Defence Scence Journal, Vol. 63, o., January 03, pp. 5-4 03, DESIDOC Optmal 4G OFDMA Dynamc Subcarrer and Power Aucton-based Allocaton towards H.64 Scalable Vdeo Transmsson G. Chandra Sekhar, Shreyans Parakh, and Adtya K. Jagannatham Indan Insttute of Technology Kanpur, Kanpur - 0806, Inda E-mal: adtyaj@tk.ac.n Abstract In ths paper, authors presented a prce mzaton scheme for optmal orthogonal frequency dvson for multple access (OFDMA) subcarrer allocaton for wreless vdeo uncast/multcast scenaros. They formulate a prcng based vdeo utlty functon for H.64 based wreless scalable vdeo streamng, thereby achevng a trade-off between prce and os farness. These parametrc models for scalable vdeo rate and qualty characterzaton are derved from the standard JSVM reference codec for the SVC extenson of the H.64/AVC, and hence are drectly applcable n practcal wreless scenaros. Wth the ad of these models, they proposed aucton based framework for revenue mzaton of the transmtted vdeo streams n the uncast and multcast 4G scenaro. A closed form expresson s derved for the optmal scalable vdeo quantzaton step-sze subject to the constrants of the uncast/multcast users n 4G wreless systems. Ths yelds the optmal OFDMA subcarrer allocaton for mult-user scalable vdeo multplexng. The proposed scheme s cognzant of the user modulaton and code rate, and s hence amenable to adaptve modulaton and codng (AMC) feature of 4G wreless networks. Further, they also consder a framework for optmal power allocaton based on a novel revenue mzaton scheme n OFDMA based wreless broadband 4G systems employng aucton bddng models. Ths s formulated as a constraned convex optmzaton problem towards sum vdeo utlty mzaton. We observe that as the demand for a vdeo stream ncreases n broadcast/multcast scenaros, hgher power s allocated to the correspondng vdeo stream leadng to a gan n the overall revenue/utlty. We smulate a standard WMAX based 4G vdeo transmsson scenaro to valdate the performance of the proposed optmal 4G scalable vdeo resource allocaton schemes. Smulatons llustrate that the proposed optmal bandwdth and power allocaton schemes result n a sgnfcant performance mprovement over the suboptmal equal resource allocaton schemes for scalable vdeo transmsson. Keywords: Orthogonal frequency dvson for multple access, subcarrer, wreless vdeo, scalable vdeo codng I. ITRODUCTIO Orthogonal frequency dvson for multple access (OFDMA) s rapdly emergng as the PHY layer scheme of choce n modern wreless communcatons and s employed by the domnatng 4G wreless standards such as WMAX and LTE for broadband wreless access. OFDMA enables the transmsson of hgh data rate symbol streams over wdeband wreless channels, whch would otherwse succumb to the dstorton arsng out of nter-symbol nterference due to the frequency selectve nature of such broadband wreless channels. OFDMA s based on orthogonal frequency dvson multplexng (OFDM) whch can be mplemented by employng low complexty IFFT/FFT operatons. OFDM converts a frequency selectve wdeband channel nto multple parallel narrowband frequency flat sub-carrers, thereby drastcally reducng the complexty of receve processng. These subcarrers are allocated to the users and groups n uncast and multcast scenaros respectvely for approprate perods of tme. Ths process s referred to as tme-frequency resource allocaton n OFDMA systems and holds key to 4G wreless network performance optmzaton. Vdeo based applcatons such as vdeo conferencng, multmeda streamng, moble TV and real-tme survellance are emergng as popular 4G applcatons. Hence, a sgnfcant component of the 4G Wreless traffc s expected to comprse of vdeo and multmeda based rch applcatons. Such vdeo applcatons requre the development of sophstcated multmeda codecs for vdeo transmsson n the moble wreless envronment. To ensure vdeo delvery whle meetng the vdeo qualty guarantees s challengng due to the erratc fadng nature of the wdeband wreless channel coupled wth the dsparate devce capabltes of the cellular users and qualty of servce (os) requrements. Ths challenge has led to the development of the scalable vdeo codng (SVC) profle of the H.64/AVC whch s attractve especally for vdeo transmsson n uncast and multcast wreless scenaros. Scalable Vdeo Codng s a unque paradgm wheren a vdeo s coded as a seres of embedded bt streams and s stored at ts hghest fdelty levels as a combnaton of several base and enhancement layers. However, a novel feature of such a stream s that partal bt streams can be extracted to fulfll the requrements of the wreless vdeo users dependng on the nature of ther ndvdual lnk qualtes and devce capabltes. SVC enables the flterng and extracton of partal bt streams Receved 5 October 0, revsed 0 ovember 0, onlne publshed 4 January 03 5
