS SPACE-TIME BLOCK CODING (STBC) AND SPACE-TIME TRELLIS CODING (STTC) 473 foud to be (see [3,6,7]): 2d Ts () t T t 2 (9) s where is the wavelegth of the carrier ad d is the distace betwee adjacet atea elemets. The sweepig of the beam patter creates a artificial fast fadig chael with a coherece time that may lead to L idepedet fades over T s. This is a direct result of the departure ad the arrival of scatterers withi the atea array beam patter widow. Simulatio results i [10] ad [11] assumig a medium size city ceter, with 0.0005 < < 0.05, reveals that time diversity gais as high as L = 7 is achievable usig BPS scheme. Assumig BPSK modulatio, the trasmitted sigal ca be represeted as s() t b cos(2 f t) g () t (10) 0 o T s where b 0 { 1,+1} is the trasmitted bit, f o is the carrier frequecy, ad g Ts (t) is the pulse shape (e.g., a rectagular waveform with uity height over 0 to T s ). The ormalized sigal received at the mobile receiver iput correspods to: M 1 0 o l (11) m0 1 rl() t b cos 2 f tm (, t ) M ( t), t[ lt / L,( l1) T / L], l{1,2,..., L} l s s where m {0,1,2,, M 1} is the m th atea array elemet (Figure 2), l (t) is a additive white Gaussia oise (AWGN), which is cosidered idepedet for differet time slots (l), l is the fade amplitude i the l th time slot, ad l is its phase offset (hereafter, this phase offset is assumed to be tracked ad removed). Moreover, i (11), (, t ) (2 d ) cos () t (12) where (2d/)cosφ is the phase offset caused by the differece i distace betwee atea array elemets ad the mobile (assumig the atea array is mouted horizotally), ad θ(t) is itroduced i Equatio (9). Applyig the summatio over m, Equatio (11) correspods to rl() t l b0 AF(, t ) M 1 (13) cos2 fot ( t, ) l( t) 2 Here, 1 si M 2 ( t, ) AF(, t ) M si 1 2 ( t, ) (14) is the atea array factor. Assumig the mobile located at φ = /2, (12) ca be approximated by (t, φ) = (t) = -(t). Moreover, assumig that atea array s peak is directed towards the iteded mobile at time 0, ad small movemets of atea array patter over T s, i.e., i Equatio (9), is small, the array factor is well approximated by AF(t, φ) 1. The time varyig phase of (9) i (12) ad (13) leads to a spectrum expasio of the trasmitted (ad the received) sigal. Because the parameter i (9) is cosidered small (e.g., = 0.05), this expasio is miimal (see Subsectio 3.2). After returig the sigal to the base-bad the received sigal correspods to: rl lb0 l, l {1,2,..., L} (15) 3. BPS versus STBC, STTC STBC, STTC ad BPS are compared i terms of physical atea dimesio, complexity, spectrum efficiecy, etwork capacity ad BER performace. 3.1. Complexity ad Physical Atea Dimesio The mai complexity of BPS scheme is at the trasmitter mouted at the BS to geerate a time varyig beam patter directed toward the desired user, whereas, the complexity of STBC scheme is maily due to the umber of trasmittig ateas, N, at the BS ad the combiig scheme at the receiver [3]. The complexity of STTC scheme is maily due to both the ecoder (trasmitter) ad decoder (receiver). The ecodig process requires a space-time chael coder to ecode the iformatio symbols accordig to a specific trellis structure (e.g., Figure 1). The decodig complexity that utilizes Viterbi algorithm icreases expoetially with the umber of states (trasmit ateas) of the trellis structure [3]. Here, we cosider: 1) Space-Time Codig (STC) techiques (i.e., both STBC ad STTC) use two atea arrays to geerate directioal beam patter: a) Each atea array cotais six atea elemets (each elemet is separated by o / 2), ad b) The atea arrays are separated far eough (e.g., by 5 o ) to esure idepedet fades. Here, o is the wavelegth of the carrier frequecy (or the average wavelegth of all carrier frequecies if multi-carrier trasmissio is used). 2) BPS techique uses: a) a sigle 6-elemet atea array (elemets are separated by o /2), ad b) Beam-patter movemet is assumed to result i up to seve fold diversity (i geeral, a fuctio of parameter ) [10]. STC schemes atea dimesio is higher tha BPS sice STBC scheme utilizes 2 atea arrays (i geeral,

