Ofdm Spectrum

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254 IEEE SYSTEMS JOURNAL, VOL. 3, NO. 2, JUNE 2009

Flexible Spectrum and Power Allocation forOFDM Unlicensed Wireless Systems

Cătălin Lăcătuş, David Akopian , Senior Member, IEEE , Prasad Yaddanapudi, andMehdi Shadaram , Senior Member, IEEE

Abstract—Future generations of communication systems willbenefit from cognitive radio technology, which significantly im-proves the efficient usage of the finite radio spectrum resource. Inthis paper we present a wireless unlicensed system that successfullycoexists with the licensed systems in the same spectrum range. Theproposed unlicensed system determines the level of signals andnoise in each frequency band and properly adjusts the spectrumand power allocations subject to rate constraints. It employsorthogonal frequency-division multiplexing (OFDM) modulationand distributes each transmitted bit energy over all the bandsusing a novel concept of bit spectrum patterns. A distributed

optimization problem is formulated as a dynamic selection of spectrum patterns and power allocations that are better suitedto the available spectrum range without degrading the licensedsystem performance. Bit spectrum patterns are designed based ona normalized gradient approach and the transmission powers areminimized for a predefined quality of service (QoS). At the op-timal equilibrium point, the receiver that employs a conventionalcorrelation operation with the replica of the transmitted signalwill have the same efficiency as the minimum mean-squared error(MMSE) receiver in the presence of noise and licensed systems.Additionally, the proposed approach maximizes the unlicensedsystem capacity for the optimal spectrum and power allocations.The performance of the proposed algorithm is verified throughsimulations.

Index Terms—Constraint optimization, distributed algorithms,

game theory, orthogonal frequency-division multiplexing, spec-trum sharing, unlicensed systems.

I. INTRODUCTION

THE increasing demand for personal high data rate wire-

less applications drives the efforts for more efficient usage

of the finite radio spectrum resource. It is envisioned that this

problem can be resolved through the deployment of cognitive

radios which detect whether a particular segment of the radio

spectrum is in use. They jump into the temporarily-unused spec-

trum very rapidly, without interfering with the transmissions

of other authorized (licensed) users. Even though the benefitsof such an approach are currently widely recognized, there are

many challenges [6], [24], [27] regarding the spectrum-alloca-

tion techniques that deal with a dynamic environment, where

Manuscript received July 28, 2008; revised November 13, 2008. First pub-lished April 14, 2009; current version published May 22, 2009. This work wassupportedin part by theOffice of Naval Research underthe Grant N00014-04-1-0088 and the Texas Higher Education Coordinating Board under Advanced Re-search Program Grant 010115-0013-2006.

The authors are with the Department of Electrical and ComputerEngineering, University of Texas at San Antonio, San Antonio, TX78205 USA (e-mail: [email protected]; [email protected];[email protected]).

Digital Object Identifier 10.1109/JSYST.2009.2017391

the licensed users require unrestricted access to their spectrum

range. Important steps in achieving the maximum rate in cogni-

tive radio channels are presented in [5], [7], and [8], where the

way the interference is treated is essential for the unlicensed sys-

tems’ performances. Game theory was introduced in the study of

spectrum sharing for unlicensed bands for different cooperativeand noncooperative scenarios [7], [8], where selfish users are as-

sumed. The greedy distributed interference avoidance algorithm

was proposed in [2], where the aggregate interference of the net-

work was chosen as the performance metric. In that case, the

distribute minimization algorithm converges to an equilibrium

point under the assumption that the sensing time is small com-

pared to the update intervals. The equilibrium point is a subop-

timal solution of the network capacity maximization problem.

Recently, in [18] the authors improved the secondary system

throughput through the multiband joint detection method. The

method consists of the joint optimization of the thresholds em-

ployed in the energy detection of different subbands. This multi-

band sensing method has the potential to significantly increase

the system performances while it decreases the level of aggre-

gate interference.

The multicarriers modulation schemes seem to be a viable so-

lution in designing unlicensed systems because of the increasedspectrum sharing adaptability provided by a wide transmission

bands. In addition recent research has contributed to this field

where we have the hardware, software package and experience

regarding the OFDM implementations and system behavior.