Def. SCI. J., Vol. 63, o., jauary 03 of dverse spatal, qualty and temporal resolutons. The bt rate and qualty of the coded vdeo streams depend ntrnscally on the frame rate, spatal resoluton and quantzaton parameters. Hence, these parameters have to be chosen approprately so as to mze the net vdeo qualty whle meetng the end user os aspects for vdeo delvery. Hence, effcent allocaton of subcarrers s essental n 4G OFDMA towards meetng the above objectve n wreless scalable vdeo transmsson. Further, generc subcarrer allocaton schemes whch are not talored to the nature of the scalable vdeo streams are not amenable to practcal wreless scenaros. Hence, one needs to develop schemes for jont codec-lnk adaptaton n such 4G wreless networks for effcent resource utlzaton. In ths context, we propose a novel revenue mzaton framework for optmal H.64 coded vdeo rate based tme-frequency resource allocaton at the 4G wreless os enforcement ponts such as base statons (BS) and access servce network gateways (AS-GW) n a 4G wreless network. The proposed scheme s based on dynamc subcarrer auctonng whch supports prcng based ncentves to stmulate users to sell and lease under-utlzed sub carrers, thereby mprovng the overall effcency. The users submt ther bds for vdeo resource allocaton ether ndvdually (uncast scenaros) or through content provders (multcast scenaros) whch are employed by the os enforcer for optmal tme/ frequency resource allocaton. Snce ratonal users are expected to pay approprate prces as per allocaton of the 4G wreless resources, ths naturally leads to revenue mzaton towards scalable vdeo transmsson n 4G wreless networks. Conventonal approaches related to schedulng and resource allocaton n 4G wreless systems are not specalzed to the context of vdeo and do not consder the scalable nature of vdeo transmsson, thereby resultng n suboptmal resource allocaton and end user vdeo qualty reducton. The proposed scheme avods ths by drect vdeo codec adaptaton, thereby enhancng ts appeal for use n practcal wreless scenaros. Towards ths end we consder parametrc scalable vdeo qualty and bt-rate models as functons of the scalable vdeo frame rate and quantzaton parameter for optmal OFDMA subcarrer allocaton. These robust models for H.64 SVC coded streams are computed usng the JSVM reference codec and hence are readly applcable n practce. We formulate a constraned convex optmzaton problem based on the above models for aucton based optmal OFDMA resource allocaton. We use the robust framework of convex optmzaton to obtan the closed form expresson for computaton of the optmal coded vdeo parameters, thus leadng to codec adaptaton. Ths results n revenue based end-user vdeo qualty mzaton and effcent bandwdth utlzaton n 4G wreless networks. Subsequently we also propose an optmzaton framework for power aucton based revenue mzaton for optmal H.64 coded vdeo transmsson n 4G OFDMA systems. Employng the parametrc vdeo models derved from the JSVM reference codec, we formulate the power constraned aucton based vdeo transmsson scenaro as an approprate convex optmzaton problem. Ths leads to revenue/ utlty based end-user vdeo qualty mzaton. Smulaton results for vdeo transmsson n 4G OFDMA systems employng several vdeo sequences llustrate that the proposed optmal subcarrer and power allocaton schemes sgnfcantly enhance the qualty of vdeo transmsson compared to vdeo agnostc suboptmal power allocaton schemes. Fgure. OFDMA System.. SCALABLE VIDEO AUCTIO MODEL The rate and qualty of the transmtted scalable vdeo streams are ntrnscally related to the quantzaton parameter and frame rate of the scalable codec and have been derved 3. The scalable vdeo rate functon R (q,t) n terms of quantzaton parameter q and frame rate t s gven as, Fgure. Wreless vdeo communcaton system wth dfferent devce capabltes. ct / t e d( q/ q mn ) Rqt (,) = R e e c R q ( q) R t () t where R =R(q mn,t ) s the hghest bt rate of the hghest qualty vdeo sequence correspondng to the mum frame rate t and mnmum quantzaton parameter q mn, and R q (q), R t (t) are the normalzed rate functon vs quantzaton parameter and frame rate respectvely. Smlarly, the scalable vdeo jont qualty functon s gven as, 6