474 P. K. TEH ET AL. ay umber of atea arrays). Cosiderig, atea array elemets are separated by o /2, the legth of the atea array would be 2.5 o. To esure idepedet fades, these ateas should be located apart eough (e.g., 5 o ). This leads to the total legth of 10 o for STBC atea array while BPS eeds just 2.5 o legth atea array. Thus, the physical atea dimesios of STC techiques are much greater tha the atea array dimesios for BPS scheme. Moreover, STTC physical atea array dimesios (specifically, with each atea elemet replaced by a atea array) icrease as the umber of atea arrays icreases. Atea array patter characteristics (e.g., its HPBW) chages with frequecy [12,13]. Hece, i widebad multi-carrier systems, (e.g., i multi-carrier code divisio multiple access, MC-CDMA, or orthogoal frequecy divisio multiplexig (OFDM) systems) each group of sub-carriers might be required to be trasmitted over uique atea arrays i order to create a ideal SDMA; ad hece, a umber of atea array clusters or atea array vector clusters are required (see [12,13] for more iformatio). I this case, the complexity ad the dimesios of STBC ad STTC are much higher tha BPS scheme. I geeral, the dimesios (ad, as a result, the complexity) of STC schemes icrease as the umber of atea arrays icreases. I additio, the complexity of STTC icreases as the umber of trellis states icreases ad as a result the required umber of atea arrays icreases (i order to create higher orders of space diversity ad codig gai). 3.2. Spectrum Efficiecy ad Throughput BPS techique creates a badwidth expasio as it is discussed i the previous sectio, while STBC scheme with static beam patters does ot geerate this expasio. BPS system badwidth is expaded by a factor correspods to f exp. ( BW..) BPS ( BW..) ( BW..) without BPS without BPS 100% (16) where (B.W.) BPS = badwidth eeded with BPS ad (B.W.) withoutbps = badwidth eeded without BPS. Cosiderig (13) ad usig (12) ad (9), the expasio factor f exp. correspods to dm ( 1) fexp. 100% (17) 2 Hece, with a costat T s,,, d ad M, for both BPS ad STBC systems, the relative reductio i badwidth efficiecy due to BPS correspods to after BPS d( M 1) R 1 100% 2 before BPS (18) Cosiderig d = /2, ad typical values of (e.g., = 0.5 rad.), ad M = 6, (18) ca be approximated by R (1 ) 100% (19) With this defiitio, the relative reductio i BPS spectrum efficiecy is determied by the cotrol parameter,. For example, cosiderig = 0.05 (a atea sweepig is equivalet to 5% of HPBW), R = 95%. O the other had, with a costat badwidth available to both BPS, ad STBC ad STTC, the throughput of BPS is less tha STC techiques by the factor f exp. (e.g., by a factor of less tha 5%). This disadvatage of BPS is very miimal with respect to advatages of BPS techiques as discussed i this paper. 3.3. Capacity ad Performace I this paper, we have assumed the same atea arrays (with the same HPBW ad approximately the same dimesio ad complexity) for both BPS ad STC systems. This assumptio leads to higher order of diversity via BPS compared to STC (e.g., up to 7 fold diversity i BPS versus 2 fold diversity i STC), which better mitigates fadig effects i BPS system compared to STC systems. Hece, while this leads to a higher probability-of-error performace i BPS systems, cosiderig a costat sigal power to oise power ratio, it leads to a higher etwork capacity as the umber of users icreases. The details of capacity ad performace ehacemets are preseted i the ext sectio via simulatios. 4. Simulatios 4.1. BER Performace Simulatios Simulatios are performed assumig: a) Mid-size city ceter (e.g., 3 scatterers per 1000m 2 ) that leads to 7 fold diversity with BPS techique; b) BPSK trasmissio for STBC ad BPS compariso ad QPSK trasmissio for STTC ad BPS compariso; c) Oe received atea; d) Switched beam smart atea arrays (with HPBW = 18 o ) are mouted at the BS; e) Quasi-static chael, i.e., chael characteristic is static over 2 cosecutive symbol periods, Ts, for STBC ad over the etire frame, for STTC-QPSK ad the chages i a idepedet maer; ad, f) STTC-QPSK frame is equal 130 symbols. For simplicity of compariso ad to illustrate the beefits of time diversity iduced by BPS scheme, Equal Gai Combiig (EGC) over time compoets is assumed. EGC techique does ot rely o chael estimatio to perform the combiig. The performace simulatios for STBC compared to BPS are show i Figure

