A General Overlay Underlay Analytic Expression Representing Cognitive Radio Waveform

A General Overlay/Underlay Analytic Expression Representing Cognitive Radio Waveform V.D. Chakravarthy∗ , Z. Wu† , A. Shaw† , M.A. Temple‡ , R. Kannan§ and F. Garber

†

∗

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Primary User 3

Primary User 2

Primary User 1

UWB

Noise Floor

Frequency

CR Band 2

CR Band 3

Primary User 3

CR Band 1

Ultra Wide Band (UWB) Underlay Waveform

Primary User 2

Fig. 1.

Power Density

I. I NTRODUCTION With an ever increasing demand for higher data rates, coupled with an increase in new applications and the number of users, spectrum crowding and congestion continue to increase. Recent Federal Communication Commission (FCC) studies suggest that spectrum congestion is primarily due to the inefficient use of spectrum, versus the lack of available spectrum [1], [2]. A number of new technologies and standards have been proposed suggesting a paradigm shift in wireless communications is eminent [3]–[7]. There are presently two techniques aiming to make more efficient use of available spectrum: Cognitive Radio (CR) and Ultra Wide Band (UWB). In UWB transmission, a very wide bandwidth is occupied by a signal having a very low power spectral density. The extremely low spectral density minimizes coexistent interference to existing narrow band communication systems operating in the UWB transmission range [8]. In CR techniques, frequency agile transmitters target unused spectrum ”holes” and transmit power within these unused regions. By doing so, CR interference to existing wireless systems is minimized. The use of UWB signaling suggests that most primary users can tolerate interference to some degree. Hence, the spectrum usage can be viewed as unused and/or underused. In this context, unused spectrum has been allocated but is not currently being used whereas underused spectrum spectrum is

Power Density

Abstract— Several studies have revealed that spectrum congestion is primarily due to the inefficient use of spectrum versus unavailability. Cognitive Radio (CR) and Ultra Wide Band (UWB) technologies have been proposed as candidates to address this problem. Currently, a CR determines unused frequency bands and transmits overlay waveforms in these bands, while UWB transmits underlay waveforms that span the entire frequency band while coexisting with primary users. This suggests that most of the spectrum occupied by primary users is underused. This work proposes a general Soft Decision Cognitive Radio (SDCR) framework, based on a previous developed Spectrally Modulated, Spectrally Modulated (SMSE) framework, to combine benefits of overlay/underlay techniques while maximizing channel capacity. We also show that current CR and UWB implementations represent two extreme SDCR cases and that current overlay/underlay waveforms are two special cases of the general waveform platform.

Primary User 1

‡

Air Force Research Laboratory, Wright-Patterson AFB, OH † Wright State University, Dayton OH Air Force Institute of Technology, Wright-Patterson AFB, OH § Louisiana State University Email: [email protected]

Frequency

Fig. 2.

Cognitive Radio (CR) Overlay Waveform

allocated and being used but not to its full capacity. Similarly, there are currently two enabling CR waveforms, including an overlay waveform and an underlay waveform. An overlay waveform only operates in unused spectral regions while avoiding interference to primary assigned users. An underlay waveform is spectrally coincident with primary assigned users and induces minimum tolerable interference [9]. Overlay and underlay transmissions are illustrated in Fig. 1 and Fig. 2, respectively. By simultaneously exploiting both unused and underused spectral regions, we proposed a soft decision cognitive radio (SDCR) approach whereby the transmitted power spectral density in each region is determined by the spectrum usage in that region [8]. This concept is illustrated in Fig. 3. To support the proposed SDCR, we need to design a enabling waveform which combines the overlay and underlay waveforms. Specifically, the SDCR waveform needs to contain

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⎞

CR Band

CR Band

CR Band

CR Band

Primary User 3

Primary User 2

CR Band

Primary User 1

Power Density

⎛ CU W B

Overlay and Underlay CR Waveform

different power spectral densities in different bands and dynamically adapt its spectral response according to time-varying environmental conditions. As developed herein, we provide a general analytic spectrally coded waveform platform to support SDCR implementation. Furthermore, we show that current UWB and CR techniques are two extreme cases the SDCR, with current overlay/underlay waveforms likewise representing two special cases of our general waveform platform.