Sekhar, et al.: Optmal 4G OFDMA Dynamc Subcarrer and Power Aucton-based Allocaton at/ t e qt (,) = ( b q+g) a e q ( q) () t t where =(q mn,t ) s the hghest qualty of the vdeo sequence correspondng to the mum frame rate t and mnmum quantzaton parameter q mn and s normalzed to 00.e. = 00. The normalzed qualty functons t (t), q (q) wth respect to the frame rate t and quantzaton parameter q are respectvely defned as, qt (,) t() t = t(; t q) =, q (, t ) mn qt (, ) q() q = q(; q t ) =. q (, t ) mn The quanttes R, a, c, d, β,γ are the vdeo characterstc parameters and are obtaned from the standard JSVM reference codec 4 for the SVC developed jontly by the Jont Vdeo Team (JVT) of the ISO/IEC Movng Pctures Experts Group (MPEG) and the ITU-T Vdeo Codng Experts Group (VCEG). The characterstc vdeo parameter values for standard vdeo sequences are avalble n lterature 5.. Aucton Bddng Model In ths secton, we present the vdeo aucton bddng models employed to derve the optmzaton framework for revenue mzaton subject to the bandwdth constrants and quantzaton parameter bounds of the vdeo sequence. Ths s employed to propose a revenue objectve functon as a functon of vdeo qualty wth the bt-rate constrants for vdeo transmsson mposed by the communcaton system. aturally, the proposed bd functon must be ncreasng wth respect to qualty of the vdeo as users are expected to pay hgher prces for ncreased vdeo qualty. Several parametrc utlty functons can be employed as vald bd functons towards revenue mzaton. In ths context a lnear prce qualty bd functon can be presented as, P=e+f; () where f s the mnmum admsson prce and e s the lnear prce control factor. Then we consder prce as a utlty functon whch s derved from the user requrements. Further, the proposed framework for aucton based revenue mzaton s general and other alled bd functons such as the logarthmc and square root functons shown n Fg. 3 can be readly ncorporated. 3. OFDMA BASED WIMAX WIRELESS ETWORKS Orthogonal frequency dvson for multple access (OFDMA) s based on the mult-carrer orthogonal frequency dvson multplexng (OFDM) modulaton scheme. In OFDM systems the gven hgh bt-rate data stream s dvded nto lower bt-rate parallel streams, each of whch s modulated and transmtted ndvdually over separate orthogonal subcarrers as shown n Fg. 4. Hence, n OFDMA systems the avalable broadband channel s subdvded nto dfferent frequency subcarrers whch convert the wdeband frequency selectve channel nto parallel narrowband flat fadng channels resultng n sgnfcantly lower processng complexty. The prmary advantage of OFDM s ts reslence to delay spread, whch arses due to the ncreased per symbol duraton. The presence of the cyclc prefx (CP) greater than the worst-case channel delay spread ensures that the effect of ISI s restrcted to the duraton of the CP, whch can be dscarded. The presence of Table. Characterstc vdeo parameters of the rate and qualty models for the H.64 SVC standard vdeo sequences Sequence a c d β ƴ m r n (multcast) R e f q b Foreman CIF 7.7000.0570.070-0.098.4475 5/6 79 3046.30 6 09 09 40 Akyo CIF 8.0300 3.490.50-0.036.4737 /3 7 6.85 0 85 53 59 Fotball CIF 5.3800.3950.4900-0.058.387 /3 0 548.90 6 9 53 488 Crew CIF 7.3400.670.8540-0.0393.5898 5/6 0 4358.0 9 30 86 53 Cty CIF 7.3500.0440.360-0.0346.596 /3 6 775.50 6 36 48 580 Akyo CIF 5.5600 4.090.830-0.036.4737 4 / 48 39.63 6 7 39 59 Foreman CIF 7.000.5900.7850-0.098.4475 3/4 05 64.73 5 89 67 357 Cty 4CIF 8.4000.0960.3670-0.0346.596 4 /3 0 0899.00 8 4 74 34 Crew 4CIF 7.3400.530.4050-0.0393.5898 / 3 80.00 9 4 5 509 7
Def. SCI. J., Vol. 63, o., jauary 03 Bddng prce Vdeo ualty Fgure 3. Comparson of vdeo prce bddng models. CP converts the lnear convolutve channel nto a wrappng based crcular convoluton, whch enables low-complexty persubcarrer frequency doman equalzaton, thus elmnatng the need for complex tme-doman equalzaton 6,7. OFDM modulaton can be mplemented usng IFFT/FFT operatons at the transmtter and recever respectvely, thereby resultng n a low complexty mult-carrer system even for a large number of subcarrers, whch cannot otherwse be mplemented employng conventonal sngle carrer modulators. In an OFDM system, OFDM symbols are consdered as the tme doman resources whle the subcarrers are consdered as the frequency doman resources, thereby renderng OFDM sutable for