The advantages of OFDM systems improved with a

Walsh-Hadamard transform (WHT) was presented formerly

in [9], where the information was overlaid on all subcarriers.

The same subject was exploited further under the concept of

interference suppression in [12], [25], while the OFDM sys-

tems updated with Walsh-Hadamard transform [9], [25], were

presented for downlink and point-to-point scenarios without

exploiting the rate flexibility or the MAI presence. Recently,

challenges and approaches of OFDM schemes improved with

a deactivating subcarrier technology are found in [19], [24]

for cognitive radio applications. These conventional spectrum

sharing approaches, switching subcarrier methods, have several

drawbacks. Each time a licensed system starts its transmission

on an authorized frequency band, the unlicensed system has

to free that band, find and switch to another unused domain.

This requires additional time for synchronization, increasing

computational loads in an unpredictable way for different

scenarios. The highly dynamic switching strategy has also

disadvantages in that the reception cannot be coherent, de-

creasing the system performance. The difficulty of adjusting

the secondary transmission rates while efficiently exploiting the

1932-8184/$25.00 © 2009 IEEE


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LĂCĂTUŞ et al.: FLEXIBLE SPECTRUM AND POWER ALLOCATION FOR OFDM UNLICENSED WIRELESS SYSTEMS 255

Fig. 1. SPA-OFDM system model.

available spectrum made us to propose an adaptive algorithm

for optimal spectrum shape. This algorithm has to reshape the

transmission spectrum according to the presence of a varying

number of sensed licensed users.In this paper,1 we propose to use an adaptive linear transform

in multicarrier OFDM systems where the bits will be transmittedon all the subcarriers similar to [9], [12], [25]. The linear trans-form is not WHT and it automatically reshapes the transmissionspectrum on available bandwidth for the secondary system. Thetransform is optimally and adaptively selected to minimize var-ious interferences including the interference with the licensedsystems. The unlicensed system will employ a dynamic pro-cessing algorithm for spectrum and power allocation to dealwith a varying number of licensed users and/or QoS require-ments. The QoS from superior layers, meaning a specified rateaccording to the application session, will be translated to thephysical layer where the QoS is a specified target bit error rate(BER) or signal to interference plus noise ratio (SINR).

More specifically, the proposed adaptive algorithm incremen-tally changes the unlicensed system transmission depending onthe required transmission rate changes and the number of ac-tive licensed users. The transmitter optimization is based on thecorrelation matrix of the received signal. The dynamic spectrumand power allocation algorithm is the solution of a distributedoptimization problem, augmented with a power control mecha-nism to provide QoS flexibility. The transition between two op-timal configurations is based on incremental updates avoidingconventional band switching procedures. Our procedure is sim-ilar to the way an adaptive equalizer tracks changes in time-varying channels by gradient-based techniques for minimizingthe channel estimation error.

The paper is organized as follows. In Section II, we presentthe new spectrum and power allocation OFDM (SPA-OFDM)system. In Section III, we formulate and discuss the problem of bit spectrum pattern design. The bit power allocation strategiesand the admissible transmission rate conditions are discussed.In Section IV, the optimal adaptive algorithm is derived. Thealgorithm convergence is discussed in Section V, followed bynumerical and simulation examples in Section VI. Finally, wepresent concluding remarks in Section VII.

II. SYSTEM CONSIDERATIONS

We consider an unlicensed system in the presence of licensed

transmissions. The unlicensed system is SPA-OFDM which is

1Part of the spectrum allocation idea developed in this paper had been pre-sented at MILCOM 2007 Conference.

based on an OFDM modulator, a linear transform and a power

control mechanism. The OFDM modulation scheme maintains

time and frequency synchronization, while the adaptive linear

transform ensures proper band occupation depending on the

licensed user transmissions. SPA-OFDM system will benefit

from coherent detection in the receiver compared with theswitching or frequency hopping techniques implemented for

spectrum sharing or jamming protection, where an additional

time or/and frequency synchronization stage is required.