BEAM PATTERN SCANNING (BPS) VERSUS SPACE-TIME BLOCK CODING (STBC) AND SPACE-TIME TRELLIS CODING (STTC) 475 Figure 5. BER/FER performace comparig (a) STBC versus BPS scheme, ad (b) STTC-QPSK versus BPS. Figure 6. BPS performace for differet R values. 5(a). It ca be observed that BPS scheme offers 5 db ad 15 db improvemet i performace at probability-of-error 10-3 compared to STBC scheme ad traditioal BPSK system without diversity, respectively. The performace improvemet i BPS scheme is due to the high order of time diversity gais achieved through beam patter movemet. The diversity order achievable via STBC is lower tha BPS, ad, therefore, its BER performace is lower compared to BPS scheme. The performace simulatios for BPS versus STTC-QPSK are show i Figure 5(b). It is observed that BPS scheme offers 12 db ad 22 db improvemets i performace at probability-of-error 10-3 compared to STTC-QPSK scheme with atea arrays ad without beam patter movemet, respectively. The performace improvemet via BPS is the result of high order of time diversity gais achieved through beam patter movemet. Although STTC-QPSK offers both diversity ad codig gai, the diversity order offered by STTC-QPSK is much iferior compared to BPS-QPSK; thus, eve without codig gai beefit i BPS-QPSK scheme, it surpasses the performace of STTC-QPSK with relatively lower complexity. I Figure 6, BER performace of BPS system is geerated for differet relative spectrum efficiecy, R. Icreasig the parameter leads to higher order of diversity that ehaces BER performace of the system; ad, o the other had, it reduces BPS relative badwidth efficiecies. For example, as it is discussed i [10], i a rich scatterig eviromet, = 0.005 leads to two-fold diversity which is equivalet to R = 99.5%. Icreasig from 0.005 to 0.05 icreases the diversity achievable to 7 folds, ad reduces the relative spectrum efficiecy to R = 95%. This is equivalet to a decrease i throughput from 0.5% to 5%. 4.2. Network Capacity Simulatios Network capacity simulatios are performed assumig: a) MC-CDMA trasmissio with N = 32 carriers; b) Four fold frequecy diversity over the etire badwidth; c) For STBC-BPS compariso, we cosider iter-cell iterferece effects from the first tier cells (see Figure 7). This iterferece is reduced via log codes assiged to sigals trasmitted to the users of each cell; d) For STTC-BPS compariso, iter-cell iterferece effects are igored, (see Figure 7); e) Mid-size city ceter (e.g., 3 scatterers per 1000m 2 ) that leads to 7 fold diversity with BPS techique; f) Users are distributed uiformly i the cell; g) Iter-user-iterferece withi the cell is reduced via radom assigmet of Hadamard-Walsh codes

476 P. K. TEH ET AL. Figure 7. Iterferig cells assumig oe-tier cellular etwork. The directio of beam patters that will iterfere with iteded mobile is represeted. (i MC-CDMA systems); h) Equal Gai Combiig (EGC) over frequecy compoets; i) Switched beam smart atea arrays (with HPBW = 18 o ) are mouted at the BS; ad, j) Sigal power to oise power ratio is SNR = 10dB for STBC ad SNR = 12dB for STTC. With these assumptios, the received BPS/MC- CDMA sigal correspods to [12]: 6 Kc 1 N 1 cl, b a c, k c, k c c0 k0 0 Rc r() t l M 1 2 AF(, t ) cos 2 ( f f ) t c o c c, l c, l (, t ) (20) Here, AF(t, φ c ) is the array factor itroduced i (14), l (t) is a additive white