tme-frequency resource allocaton based optmal transmsson. The OFDMA s a multuser multple access scheme n whch the data streams of multple users are multplexed onto the downlnk (DL) and uplnk (UL) subchannels of the OFDM PHY layer. The sub-carrer structure of a typcal OFDMA system s shown n Fg. 4 and conssts of three types of sub-carrers - data, plot, and null sub-carrers. Whle data sub-carrers are employed for transmsson of the modulated user nformaton symbols, the plot sub-carrers are employed to carry out PHY layer procedures such as jtter, tmng delay estmaton and frequency synchronzaton so that the offset errors are mnmzed. The null or guard subcarrers avod overlap wth adjacent OFDM bands. Wreless standards such as DSL, wreless metropoltan area networkng (WMA) (IEEE 80.a), WMA (IEEE 80.6) and fxed worldwde nteroperablty for mcrowave access (WMAX) (IEEE 80.6-004) employ OFDM as the PHY layer scheme n whch a sngle user uses all the subcarrers at a tme. Most of the 4G wreless standards such as LTE, Moble WMAX (IEEE 80.6e-005) employ OFDMA as PHY layer scheme n whch subcarrers and tme slots are shared among the users. Multuser dversty and adaptve modulaton makes OFDMA a flexble multple access technque that allocates subcarrers to the many users wth broadly varyng applcatons, data rates and os requrements. In our smulatons we use the moble profle of the WMAX standard, whch s based on the WMA standards developed by the IEEE 80:6 group and adopted by both IEEE and ETSI HIPERMA groups. WMAX enables the Fgure 4. OFDMA sub-carrer structure. transmsson of very hgh data rates through the use of dfferent modulaton rates and error correctng codng schemes. WMAX based on OFDMA PHY supports scalable bandwdth, datarates and also flexble, dynamc per user resource allocaton. WMAX MAC s desgned to support a large number of users, wth multple connectons per termnal, each wth ts own os requrement. WMAX supports strong encrypton usng advance encrypton standard (AES), and has a robust prvacy and key management protocol. All end-to-end servces are delvered over an IP archtecture relyng on IP-based protocols for end-to-end transport, os, sesson management, securty and moblty 8. 4. OPTIMAL SUBCARRIER AUCTIO The os enforcer ntally solcts the qualty based prcng bds P( ) from the users/ content provders n the 4G wreless network. The adaptve modulaton codng (AMC) rate aware constraned optmzaton framework for symbol rate allocaton towards aucton based revenue mzaton n the 4G network can be formulated as,. np ( ) R ( q, tf ) RS mr st. P ( ) = e + f, q q q mn where R s denotes the aggregate symbol rate of the OFDMA system and n ; denotes the number of users correspondng to the th multcast group, where denotes the total number of groups. The quanttes = (q, t f, ) and R (q, t f, ) represent the qualty and rate of the th vdeo sequence correspondng to the quantzaton parameter q and fxed frame rate t f. The adaptve modulaton order m correspondng to the number of bts per symbol and r as code rate of the th scalable vdeo stream, whch s allocated dynamcally by the scheduler as per the user DL channel condtons. It can be readly seen that the above problem s convex n nature and the optmzaton framework can be naturally converted to a standard form convex optmzaton problem Eqn (9) by modfyng the optmzaton objectve as, () 8
Sekhar, et al.: Optmal 4G OFDMA Dynamc Subcarrer and Power Aucton-based Allocaton mn. - np( ). The above standard form convex optmzaton problem can be convenently solved employng standard convex optmzaton technques whch employ the Karush-Kuhn- Tucker (KKT) framework. The Lagrangan functon Lqlµd (,,, ) for the above revenue mzaton problem s gven as, Lq (, l, µ, d ) = n( b q+g ) + l d( q/ qmn ) ke + µ ( q q ) + d ( q q ) mn R where λ,μ,δ, are Lagrange multplers, b = e t( tf ) b, g = e t( tf ) g, and R s the mum btrate correspondng to the th vdeo stream. The quantty k s defned as, R k = mr e ct / t f e c Applyng the KKT condtons for the above Lagrangan optmzaton crteron and settng ( e.. L( q, lµ,, d ) = 0) wth l 0, µ 0, d 0, we obtan n k d e b l mn +µ d = d ( q / q ) qmn From (), the KKT complementary slackness condton correspondng to the rate nequalty constrant s gven as, l mn = d ( q / q ) ke R Therefore, the Lagrangan multpler λ correspondng to the optmal scalable vdeo quantzaton parameter adaptaton obtaned by settng µ = 0 and d = 0 (correspondng to slack quantzaton