In the SPA-OFDM system, data bits are precoded and

transmitted on orthogonal subcarriers using a linear transform

which is called in the following a spectrum precoding matrix,

of dimension . The transmission rate, is defined

asthenumber oftransmittedbits, , per OFDMsymbol. can

be different from the number of subcarriers, . The SPA-OFDM

transmitter model is presented in Fig. 1, where we denoted by

IGI the insertion of guard interval and PA is the power amplifier.

In the following, denotes the L-point fast Fourier transform(FFT) transform matrix and its inverse, , is the L-point in-

verse FFT (IFFT) matrix.

We represent the transmitted information in -dimensional

signal space and define the spectrum precoding ma-

trix having as columns the bit spectrum pattern vectors, , for

. In OFDM modulator, using a finite set of or-

thonormal basis functions, defined

on , for , each bit will be sent

on all frequencies according to its spectrum pattern allocation

, that has unit norm. defines the bit

duration and denotes the carrier frequency.

The transmitted signal corresponding to the OFDM symbol

is the following:

(1)

where the spectrum pattern matrix is

is a diagonal matrix of trans-

mitted bit powers , and

is the vector containing the information bits sent by the un-

licensed system. The transmitted unlicensed information is

considered an i.i.d. process with zero-mean and unit variance.

In order to separate the spectrum-allocation procedure and

power control mechanism, the bit spectrum patterns will beunit norm vectors, for .


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In order to simplify the spectrum and power control algorithm

presentation, we assume that the system is corrupted only by the

additive noise and licensed user transmission. The SPA-OFDM

receiver model is also presented in Fig. 1. We denoted by RGI

the removing guard interval operation. Thus, for a bit duration,

the baseband received signal is given by

(2)

where is the additive noise that corrupts the received signal

with zero-mean and covariance equal to an diagonal ma-

trix . We denoted by the transmission of

licensed systems for which the covariance of is , a

diagonal matrix with its elements being zero for unused licensed

frequency and with a certain power seen by the unlicensed sys-

tems on licensed used frequencies. We assume that SPA-OFDM

system is designed in such a way that the SPA-OFDM sub-

carriers bands perfectly coincide with the licensed frequencybands.

After the FFT transform at the receiver site, we denote by

the following received signal:

(3)

Providing at the receiver side a replica of the bit spectrum pat-

tern vector, for each transmitted bit we employ a conventional

correlator where the decision variable for the bit is

(4)

The SINR for bit is given by (5), as shown at the bottom

of the page.

Considering that the transmitted information, the noise,

and the licensed transmissions are independent processes, the

th-bit SINR becomes (6), shown at the bottom of the page.

We define the interference function seen by a given bit de-

tector as the denominator of the th bit SINR

(7)

where

(8)

is the correlation matrix of the interference plus noise plus li-

censed activity seen in bit estimation process, and

is the correlation matrix of the received signal

defined in (3).

Our goal is to derive a distributed processing algorithm that

adjusts the transmitter spectrum precoding matrix and powers to

minimize the interference function associate with each bit, in thepresence of additive white Gaussian noise (AWGN) and narrow

band interference (NBI) from licensed transmissions, subject to

QoS constraints. According to (6), we note that the minimiza-

tion of the interference function is equivalent to the maximiza-

tion of user SINR for a fixed bit power.

III. PROBLEM FORMULATION

The control layers of the unlicensed system will define the

transmission rate depending on the current applications. From

the physical layer point of view, each bit has to be received with

an established probability of error or otherwise an SINR target,

, has to be obtained for each sent bit.As in the general case of OFDM systems, we consider that

the bits have equal powers, during an

OFDM symbol period. For flexibility, it is suitable to define

the cost function for each transmitted bit and not for the entire

system. Our approach allows us to design a system that has an

(5)

(6)


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adaptive traffic according to the upper layer applications of un-

licensed system and the network operating conditions. This is a

must for cognitive radio systems [26]. The total amount of infor-

mation will be regulated by the control layers of the unlicensed

system, which have to restrict the power transmitted by the unli-

censed system and the number of bits per OFDM symbol. Even

if the unlicensed transmitter does not have a precise informationabout the licensed traffic, it has the ability to adapt its transmis-

sion based on the received correlation matrix forwarded by the

unlicensed receiver. Different approaches of correlation matrix

feedback are proposed in [15], where the amount of feedback

information can be reduced significantly for the iterative algo-

rithms as in our case. In order to develop a distributed processing

algorithm, next, we define the bit spectrum pattern and power al-

location strategies under QoS constraints.