Gaussia oise (AWGN), which is cosidered idepedet for differet time slots (l), b c,k {+1,-1} is the c th cell s k th user s trasmitted bit, ck, is the Hadamard-Walsh spreadig code for k th user ad th sub-carrier i the c th cell, c is the log code of the th sub-carrier for c th cell, cl, is the Rayleigh fade amplitude o the th sub-carrier i the l th time slot i the c th cell ad cl, is its phase (which is assumed to be tracked ad removed). cl, is assumed idepedet over time compoets, l, ad correlated over frequecy compoets, [14]. K c represets the umber of users effectively iterfere with the desired user. I the eighborig cells, these users are located at the atea patter (sector) with directios show i Figure 7. Cosiderig assumptios (f) ad (i) HPBW EK ( c ) K (21) 2 whe E( ) deotes the expectatio ad K is the umber of users available i each cell. I (20) 1/(R c ) a represets the log-term path loss of the sigal received by the mobile (MS) i the cell 0. This sigal is trasmitted by the BS of eighborig cells to the users located i those cells, ad i the directios which iterfere with the iteded mobile (see Figure 7). I Figure 7, D is the cell radius. Assumig the iteded mobile is located at D / 2 ad approximatig the coverage area by a triagle, D / 2 represets the approximate ceter of mass of users i the beam patter coverage area. R c represets the distace betwee the BS of the cell c, c {0,1,2, 6}, ad the iteded mobile i the cell 0. From the geometry i Figure 7, vector R formed by the elemets R c, c {0,1,2, 6}, correspods to [12] R = [1.00 3.83 3.44 1.975 1.83 1.975 3.44] (22) where R 0 is ormalized to oe ad the others are ormalized with respect to this value. I (20), the power factor a is a fuctio of user locatio, BS atea height ad eviromet. Cosiderig urba areas, parameter a chages with the carrier frequecy ad BS atea height. I urba areas, a = 1, if R c < D max, ad a = 2 if R c > D max, where D max = D(f o,h a ), (D max is a fuctio of the carrier freuquecy f o ad atea height h a ). Cosiderig f o = 900MHz, ad BS height, h a > 25m, D max 1000m (see [15]). Assumig a cell of radius D 500m, ad by referrig to [15], we fid that a = 2 for cells 1, 2 ad 6 whereas a = 1 for cells 3, 4 ad 5. Thus, i the simulatios we igore the iterferece from cells 1, 2 ad 6 ad oly cosider iter-cell iterferece from cells 3, 4 ad 5 with a little loss i accuracy. With the model itroduced i (20), the received STBC/MC-CDMA sigal correspods to r () t 0 r() t 1 6 Kc 1 N 1 c,0 bc, k[] i c,1 bc, k[ i1] a c0 k0 0 Rc ck, c o c, 0 0 cos(2 ( f f) t ) ( t) (23) 6 Kc 1 N 1 c,0 bc, k[ i1] c,1 bc, k[ i] a c0 k0 0 Rc ck, c o c, 1 1 cos(2 ( f f) t ) ( t) where b c,k [i] ad b c,k [i+1], i {0,2,4, } is the k th user i th iformatio bit i the c th cell for STBC, c,0 ad cl, are the Rayleigh fade amplitude due to atea 0 ad atea 1 i the th sub-carrier i the c th cell ad c,0 ad cl, are their phase, respectively, ck, is the Hadamard- Walsh spreadig code for k th user ad th sub- carrier, c is the log code of the th sub-carrier i the c th cell, 1/(R c ) a characterizes the log-term path loss ad (t) is a additive white Gaussia oise (AWGN). Figure 8(a) represets etwork capacity simulatio results geerated cosiderig MRC across time compo

BEAM PATTERN SCANNING (BPS) VERSUS SPACE-TIME BLOCK CODING (STBC) AND SPACE-TIME TRELLIS CODING (STTC) 477 Figure 8. Capacity performace (a) STBC ad BPS, ad (b) STTC ad BPS ets i BPS ad across space compoets i STBC (see [3] ad [4]) ad EGC across frequecy compoets i both BPS ad STBC. It is observed that a higher etwork capacity is achievable with BPS/MC-CDMA. For example, at the probability-of-error of 10-2 BPS/MC-CDMA offers up to two-fold higher capacity. It is also observed that STBC/MC-CDMA offers a better performace compared to the traditioal MC-CDMA without diversity whe the umber of users i the cell are less tha 80. However, as the umber of users i the cell icreases beyod 80, the