parameter constrants) can be derved as, q l = R mn S s 0, S 0 (3) (4) b jn j. j= d (5) j We substtute the above expresson for λ n Eqn (4) to derve the closed form expresson for the optmal quantzaton parameter q as, q q b mr mn = qmn ln d l kd RS nb ( d) = qmn ln d k njb j( d j) j= The above expresson yelds the optmal quantzaton parameter q for the scalable vdeo codec adaptaton and tme-frequency resource allocaton towards vdeo revenue mzaton. Thus the above closed form soluton provdes a fast and low computatonal complexty scheme for optmal scalable vdeo adaptaton compared to employng convex solvers such as CVX and s applcable for both uncast and multcast scenaros. Further, as descrbed n the earler secton, the proposed optmal framework for the rate constraned tme-frequency allocaton towards revenue mzaton s not restrcted to lnear bddng models and can be readly employed for a large class of utlty functons. For nstance, consder the general parametrc bddng model P( ) =q log 0( ). The correspondng framework for aucton based revenue mzaton can be formulated as,. np( ) st.. R ( q, t ) R mr mn q q q f S Further, another such utlty functon that can be consdered s P( ) =d. Smulaton results n the later secton demonstrate the performance of the proposed algorthms for scalable vdeo rate adaptaton. 5. POWER AUCTIO BIDDIG MODELS Dynamc auctonng of the lmted power resources leads to prcng based ncentves to stmulate the users to compete for allocaton, thereby mprovng the overall effcency. Varous vdeo prce versus qualty based aucton bddng models are presented n ths secton. These models can then be convenently employed to construct the power constraned optmzaton problem for revenue/ utlty mzaton of the transmtted vdeo sequences. aturally, as users are expected to pay hgher prces for progressvely ncreasng vdeo qualty, the utlty functons for ratonal users are constraned to belong to a parametrc class of monotoncally ncreasng prce wth respect to vdeo qualty. The users submt ther bds for vdeo resource allocaton ether ndvdually (uncast scenaros) or through content provders (multcast scenaros) whch are employed by the os enforcer for optmal power allocaton. The optmal power allocaton soluton of the optmzaton problem thus consdered leads to effcent wreless power allocaton for vdeo transmsson. Below we present the lnear, (6) (7) 9
Def. SCI. J., Vol. 63, o., jauary 03 logarthmc and square root based vdeo bddng models. A lnear utlty prce bd s gven by the canoncal expresson, B( ) = e + f, (8) where f s the mnmum admsson prce for the lnear prce bddng model and e s the lnear prce control factor. A more practcal logarthmc bd model whch consders the concave natureof the vdeo utlty as a functon of qualty s descrbed as, B ( ) =d log ( ) + l, (9) 0 where l s the mnmum admsson prce for the logarthmc prce bddng model and d s the logarthmc prce control factor. Another related smplstc bddng model s the squareroot bd functon gven as, B ( ) =q +, (0) b where b s the mnmum admsson prce for the square root prce bddng model and q s the square root prce control factor. In all the above models denotes the th user/user group n uncast/multcast scenaros. In the practcal parametrc scenaro descrbed above, the users smply submt the parameter values characterzng ther bds based on ther requrements and the demand for the vdeo sequences. The prce varaton for each of the above aucton bddng models s shown n Fg. 3. ext we descrbe the framework for optmal OFDMA power allocaton. 6. OPTIMAL POWER AUCTIO In ths secton, we begn by proposng an optmzaton frame work for mzng the qualty of the transmtted vdeo sequence wth optmal allocaton of power n 4G OFDMA systems. Ths optmzaton problem s based on the scalable vdeo rate and qualty parametrc models as dscussed earler for the vdeo transmsson n both uncast and multcast 4G wreless broadband scenaros. The standard Shannon channel capacty C of a communcaton channel for a total transmtted power P and nose level σ s gven as, P C = Blog +, σn n () where B s the channel bandwdth. Consderng transmsson of vdeo sequences at the mum frame rate t, the bt-rate of the vdeo stream can be related to the quantzaton parameter as, d( qq / mn ) P Re = Blog + σn B P q= qmn ln log + d R σn Therefore, the normalzed qualty of the vdeo sequences n terms of transmtted vdeo power can be expressed as, B P =bqmn ln log + +g. d R σn Hence, the power constraned convex optmzaton problem