A. Spectrum Allocation Strategy

We associate the bit cost function with the interference

seen in decoding each bit, , defined in (7) for

. As we mentioned earlier, we have chosen the

interference function as a cost function because it is inversely

proportional to the bit SINR for a fixed power. In order to

minimize the transmitted bit cost function, the system spectrum

allocation strategy is the greedy adjustment of the bit spectrum

pattern, , for while the transmitted power

per bit is fixed to . The optimal bit spectrum patterns are found

by solving individually the constrained optimization problems

(9)

where the inputs are the previously transmitted bit spectrum pat-

tern, , and the received correlation matrix, . Based on (8)

can be found.

The Lagrange multiplier method is a classical approach to

solve individual optimization problem for which we construct

the Lagrangian

(10)

where represents the Lagrange multiplier associated with

the nonlinear constraint, for . From the Kuhn-

Tucker (KT) necessary condition, we find that the optimal bit

spectrum pattern has to satisfy the following condition:

(11)

with expressed in terms of the Lagrange multipliers , im-

plying that the optimal spectrum pattern has to be the eigen-

vector corresponding to the minimum eigenvalue of for

. This spectrum pattern optimization is similar

to optimal codeword optimization for the uplink of a CDMA/

FDMA systems. Optimal codewords that maximize the system

capacity, , and minimize the interference are a set of orthog-

onal sequences for or a set of Welch bound equality

(WBE) sequences if [21], [23]. For equal bit SINR

target, the minimum of all the interference functions is the samefor all the transmitted bits.

The spectrum pattern equilibrium point of the optimization

problem (9), is not unique, but it is

optimal because each bit player cost function reaches a unique

optimal value. According to [11] we can consider that our

problem has an asymptotic optimal equilibrium in the sense

that starting with an arbitrary bit spectrum pattern matrix

, minimizing individually the bit interfer-ence functions, the system converges to a fixed point, , for

which the interference function reaches its minimum for

.

B. Power Allocation Strategy

Assuming that each bit has to be received with the same SINR

target, , the received powers have to be the same for all the

bits corresponding to an OFDM symbol at the optimal equilib-

rium point [21], [23]. Once the system reaches its equilibrium

point, the algorithm adapts the power corresponding to each

transmitted bit to the value

(12)

The computation of the optimal transmitted power requires the

knowledge of the target SINR in addition to the parameters

employed in the optimization of the bit spectrum patters. The

power allocation is a power translation of the equilibrium point

of previous spectrum allocation that preserves the optimality of

the system equilibrium point.

The coexistence of a licensed and unlicensed systems in the

same frequency bands imposes additional restrictions regarding

the maximum transmitted power per frequency for the unli-

censed system. We assume that the received powers per each

frequency band are limited to a superior value for the unli-censed system. In all cases, is smaller than the transmitted

powers from the licensed systems, . In this

way, the unlicensed system will be able to sense any licensed

activity during its continuous transmission-reception process.

We will note the number of unused licensed frequencies by

, where is the number of licensed active users. This

knowledge is needed at higher control superior layers to decide

what application can be supported by the unlicensed system at

a certain instance of time. Additionally, the power limit, ,

assumed for the unlicensed system, can be regarded as an iso-

lation factor that is chosen to avoid the distortion of the active

licensed users transmissions.Based on previous characterization of the optimal spectrum

allocation [22], [23], when , the minimum bit power

allocation that corresponds to the minimum cost function is

(13)

For the case, the power allocation that corresponds to

the minimum cost function is

(14)

Next, we propose an admissibility condition for the maximumnumber of simultaneously transmitted bits, i.e., the maximum


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transmission rate per OFDM symbol, that can be accommo-

dated by the SPA-OFDM system without perturbing the active

licensed users. Thus, the sum of all bit received powers has to be

smaller than the total allowed powers to be received per unused

frequencies

(15)