⎛

According to Shannon’s channel capacity condition given by (1), channel capacity can be optimized by increasing the signal-to-noise ratio (S/N ) and/or channel bandwidth (W ). C = W log (1 + S/N )

(1)

In the current CR framework, the transmitter continuously monitors the radio spectrum and identifies frequency bands as being in one of two categories, either used or unused. The unused frequency bands are identified as CR bands for secondary users. The channel capacity when utilizing unused CR bands can be written as shown in (2) [8].

 CCR =

N 

k=1

 W uk

(3)

where n0 is the additive Gaussian noise power spectral density, ΦU W B is the average power spectral density of the UWB transmission, M is the total number of primary users operating within total bandwidth W , Φpi is the narrow band average power spectral density of the ith primary user and Wpi is the corresponding bandwidth of ith primary user. The coexistence of an UWB transmission with primary narrow band transmissions suggests that most of the narrow band transmission can tolerate a certain level of interference, i.e., even though some frequency bands are occupied by primary users they are likely to be underused. To maximize channel capacity, the so called used bands also need to be considered. Accounting for both unused and underused bands, the new SDCR [8] channel capacity can be written as [8],

II. C HANNEL C APACITY A NALYSIS

⎛

⎟ ⎟ ΦU W B W ⎟ ⎟ M  ⎠ n0 W + Φpi Wpi i=1

CR Band

Frequency

Fig. 3.

⎜ ⎜ = W log ⎜ ⎜1 + ⎝

CSDCR

⎜ ΦCRk Wuk ⎟ ⎜ ⎟ ⎜ ⎟ k=1 log ⎜1 + ⎟ N ⎜ ⎟  ⎝ n0 W uk ⎠

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ΦCR2i Wpi ⎟ ⎟ ⎟ ⎟ M ⎟  ⎠ n0 W + Φpi Wpi

ΦCR1k Wuk +

i=1

ΦCR2i ≤ Ii , ∀i ΦCR1k ≤ φk , ∀k N M   ΦCR1k Wuk + ΦCR2i Wpi ≤ S k=1

where N is the total number of unused spectral bands in the total CR monitored bandwidth W , Wuk is the bandwidth of the k th unused band and ΦCR1k is the power spectral density of the CR transmission in the k th unused band. UWB signaling can be used as underlay technique to support CR transmission. In UWB signaling, a very large contiguous bandwidth is used in a coexistence manner such that spectrum is simultaneously shared with primary narrow band transmissions. In this way, the total bandwidth W in (1) is maximized. However, to avoid interferences to primary (licensed) users, UWB transmissions are regulated by an FCC who limits the UWB transmitted power spectral density to a very low level. Hence, the channel capacity of UWB transmission is extremely limited and is given by (3) [8].

⎞

(4) where ΦCR1k is the CR transmitted power spectral density in the k th unused band, and ΦCR2i is the CR transmitted power spectral density in the ith underused band. The following constraints are imposed to maximize overall channel capacity while minimizing mutual interference between CR users and other primary users:

(2)

k=1

k=1

M 

i=1

⎞

N 

⎜ ⎜ ⎜ = W log ⎜1 + ⎜ ⎝

N 

(5)

i=1

where Ii is the interference tolerance level in the ith used band, φk is the maximum allowed transmitted power spectral density (e.g., FCC mandated interference temperature) in the k th unused band, and S is the total transmit power of the cognitive user across all unused and underused frequency bands. III. SMSE F RAMEWORK BACKGROUND Previous work proposed a general analytic framework for spectrally modulated, spectrally encoded (SMSE) waveforms to accommodate multi-carrier CR-based waveforms [10], [11]. Specifically, an arbitrary CR waveform can be expressed in terms of amplitude (A), phase (Θ) and frequency (F). These three factors aid in the design of SMSE waveforms using six design variables namely Data, Code, Window, Orthogonality