for optmal power allocaton towards qualty mzaton for vdeo transmsson n both uncast and multcast wreless broadband 4G OFDMA systems can be formulated as,. st.. =bqmn ln log + +g d R σn P 0,, P P t n B P () where P t denotes the total avalable power n OFDMA system and n ; denotes the number of users correspondng to the th multcast group and denotes the total number of such groups. It can be readly observed that the above problem s convex n nature and can be solved usng CVX solver 0 to obtan the optmal power and the qualty of the vdeo sequence by mzng the sum qualty under the power constrants. Fg. 5 shows that the sum qualty of the vdeo sequences ncreases wth the ncrease of total transmtted power. Further, the above optmzaton framework can be readly extended to the aucton bddng models presented n the earler secton correspondng to the dfferent vdeo utlty functon based parametrc bddng models. The proposed aucton based optmzaton framework for optmal power allocaton towards aucton based revenue mzaton n the 4G network can be formulated as,. nu ( ) subject to U =q + b bqmn ln log + +g d R σn P 0; P P t B P where U can be chosen n general as any one of the utlty functons of vdeo qualty presented n the earler secton. We llustrate the performance of the proposed optmzaton framework for optmal vdeo power allocaton through smulaton results n the next secton. 7. SIMULATIO RESULTS In our smulatons we consder the streamng of = 9 standard test vdeo sequences and we employ a standard WMAX profle to llustrate the performance of the proposed optmal OFDMA tme-frequency resource allocaton schemes. The parameters e, f, q and b correspondng to the bds of the dfferent users are lsted n Table. The mnmum admsson prces f and the lnear prce control factors e for the lnear prce bddng models are chosen randomly n the range 00 to 0
Sekhar, et al.: Optmal 4G OFDMA Dynamc Subcarrer and Power Aucton-based Allocaton Sum ormalzed ualty Sum Prce (normalzed wth 00) q Total Power Fgure 5. Total power vs. Sum normalzed qualty for multcast scenaro at t = 30 fps. 300 and 5 to 0 respectvely. The parameters q and b for the nonlnear bddng models are chosen randomly n the range 00 to 300 and 300 to 600. The optmal prce mzng btrate allocaton and the correspondng optmal quantzaton parameter q are evaluated by formulatng the optmzaton problem and computng the optmal soluton usng the closed form expresson n Eqn (6). We compare our allocaton wth the one obtaned from the standard CVX based convex solver 0. The correspondng per vdeo sequence optmal quantzaton parameter q optmal prce mzng bt-rate allocaton are lsted n Table for the logarthmc bddng model usng the WIMAX profle mentoned 5 wth the effectve downlnk symbol rate R s = 6.336 Msym/s. Further, the correspondng values for the sub-optmal equal bt-rate allocaton are also gven theren. The assocated net revenue comparson for the optmal bt-rate allocaton and equal bt-rate allocaton for a uncast scenaro at varous values of symbol rates R s s gven n Fg. 6 for the lnear bddng functon aucton. Smlarly, Fg. 7 demonstrates the comparson for a multcast scenaro wth the number of Fgure 6. Symbol rate vs sum prce for uncast scenaro at t = 30 fps and prce as a lnear functon of qualty (P = e + f). Sum Prce (normalzed wth 00) Symborate (ormalzed by 000) Symborate (ormalzed by 000) Fgure 7. Symbol rate vs sum prce for multcast scenaro at t = 30 fps and prce as a logarthmc functon qualty ( P ( ) =q log 0( ) + b ). Table. Symbol allocaton for equal and optmal symbol rate usng logarthmc bddng prce P ( ) =q log 0( ) + b, n uncast and multcast scenaros. The bddng prce values for multcast are normalzed by 00. Sequence Equal symbol rate allocaton Optmal symbol rate allocaton Uncast scenaro Multcast scenaro R equal qp equal R opt q np( ) R opt q np( ) Foreman CIF 704 6.95 376.67 9.07 777.96 355.06 9.608 63.08 Akyo CIF 704 5.000 463.6 6.864 08.30 40.36 7.809 737.87 Football CIF 704 39.307 6.7 36.648 904.06 679. 35.587 99.78 Crew CIF 704 3.5 9.64 7.570 09.30 078.0 6.30 34.0 Cty CIF 704 6.46 400.7 7.489 05.00 499.05 6.065 87.80 Akyo CIF 704 5.000 39.63 5.000 070.00 39.63 5.000 53.60 Foreman CIF 704 6.639 360.6 9.843 87.9 4.78 8.507 9.0 Cty 4CIF 704 30.7 03.0 9.797 433.50 85.90 9.04 468.60 Crew 4CIF 704 39.547 80. 34.40 853.38 58.0 37.06 53.88