From (13) and (15), the maximum number of transmitted bits

for the SPA-OFDM system subject to bit SINR and con-

straints is

(16)

According to the isolation that is established between the li-

censed and unlicensed systems, defined by , the control

layers of the SPA-OFDM system can decide how many and what

applications can be run by the system at any point of time. Thus,

when the unlicensed system wants to initiate a new application,it will inform the control layer about its intention. The control

layer decides if the application can be run or not, according to

the admissibility condition (16). Finally, it will notify the unli-

censed system about the possibility to start or discharge the new

application. On the other hand, the inequality (16) can be used to

define the QoS at the physical layer for a predefined number of

applications or predefined transmission rate per OFDM symbol,

, and maximum transmitted power on each unused frequency,

, as follows:

(17)

For a predefined bit SINR and restrictions on each frequency

defined by , the SPA-OFDM system has the freedom to

adapt its transmission rate, without perturbing the licensed

active users. The equilibrium point will be optimal and it is char-

acterized by the minimum power allocation for a predefined

SINR target, . Up to this point, we know that we have an

optimal equilibrium for the unlicensed system, providing that

the optimization problem (9) has an optimum equilibrium point

and the power allocation mechanism preserves the spectrum al-

location optimality. Next, we have to develop an algorithm that

drives the system toward the optimal equilibrium point and we

have to prove its convergence.

IV. ALGORITHM DERIVATIONS

The optimal bit spectrum patterns are found by solving indi-

vidually the constrained optimization problems (9). The solu-

tion suggested by (11) is not feasible in mobile end user com-

munications because of the computational complexity of re-

quired eigen value decomposition. For more robustness, it is

also preferable to use adaptive algorithms with very small ad-

justment steps toward the optimal point. Some such adaptive al-

gorithms can be found elsewhere, e.g., for power control, auto-

matic gaincontrol,equalization, andso on. has atmost

a global minimum over for , and to solvethe problem (9), we apply a normalized gradient method. Also,

the paper [20] suggested that a modified gradient method can be

a way to find the optimal equilibrium point for distributed op-

timization problems. For a feasible vector, , we generate

the next sequence according to the rule

(18)

where is the step size at moment and where the first

derivative of with respect to is

(19)

We will implement the iteration (18) as following:

(20)

for a fixed and small enough step size .

The proposed algorithm for interference minimization con-

sists of two stages. The first stage is a round robin iterations per-

formed sequentially for all transmitted bits per OFDM symbol,

in which the current bit spectrum pattern, , is replaced with

according to (18) up to the bit spectrum pattern equi-

librium point. In the second stage the algorithm adapts the power

according to (12) to meet the SINR constraints with the min-

imum power. Formally, we state the algorithm as below.

Algorithm

1) Input data: correlation matrix of the received

signal— , power limit , constant and tolerance.

2) If the admissibility condition (16) is satisfied GO TO

Step 3 ELSE reject the new request.

3) If the change in bit cost function is less than for any

transmitted bit GO TO Step 5, else GO TO Step 4.

4) For each bit do:

a) Compute using (8).

b) Replace its current bit spectrum pattern

with according to (18).

c) Go to step 3.

5) Adapt the power for transmitted bits to reach the target

SINR, , Go TO Step 2.

Assuming that the correlarion matrix of the received signal

is estimated at the receiver and made available at the trans-

mitter, the algorithm can be implemented in a distributed pro-

cessing manner and run independently for each transmitted bit.

We stress again, that our distributed processing algorithm al-

lows the unlicensed system to adapt dynamically the transmis-

sion rate by transmitting a variable number of bits with the same

target SINR . Thus, the algorithm allows the transition from

an optimal configuration to another one where the transmission

rate varies. The same dynamic properties cannot be exploited

for the centralized algorithms that employ the classical spectral

decomposition because they can be implemented just for a fixednumber of transmitted bits and fixed powers.