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and two frequency allocation variables. See [10], [11] for an in-depth treatment of the analytic development of SMSE waveforms. The coding c = [c1 , c2 , . . . , cNf ], ci ∈ C, data modulation, d = [d1 , d2 , . . . , dNf ], di ∈ C, and windowing function, w = [w1 , w2 , . . . , wNf ], wi ∈ C account for component-by-component amplitude and/or phase variations. A phase only variable ø = [o1 , o2 , . . . , oNf ], oi ∈ C is used for orthogonality between symbol streams and facilitate multiple access. Data, code and window variables are first considered in SMSE development. The mth frequency component of the k th symbol can be written as, sk [m] = cm dm,k wm e

j(θd

m,k

+θcm +θwm )

(6)

where m = 0, 1, ..., NF − 1 is the frequency index and cm , dm,k , etc. are magnitude and phase design variables. The expression in (6) can be further modified to include frequency and orthogonality variables. Frequency component selection in SMSE waveforms is a function of two variables a = [a1 , a2 , . . . , aNf ], ai ∈ {0, 1} and u = [u1 , u2 , . . . , uNf ], ui ∈ {0, 1}. Given an Nf -point fast Fourier transform (FFT) process, Nf frequency components or spectral bands are initially available. It is important to note that frequency assignment variable a takes on binary values of 0 or 1, the complement of which indicates spectrum availability for secondary users. Thus, this pool of frequencies is reduced by component selection to create a number of CR assigned (a) and usable/available (u) frequencies. The mth component of the k th CR symbol corresponds to j(θd

sk [m] = am um cm dm,k wm e

m,k

+θcm +θwm +θom,k )

(7)

where the product ai ui ∈ {0, 1} The discrete time domain waveform is obtained using Inverse Discrete Fourier Transform (IDFT) on (7), ⎧ f −1 ⎨N 1 Re am um cm dm,k wm sk [n] = ⎩ Nf m=0  ej(2πfm tn +θdm,k +θcm +θwm +θom,k ) .

of power does not exceed the established IT threshold [12] [13]. Figure 4 illustrates a conceptual view showing primary users (P) and unused / underused spectrum utilization for an arbitrary IT threshold. The figure identifies two cases of spectrum inefficiency: 1) since spectral assignment is based on a binary decision, the adjacent bands next to the primary users will be unavailable to CR users and 2) primary users bands falling below the IT threshold will be unavailable to CR users. A soft decision cognitive radio will be able to exploit these underused frequency bands to increase channel capacity and improve performance. To support such a SDCR system, the SMSE framework requires an extension to account for underused frequency bands. The first step in modifying the SMSE framework is to re-examine the original design variables. Frequency related factors are now termed as primary variables while amplitude and phase related factors are termed as secondary variables. Since the objective here is to optimize the spectrum usage, only frequency related design variables are considered. First, we illustrate the newly proposed SMSE framework using Fig. 5 and Fig. 6, then define the design variables. Fig. 6a and Fig. 6b show how the current CR framework identifies the used and unused spectrum based on binary decisions. Fig. 6c shows the weighted spectrum estimation resulting from the spectrum sensing block in Fig. 5. The weighted spectrum estimate(WSE) (a) is further processed taking into account the IT threshold, primary users, other secondary users requirements and channel conditions. Specifically, the weighted spectrum estimate provides a metric of allowable transmission power density at each and every frequency components in the entire bandwidth. Hence, the WSE divides the entire bandwidth into unused (u) and underused (b) frequency components and both the unused and under used frequency components can be exploited. Notice in Fig. 6d that different under used frequency components have different allowable CR transmission power densities. In the new SMSE framework, we relax the frequency

(8)

for tk ≤ tn ≤ tk + Tsym , fm = fc + mΔf , and Δf is the frequency resolution [11]. IV. S OFT D ECISION SMSE (SD-SMSE) F RAMEWORK The SMSE framework provides a unified expression for generating and implementing a host of multi-carrier type waveforms (e.g., OFDM, MC-CDMA, CI/OFDM, TDCS, etc) which satisfies present CR models designed to utilize unused spectral bands. However, it does not take into account the under used spectrum. The FCC has proposed Interference Temperature (IT) as a metric to aid in interference analysis and for establishing a threshold on the allowable interference induced by secondary users. This means that secondary users can use different transmit power levels provided the sum total

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Fig. 4.