performace of STBC/MC-CDMA becomes eve worse tha traditioal MC-CDMA (i.e., MC-CDMA with atea array but without diversity beefits). This is because STBC scheme discussed i this paper (see [1]) is desiged to utilize MRC. It has bee show that MRC combiig scheme is the optimal combiig scheme whe there is oly oe user available, while i a Multiple Access eviromet, MRC ehaces the Multiple Access Iterferece (MAI) ad therefore degrades the performace of the system [16]. Cosiderig STTC-QPSK, with assumptio (d), STTC-QPSK/MC-CDMA received sigal correspods to K 1 N 1 0() 0 0, k 1 1, kk k0 0 o 0 0 r t s s (24) cos(2 ( f f) t ) ( t) Here s 0,k ad s 1,k is the k th user iformatio bit trasmitted from atea 0 ad atea 1, respectively, 0 ad 1 are the Rayleigh fade amplitude due to atea 0 ad atea 1 i the th sub-carrier ad 0 ad l are their phase, respectively, k is the Hadamard-Walsh spreadig code for k th user ad th sub-carrier, ad (t) is a additive white Gaussia oise (AWGN). Network capacity simulatios for STTC-QPSK are geerated assumig EGC across time compoets (i BPS), space compoets (i STTC-QPSK) ad frequecy compoets for BPS ad STTC-QPSK [Figure 8(b)]. Figure 8(b) represets STTC versus BPS-QPSK simulatio results. This figure shows that BPS-QPSK is superior compared to STTC-QPSK ad QPSK without diversity. I this simulatio, BPS-QPSK leads to sigificatly better capacity due to the time diversity iduced by beam-patter movemet ad frequecy diversity iheret i MC-CDMA. The results also show that QPSK performace is superior compared to STTC-QPSK. This agrees with the FER simulatio results i Figure 5(b), where QPSK is better tha STTC-QPSK at low SNRs (e.g., at SNR = 10 db). This is because STTC-QPSK is desiged uder the assumptio of high eough SNR values; thus, it is less efficiet compared to QPSK at low SNRs [17]. (The capacity curve for higher SNR values may lead to better STTC-QPSK performace compared to QPSK; however, STTC-QPSK shows a lower performace compared to BPS-QPSK for all SNRs). Thus, it is observed that a higher etwork capacity is achievable via BPS/MC-CDMA. It is also worth metioig that STTC-QPSK performace ca be sigificatly improved via iterferece suppressio/cacellatio techiques at the cost of system complexity as discussed i [19 21]. I this paper, we coducted the compariso without a complexity added to the STTC scheme via implemetig iterferece suppressio algorithms. Simulatios cofirm that BPS offers superior etwork capacity compared to STC schemes; however, there are two issues associated with BPS scheme: 1) diversity achievable via BPS chages with distace; greater the distace of mobile from the BS, higher the diversity ad etwork capacity [10]. It is otable that i geeral, the average umber of users located i costat width auluses (with BS at the ceter) icreases as the distace

478 P. K. TEH ET AL. from the BS icreases; ad 2) BPS works just i urba areas (or i rich scatterig eviromets); but, because a high etwork capacity is oly required i urba areas, this is ot a critical issue. Moreover, BPS ca also be merged with STC techiques, e.g., via the structure show i Figure 4. I this case, the traditioal atea arrays are replaced with time varyig weight vector atea arrays to direct ad move the atea patter. Aother approach for mergig BPS with STBC is itroduced i [18]. Nevertheless, it is worth metioig that BPS scheme achieve the probability-of-error performace ad the etwork capacity beefits with a relatively less complexity. This makes BPS a promiet scheme for future wireless geeratios with smart ateas. However, the spectrum efficiecy of BPS is about 5% less tha STC which is a miimal disadvatage compared to the beefits created by BPS techique. 