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Extensive simulations of the algorithm have shown that the

algorithm always reaches the optimal bit spectrum patterns that

are either orthogonal sequences for or WBE sequence

sets for the case. The tolerance and speed of conver-

gence of the algorithm can be adjusted through parameters ,

and similar to the case of gradient-based approaches. Next,

we will present explicitly the algorithm convergence proof andwill discuss the equilibrium point properties.

V. ALGORITHM CONVERGENCE AND THE

FIXED-POINT PROPERTIES

In order to prove the algorithm convergence, one can see that

the proposed normalized gradient method is similar to that of

gradient methods applied for convex optimization, but only for

the interference function defined in (7). Based on [3, Sec. IV], it

can be shown that there is a small enough step size such that

(21)

In order to prove the distributed processing algorithm conver-

gence, mathematical approaches define a function that globally

characterizes the system. In many cases, it is the sum of all cost

functions [10], [20]. Here, we define a metric that globally char-

acterizes the SPA-OFDM system behavior, that is the general-

ized total squared correlation defined according to [1]

as

(22)

where represents the Frobenius norm of the received cor-

relation matrix, . Expanding the function in terms of

[13], for any , we get

(23)

Now, in order to prove the algorithm convergence we have to

prove that the bit spectrum allocation procedure reaches its equi-

librium point, while the power allocation mechanism does not

change the problem optimality, but translates the spectrum allo-

cation equilibrium point. The algorithm consists of two stages,the first one is defined by the bit spectrum allocation proce-

dure, where each bit minimizes its interference function and the

second stage represents the bit power adaptation.

Proposition 1: The of the SPA-OFDM system con-

verges to a fixed point for the robin round bit spectrum pattern

iterations defined by the replacement of with

according to (18).

Proof: For each bit , we perform a robin round iteration

where the iteration of th bit is denoted by

(24)

At the iteration is replaced with :

(25)

where and represent the current and next iteration at

the moment for the th bit.

Based on inequality (21), we compare the from

(24) with from (25) and we get that

(26)

We notethat converges toa fixedpoint because itis lower

bounded and decreases with each iteration.

From (24), if is minimum then is also min-

imized for each bit . Given that has no local minima

other than the global minima [1], we can consider that oursystem converges asymptotically at the optimal equilibrium

point. It implies that the algorithm will provide an optimal

solution; however it is not unique. This result is according to

the previous spreading sequence design theory.

In order to assure a proper reception, each bit has to be re-

ceived with an established SINR threshold, , implying an

equal received power, p, for white or colored noise [22], [23].

The power allocation mechanism translate the optimum spec-

trum equilibrium point without changing the fixed point prop-

erties. Thus, the algorithm converges to a fixed point according

to Proposition 1.

Based on relation (11), for any transmitted bit , the

quadratic expression of each bit cost function reaches its

minimum when the codeword is the eigenvector

corresponding to the minimum eigenvalue of . The optimal

spectrum equilibrium point will be characterized by

(27)

with and the minimum eigenvalue and the corre-

sponding eigenvector of .

Based on relations (6) and (27) the maximum SINR of bit is

obtained using correlators that use the replica of the transmitted

bit spectrum pattern vectors for which the received bit SINR

becomes

(28)

According to [16], is the expression of SINR

obtained for the optimal linear receiver, the minimum mean

squared error (MMSE) receiver, that has the property to max-

imize the SINR in the presence of multiple access interference

and white/colored noise. It implies that for the optimal equilib-

rium point, the receiver that employs correlators with the trans-

mitted bit spectrum pattern replica for bit reception is equivalent

with the MMSE receiver. Thus, the optimal bit spectrum pattern

reduces the MMSE receiver to the simplest possible receiver, theconventional correlator for the optimal bit spectrum pattern and


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power allocation. The optimal bit power, , will be the minimum

power that satisfies (12) for a specified admissible rate .

We particularize the definition of sum capacity of a CDMA

system with colored noise [22] for SPA-OFDM system capacity

for a fixed bit power allocation, AWGN, and active licensed user

presence

(29)

According to [4] the system capacity of SPA-OFDM system

is Schur-concave, while the that is the norm of , is

a convex function for a fixed power , where is a positive

definite matrix. According to [4], [17] the bit spectrum pat-

terns that minimize the norm (23) will maximize the capacity

of SPA-OFDM system. Thus, the optimal bit spectrum patterns

will maximize the capacity, , of SPA-OFDM system for the

minimum power allocation subject to bit SINR constraints.