Primary users (P) and Unused / Underused Spectral Regions

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architecture shown in Fig. 5. Applying an IDFT to (11) results in the discrete time domain waveform given by ⎧ f −1 ⎨N 1 sk [n] = Re am um cm dm,k wm ⎩ Nf m=0 ej(2πfm tn +θdm,k +θcm +θwm +θom,k ) + ej(2πfm tn +θdm,k +θcm +θwm +θom,k ) Fig. 5.

Block diagram representation of SD-SMSE framework



(12)

Nf −1



am bm cm dm,k wm

m=0

where the first summation represents unused frequency components and the second summation accounts for underused frequency components. Development of the new SD-SMSE framework primaryly dealt with spectrum allocation. The secondary variables such as code, data modulation, windowing and orthogonality function are kept the same as in the original SMSE framework. Since all the SD-SMSE waveforms are generated by applying secondary variables in the allocated primary variables space, all the OFDM, NC-OFDM, MC-CDMA, NC-MC-CDMA, TDCS and CI/ODFM are applicable using the new SD-SMSE [10], [11], [14]. A. Case 1: Overlay Waveform - CR

Fig. 6. Spectrum parsing using weighted spectrum estimation in realization of SD-SMSE waveform

assignment variable a from binary values (hard decision) to real values (soft decision), i.e., a = [a1 , a2 , . . . , aNf ], 0 ≤ am ≤ 1

(9)

Next, we introduce a new variable b to account for the under used spectrum, i.e., b = [b1 , b2 , . . . , bNf ], 0 ≤ bm < 1

(10)

Note that bm = 1 since it represents a underused frequency component. The unused variable u stays the same as in hard decision CR. It is obvious that if one frequency component is under used, it cannot be unused and vice versa, i.e., um = 0 if bm > 0 and bm = 0 if um = 1. The other SMSE waveform design variables such as code, data, window and orthogonality remain same as defined in the original framework. Applying both the original and new design variables, the mth component of the k th SDCR data symbol can be expressed as j(θd

sk [m] = am bm um cm dm,k wm e

m,k

+θcm +θwm θom,k )

(11)

The expression in (11) can be decomposed into unused and underused SMSE components as represented in the new SMSE

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Current cognitive radio transmission employs an overlay waveform which only operates in unused spectral bands. Thus, it is apparent that current CR transmission is a special case of the soft decision cognitive radio when no underused frequency components are exploited. In the SMSE framework, if we force the underused variable b to be zero and the frequency assignment variable a to be binary, expressed as: b = [0, 0, . . . , 0]

(13)

a = [a1 , a2 , . . . , aNf ], am ∈ {0, 1}

(14)

then the second summation in (12) is eliminated and reduces to current hard decision CR expression of ⎧ f −1 ⎨N 1 Re am um cm dm,k wm (15) sk [n] = ⎩ Nf m=0  ej(2πfm tn +θdm,k +θcm +θwm +θom,k ) . The maximum channel capacity of such a overlay waveform cognitive radio system is shown in (2). B. Case 2: Underlay Waveform - UWB Ultra wide band transmission uses an underlay waveform which operates across all spectral components and minimizes interference to primary users by limiting transmitted power spectral density. Hence, the UWB transmitted power spectral density is dictated by the primary user deemed as being most sensitive to interference. In this case, all frequency components are treated as underused by setting

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u = [0, 0, . . . , 0]