5. Coclusios A compariso was preformed betwee STBC, STTC- QPSK ad BPS trasmit diversity techiques i terms of etwork capacity, BER/FER performace, spectrum efficiecy, complexity ad atea dimesios. BER performace ad etwork capacity simulatios are geerated BPS, STBC, ad STTC schemes. This compariso shows that BPS trasmit diversity scheme is much superior compared to both STBC ad STTC-QPSK schemes: a) The BS physical atea dimesios of BPS is much smaller tha that of STC techiques, ad b) The BER/FER performace ad etwork capacity of BPS is much higher tha that of STC schemes. The complexity of BPS system is miimal because the complexity is maily located at the BS, ad the receiver complexity is low because all the diversity compoets eter the receiver serially i time. I terms of spectrum efficiecy, both STC schemes outperform BPS scheme by a very small percetage (e.g., i the order of 5%). BPS scheme itroduces a small badwidth expasio due to the movemet i the beam patter that evetually results i a lower throughput per badwidth. 6. Refereces [1] S. M. Alamouti, A simple trasmit diversity techique for wireless commuicatios, IEEE Joural o Selected areas i Commuicatios, Vol. 16, No. 8, pp. 1451 1458, 1998. [2] V. Tarokh, H. Jafarkhai, ad A. R. Calderbak, Space-time block codes from orthogoal desigs, IEEE Trasactios o Iformatio Theory, Vol. 45, No. 5, pp. 1456 1467, July 1999. [3] V. Tarokh, N. Seshadri, ad A. R. Calderbak, Space-time codes for high data rate wireless commuicatio: Performace criterio ad code costructio, IEEE Trasactios o Iformatio Theory, Vol. 44, pp. 744 765, March 1998. [4] V. Tarokh, A. F. Naguib, N. Seshadri, ad A. Calderbak, Space-time codes for high data rate wireless commuicatios: Performace criteria i the presece of chael estimatio errors, mobility, ad multiple paths, IEEE Trasactios o Commuicatios, Vol. 47, No. 2, February 1999. [5] A. F. Naguib, V. Tarokh, N. Seshadri, ad A. R Calderbak, A space-time codig modem for high-data-rate wireless commuicatios, IEEE Joural o Selected Areas i Commuicatios, Vol. 16, No. 8, October 1998. [6] N. Seshadri ad J. H. Witers, Two sigalig schemes for improvig the error performace of frequecy divisio-duplex trasmissio system usig trasmitter atea diversity, Iteratioal Joural Wireless Iformatio Networks, Vol. 1, No. 1, pp. 49 60, Jauary 1994. [7] J. H. Witers, The diversity gai of trasmit diversity i wireless systems with Rayleigh fadig, i Proceedigs of the 1994 ICC/SUPERCOMM, New Orleas, Vol. 2, pp. 1121 1125, May 1994. [8] R. W. Heath, S. Sadhu, ad A. J. Paulraj, Space-time block codig versus space-time trellis codes, Proceedigs of IEEE Iteratioal Coferece o Commuicatios, Helsiki, Filad, Jue 11 14, 2001. [9] V. Tarokh, A. Naguib, N. Seshadri, ad A. R. Calderbak, Combied array processig ad space-time codig, IEEE Trasactios o Iformatio Theory, Vol. 45, No. 4, pp. 1121 1128, May 1999. [10] S. A. Zekavat ad C. R. Nassar, Atea arrays with oscillatig beam patters: Characterizatio of trasmit diversity usig semi-elliptic coverage geometric-based stochastic chael modelig, IEEE Trasactios o Commuicatios, Vol. 50, No. 10, pp. 1549 1556, October 2002. [11] S. A. Zekavat, C. R. Nassar, ad S. Shattil, Oscillatig beam adaptive ateas ad multi-carrier systems: Achievig trasmit diversity, frequecy diversity ad directioality, IEEE Trasactios o Vehicular Techology, Vol. 51, No. 5, pp. 1030 1039, September 2002. [12] S. A. Zekavat ad C. R. Nassar, Achievig high capacity wireless by mergig multi-carrier CDMA systems ad oscillatig-beam smart atea arrays, IEEE Trasactios o Vehicular Techology, Vol. 52, No. 4, pp. 772 778, July 2003. [13] P. K. Teh ad S. A. Zekavat, A merger of OFDM ad atea array beam patter scaig (BPS): Achievig directioality ad trasmit diversity, accepted i IEEE 37th Asilomar Coferece o Sigals, Systems ad Computers, November 9 12, 2003. [14] J. W. C. Jakes, Microwave Mobile Commuicatios, New York, Wiley, 1974. [15] A. J. Rustako, N. Amitay, G. J. Owes, ad R. S. Roma, Radio propagatio at microwave frequecies for lie-ofsight microcellular mobile ad persoal commuica-

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