VI. SPA-OFDM SYSTEM ANALYSIS AND DISCUSSIONSFor a detailed study, Section VI-A presents the optimal bit

spectrum pattern and power allocations not only per bit, but also

per each subcarrier frequency for small systems. Section VI-B

analyzes the 128 SPA-OFDM system for different scenarios,

using the computer simulation methodology [14].

A. Algorithm Behavior

In this section we consider a SPA-OFDM system that trans-

mits a total of bits on orthogonal subcarriers and

AWGN with . The algorithm constants are ,

and tolerance . Plotting the BER, we always consider

during the next simulations. Experiment 1: Unlicensed User Rate Flexibility: We started

with the system where the unlicensed user transmits a total

number of bits on subcarriers with the target

SINRs and for which the algorithm designed

the transmit optimal bit spectrum pattern matrix

and powers

which satisfies , and implies that in

the resulting configuration the active bit spectrum patterns are

orthogonal.

We increase the number of transmitted bits of the system,

so that the new number of transmitted bits becomes ,

assuming that all bits have to meet the original target SINRs

. This change in the system transmitted rate triggers the

algorithm, which yields the bit spectrum pattern matrix shown

at the bottom of the page, and powers

The weighted correlation matrix is , and

is within similar tolerance from the corresponding matrix im-

plied by [23]. The power assignments of each bit per frequency

space are presented in Fig. 3 for the above two cases. This ex-

periment proved that SPA-OFDM is different from other OFDM

approaches, where the maximum transmitted rate was limited by

the maximum number of subcarriers. In SPA-OFDM systems,

there is the possibility to transmit with a higher rate than that of

the number of allocated frequencies if the transmitted power on

each frequency is less than the established threshold .

Experiment 2: Unlicensed and Licensed User Coexistence:We started with the system having a total of transmitted

bits on subcarriers, target SINRs and a licensed

user that transmits on the third

frequency band with a power equal to 1. The algorithm allocates

the optimal bit spectrum pattern matrix

and powers

Similar to the first case and

implies that in the re-

sulting configuration, the transmitted bits are orthogonal among

them and orthogonal to the licensed user. We increase the rate

of the transmitted unlicensed system by adding a bit, so that the

new number of transmitted bits becomes , and we as-

sume that this continues to keep the same target SINRs .

This change in system configuration triggers the algorithm

which in this case yields the bit spectrum pattern matrix

and powers


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Fig. 2. Bit power assignment on each frequency for AWGN presence (a) SPA-OFDM . (b) SPA-OFDM .

They satisfy

implying that in the resulting configuration, the transmitted bit

spectrum pattern vectors are a WBE set. Also,

implies that the bit spec-

trum pattern set is orthogonal on the licensed user. Thus, intro-

ducing individual bit optimization criteria and bit admissibilitycondition, we increase the rate and the system rate flexibility.

Fig. 3. Bit power assignment on each frequency for AWGN presence and li-censed user. (a) SPA-OFDM and one licensed user. (b) SPA-OFDM and one licensed user.

This system may accommodate a higher rate than that of the

conventional OFDM systems, but limited by the admissibility

condition (16). Thepower assignments of each bit per frequency

space are presented in Fig. 2 for the above two cases.

B. 128 SPA-OFDM System Simulation

To illustrate the performance of the dynamic spectrum and

power allocation procedure for cognitive radio environment, we

perform computer simulations [14] in which we obtain the biterror rate performance of the proposed unlicensed SPA-OFDM


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Fig. 4. BER performances of SPA-OFDM system for different transmittedrates.

system operating in the 850-MHz band in the presence of li-

censed transmission. We consider the SPA-OFDM system that

uses a total of orthogonal carrier frequencies. Each of

the 128 frequency subband occupies a bandwidth of 312.5 kHz,

resulting in a total bandwidth of 40 MHz for the system. Each

transmitted bit is spread in frequency by a unique bit spectrum

pattern designed using our distributed algorithm described in the

previous section. Depending upon the rate requirements of the

upper layer applications, the unlicensed system may transmitdifferent rates using several bit spectrum patterns that form the

matrix, . The SPA-OFDM system has to coexist with a nar-

rowband licensed system consisting of several channels, each

occupying a bandwidth smaller than 312.5 kHz similar to a

GSM system, that matches to our 128 SPA-OFDM subcarrier

bands. During presented simulations we will not take into ac-

count the losses introduced by the IGI.