Def. SCI. J., Vol. 63, o., jauary 03 multcast subscrbers for each group chosen randomly n the range 0 to 50. From Fg. 6 we can observe that the closed form soluton allocaton from Eqn (6) closely agrees wth the CVX solver based allocaton. We also present the OFDMA mult-user DL-MAP for subcarrer allocaton n both equal and optmal btrate allocaton scenaros n Fgs. 8 and 9 respectvely, for the log prcng based vdeo aucton. Subcarrers Symbols Fgure 8. Allocaton of symbols to vdeos wth equal symbol rate allocaton. Subcarrers optmzaton framework. The bandwdth B correspondng to a WMAX scenaro s set equal to B = 4 0.94 = 6.56 KHz, where each subchannel conssts of 4 subcarrers wth a spacng of 0.94 KHz. The normalzed nose power σ n s set equal to 0 db. The characterstc parameters of the vdeo sequences R, a, c, d, γ, β obtaned from the JSVM software are lsted n the Table. The parameters e, f, d, l, qand b of the aucton bddng models lsted n the Table are obtaned from the bds submtted by the users based on ther requrements and the demand for the vdeo sequences n practcal scenaros. In our smulatons, the mnmum admsson prces f and the lnear prce control factors e for the lnear prce bddng models are chosen randomly n the range 00 to 300 and 5 to 0 respectvely. The parameters d and q, l and b for the non-lnear bddng models are chosen randomly n the range 00 to 300 and 300 to 600. In multcast scenaros, the numbers of subscrbers n each multcast group are chosen randomly n the range 0 to 50. In the smulatons, we frst solve the drect power constraned qualty optmzaton problem proposed to mze the sum qualty of the vdeo sequences for optmal power allocaton employng the parametrc vdeo models n 4G OFDMA uncast/multcast scenaros usng the CVX solver 0. From the Fg. 5 we can observe that the sum qualty of the vdeo sequences ncreases wth the total power and we can also observe that the sum qualty wth optmal power allocaton s sgnfcantly hgher than the sum qualty wth equal power allocaton. ext we solve the revenue mzaton problem 3 under the power constrants of the vdeo transmsson for optmal power allocaton employng the aucton bddng models n both uncast and multcast scenaros usng the CVX solver. The results obtaned from the revenue mzaton scheme for optmal power allocaton and sub-optmal equal power allocaton scheme are lsted n the Table 3 for the square root bddng model for both uncast and multcast scenaros n 4G OFDMA systems. The assocated net revenue comparson for the optmal power allocaton and equal power allocaton for a uncast scenaro and multcast scenaro at varous values of total power P t s gven n Fgs. 0 and respectvely for the square root bddng functon aucton. Also, we compare equal power allocaton and optmal power allocaton for both uncast/multcast scenaros n the Fg. for the sad Symbols Fgure 9. Allocaton of symbols to vdeos wth optmal symbol rate allocaton usng prce as a logarthmc functon of qualty ( P( ) =q log 0 ( ) + b ) n multcast scenaro. From the smulaton results we can observe that the optmal symbol rate allocaton framework yelds sgnfcant mprovement n the net vdeo revenue and can be convenently employed by the os ponts and Core etwork n 4G wreless scenaros. For the optmal power aucton we agan consder = 9 standard test vdeo sequences to smulate the proposed Sum ormalzed ualty Total Power Fgure 0. Total power vs sum prce for uncast scenaro at t = 30 fps and prce as a square root functon of qualty ( P( ) =q + b ).
Sekhar, et al.: Optmal 4G OFDMA Dynamc Subcarrer and Power Aucton-based Allocaton Sum ormalzed ualty Total Power Fgure. Total power vs sum prce for multcast scenaro at t = 30 fps and prce as a square root functon of qualty ( P( ) =q + b ). Power Allocated to the streams Vdeo Streams Fgure. Comparson of dfferent power allocaton schemes at t = 30 fps and bddng prce as a square root functon of qualty ( P( ) =q + b ). bddng model. One can observe that as the number of users n a group ncreases, the power allocated to the vdeo stream progressvely ncreases, leadng to optmzaton of the precous power resources. Ths mples that as the demand for a vdeo stream ncreases, the potental revenue produced by the vdeo ncreases, thus requrng a hgh level of power to be allocated to the correspondng vdeo for overall vdeo utlty mzaton. From the smulaton results we can observe that the proposed optmal power allocaton scheme presents a sgnfcant mprovement n the net vdeo revenue and the qualty of the vdeo sequences over the equal power allocaton scheme. 