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(16)

b = [K, K, . . . , K], 0 < K < 1

which effectively eliminates the first summation in (12). The resultant CR signal corresponds to a UWB transmission spanning all frequency components and is expressed as: ⎧ f −1 ⎨N 1 Re Kdm,k wm (18) sk [n] = ⎩ Nf m=0  ej(2πfm tn +θdm,k +θcm +θwm +θom,k ) . where K is a constant obtained by taking the minimum value of the weighted power spectral density shown in Fig. 6. The maximum channel capacity of such an UWB underlay waveform transmission is shown in (3). C. Case 3: Overlay/Underlay - SDCR In our proposed soft decision cognitive radio, the waveform combines the benefits of overlay and underlay waveforms to take advantage of both unused and underused spectrum by employing a soft decision at each and every frequency component, while minimizing the interference to primary users. This way, the channel capacity given by (4) is maximized. V. C ONCLUSION In this paper we extend the previous framework of spectrally modulated, spectrally encoded (SMSE) waveforms to accommodate soft decision cognitive radio (SDCR) waveforms. This general framework allows a multi-carrier based waveform to combine overlay and underlay waveforms and exploit both unused and underused frequency bands to maximize channel capacity of cognitive radio transmission. It is also shown that current cognitive radio and ultra wide band techniques are two extreme cases of the SDCR and current overlay/underlay waveforms are two special cases of the general waveform supported by this framework. ACKNOWLEDGMENT This research was partially funded by the Air Force Office of Scientific Research (AFOSR).

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[1] “Fcc - notice of proposed rulemaking and order, facilitating opportunities for flexible, efficient and reliable spectrum use employing cognitive radio technologies,” FCC Document ET Docket No. 03-108, Dec. 2003. [2] “Fcc - adopts rule changes for smart radios, facilitating opportunities for flexible, efficient and reliable spectrum use employing cognitive radio technologies,” FCC Document ET Docket No. 03-108, March 2005. [3] V. Chakravarthy, A. Shaw, M. Temple, and A. Nunez, “Tdcs, ofdm and mc-cdma : A brief tutorial,” IEEE Communications Magazine, September 2005. [4] V. Chakravarthy, A. Shaw, M. Temple, and J. Stephens, “Cognitive radio: An adaptive waveform with spectrum sharing capabilities,” IEEE WCNC, March 2005. [5] R. Rajbanshi, A. M. Wyglinski, and G. J. Minden, “An efficient implementation of nc-ofdm transceivers for cognitive radios,” Proceedings of the First International Conference on Cognitive Radio Oriented Wireless Networks and Communications (Mykonos Island, Greece), June 2006. [6] J. D. Poston and W. D. Horne, “Discontigous ofdm considerations for dynamic spectrum access in idle tv channels,” IEEE Dynamic Spectrum Access Networks, Nov. 8-11, 2005. [7] S. Hijazi, M. Michelini, B. Natrajan, Z. Wu, and C. Nassar, “Enabling fcc’s proposed spectral policy via carrier interferometry,” IEEE WCNC, 2004. [8] Z. Wu and B. Natrajan, “Interference tolerant agile cognitive radio: Maximize channel capacity of cognitive radio,” IEEE CCNC, January 2007. [9] R. Menon, R. M. Buehrer, and J. H. Reed, “Outage probability based comparison of underlay and overlay spectrum sharing techniques,” IEEE DYSPAN, pp. 101–109, November 2005. [10] M. Roberts, M. A. Temple, M. E. Oxley, R. F. Mills, and R. A. Raines, “A spectrally modulated, spectrally encoded analytic framework for carrier interferometry signals,” International Wireless Communications and Mobile Computing Conference (IWCMC), 2006. [11] M. Roberts, M. A. Temple, M. E. Oxley, R. F. Mills, and R. A. Raines, “A general analytic framework for spectrally modulated, spectrally encoded signals,” IEEE Journal of Selected Areas on Signal Processing), 2007. [12] P. Kolodzy, “Interference temperature: a metric for dynamic spectrum utilization,” Int. J. Network Mgmt,Published online in Wiley InterScience, pp. 103–113, 2006. [13] M. H. R. C. K. S. Yiping Xing, Chetan N. Mathur, “Dynamic spectrum access with qos and interference temperature constraints,” IEEE TRANSACTIONS ON MOBILE COMPUTING, April 2007. [14] R. Rajbanshi, Q. Chen, A. Wyglinski, G. Milden, and J. Evans, “Quantitative comparision of agile modulation technique for cognitive radio tranceivers,” IEEE CCNC, January 2007.

“The views expressed in this article are those of the author(s) and do not reflect official policy of the United States Air Force, Department of Defense or the U.S. Government.”

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