8. COCLUSIO We proposed and presented aucton based schemes for optmal sub carrer and power allocaton towards revenue mzaton n a 4G OFDMA system. The proposed schemes are based on the bddng mechansm, where users of uncast vdeo streams and servce provders n multcast scenaros submt ther bds to the resource scheduler at the base staton. An optmzaton framework has been proposed for optmal resource allocaton wth respect to the OFDMA aggregate rate constrants and adaptve modulaton and codng paradgm n 4G systems. A closed form soluton has been derved for the optmal quantzaton parameter based lnk-codec adaptaton n OFDMA systems. Further, ths framework has been shown to be general n nature and can be readly extended to a varety of sutable utlty functons for optmal resource allocaton. It has been shown through smulatons that the presented optmal subcarrer and power allocaton yeld mproved performance compared to the suboptmal equal subcarrer and power allocaton respectvely for the case of DL/UL PUSC WMAX. Table 3. Smulaton results for equal and optmal power allocaton usng square root as bddng prce and utlty functon of qualty B( ) =q + b, n uncast and multcast scenaros. The bddng prce values for multcast are normalzed by 00. Sequence Equal power allocaton Optmal power allocaton Uncast scenaro Multcast scenaro P equal equal p opt nb( ) p opt nb( ) Foreman CIF. 0.9403 6.86 0.998 60.45 5.35 0.956 48.75 Akyo CIF..0000 7.8.0000 78.00 5.076.0000 563.04 Football CIF. 0.789 4.334 0.7890 7.73 7.786 0.799 7.30 Crew CIF. 0.793 3.003 0.83 79.50 37.830 0.8405 873.6 Cty CIF. 0.9549 9.764 0.9468 8.3 5.30 0.963 955.3 Akyo CIF..0000 7.04.0000 83.00.043.0000 398.88 Foreman CIF..0000 0.9.0000 64.00 3.79.0000 655.0 Cty 4CIF. 0.55 6.679 0.544 69.40 30.648 0.653 573.68 Crew 4CIF. 0.498 7.60 0.5076 688.54 3.38 0.4903 9.34 3
Def. SCI. J., Vol. 63, o., jauary 03 REFERECEs. Wang, Y.; Ostermann, J. & Zhang, Y. Vdeo processng and communcatons. Prentce Hall, 00. Gandh, S.; Buragohan, C.; Cao, L.; Zheng, H. & Sur, S. A general framework for wreless spectrum auctons. In nd IEEE Internatonal Symposum on ew Fronters n Dynamc Spectrum Access etworks, DySPA 007. Aprl 007, pp. -33. 3. Wang, Y.; Ma, Z. & Ou, Y.F. Modelng rate and perceptual qualty of scalable vdeo as functons of quantzaton and frame rate and ts applcaton n scalable vdeo adaptaton. In 7 th Internatonal Workshop of Packet Vdeo, PV 009. May 009, pp. -9. 4. JSVM Software, Jont Scalable Vdeo Model. Jont Vdeo Team, Verson 9.9.7. 5. Parakh, S. & Jagannatham, A.K. Optmal subcarrer allocaton for H.64 based scalable vdeo transmsson n 4G OFDMA systems. In Australasan Telecommuncaton etworks and Applcatons Conference ATAC, Melbourne, Australa, 0. 6. Tse, D. & Vswanath, P. Fundamentals of wreless communcaton. Cambrdge Unversty Press, 005. 7. Goldsmth, A. Wreless communcaton. Cambrdge Unversty Press, 005. 8. Ghosh, R.M.A. & Andrews, J.G. Understandng the fundamentals of WMax: Understandng broadband wrelessnetworkng. Prentce Hall, 007. 9. Boyd, S. & Vandenberghe, L. Convex optmzaton. Cambrdge Unversty Press, 004. 0. Boyd, S. & Vandenberghe, L. CVX: Matlab software for dscplned convex programmng. 00, ver.., Buld 80.. Standard test vdeo sequences. http://meda.xph.org/ vdeo/derf/. Contrbutors Mr Garlapat Chandra Sekhar obtaned hs MTech (Electrcal Engneerng) wth focus n Sgnal Processng, Communcton and etworkng at IIT Kanpur n 0. He s currently Member of Techncal Staff, System Solutons, Cadence Desgn Systems Inda Pvt. Ltd., Bangalore. Mr Shreyans Parakh has completed hs MTech (Sgnal Processng, Communcaton and etworks) from Indan Insttute of Technology, Kanpur n 0. He has worked wth Csco and s currently workng to start a project on polluton control and fuel producton from waste materals. He has 4 publshed papers n conferences/ journals. Hs research area ncludes: Wreless systems, vdeo codng, optmzaton and game theory. Prof Adtya K. Jagannatham receved hs MS and PhD from the Unversty of Calforna, San Dego, US. Presently he s workng as a faculty member n the Department of Electrcal Engneerng at Indan Insttute of Technology, Kanpur and also assocated wth the BSL-IITK Telecom Center of Excellence (BITCOE). He has contrbuted to the 80.n hgh throughput wreless LA standard. Hs research area ncludes: ext-generaton wreless communcatons and networkng, sensor and ad-hoc networks, dgtal vdeo processng for wreless systems, wreless 3G/4G cellular standards, and CDMA/OFDM/MIMO wreless technologes. 4