Collaborating the algorithm behavior with the system be-

havior, we have tested the rate flexibility of SPA-OFDM system

to accommodate a higher number of unlicensed transmitted

bits, , than the number of subcarriers in the absence of the

licensed users. The results of this experiment are shown inFig. 4, where we can observe that when the number of trans-

mitted bits is less than or equal to the number of subcarriers

, the SPA-OFDM and the conventional OFDM system

have the same BER performances. This is because of the

orthogonality between the bit spectrum pattern vectors used to

overlay the user information across the available frequencies.

However, when the number of transmitted bits is greater

than , then the BER performance of the system deteriorates as

the transmission rate is increased. In order to obtain the same

BER of , the SPA-OFDM system with a transmission

rate of (bits/OFDM symbol) requires approximately

1 dB more signal-to-noise ratio (SNR) than the system with

(bits/OFDM symbol). We also note that when thetransmission rate is (bits/OFDM symbol) the BER

Fig. 5. Power spectrum density of the unlicensed transmission, AWGN, andlicensed activity.

curve levels off, which implies that the BER decreased very

slowly by increasing further the user powers. This is the point

when the allocated SINRs are very close to the limits imposed

by condition (17). For a fixed transmission rate beyond the

admissibility condition of the SPA-OFDM system, we can

increase the bit powers to infinity without any BER improve-

ments. However, the SPA-OFDM system has the ability to

accommodate higher rates than that of the conventional OFDMsystems.

To illustrate the ability of SPA-OFDM system to coexist with

the licensed systems, we first plot in Fig. 5 the power spectrum

density (PSD) of the transmitted signal for both systems along

with the AWGN for a SNR level equal to zero. In our exper-

iment the licensed user transmitted powers are 10 dB higher

than the . The licensed systems consist of 30 channels

distributed across the total available bandwidth, while there are

98 transmitted bits for the SPA-OFDM system. The unlicensed

system designs the spectrum pattern matrix according to the

upper layer rate requests and interference levels seen for each

transmitted bit, using the distributed algorithm described inthe previous section. Each bit is spread in frequency where the

subcarriers occupied by the licensed users are avoided ensuring

smooth coexistence of the two systems. We observe from Fig. 6

that there are spectrum nulls in the PSD of the transmitted

signal corresponding to the licensed system transmission,

thereby decreasing with around 35 dB the mutual interference

between the two systems. Additionally, we noted that the

unlicensed system whitens the PSD of transmitted signal on

free subchannels making the transmitted signal to look like

noise. These properties can be exploited to improve the system

security by designing bit spectrum patterns that maximize the

system performances while appear as noise for outside users.

In fact we have an infinity of optimal bit spectrum pattern sets[Section III] that depend on random factors such as the start


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Fig. 6. Power spectrum density characteristics of the unlicensed transmissionin the presence of AWGN and licensed activity.

Fig. 7. BER performances of SPA-OFDM system for different number of ac-tive licensed users.

configuration, the number of transmitted bits at a moment,the number of occupied licensed frequencies or the channel

conditions.

We then study the performance of the unlicensed system in

the presence of licensed users, . We consider a system with

a fixed total number of transmitted bits and a vari-

able number of channels occupied by the licensed system. Fig. 7

shows that the BER performance of the unlicensed system when

the licensed users occupy subchannels is identical

to a system with no active licensed users. Thus, the optimal

spreading on frequency of the information bits helps to elimi-

nate the mutual interference between the two systems. We also

note that the BER performance of the SPA-OFDM system de-

teriorates by increasing the number of subchannels occupied bythe licensed users while keeping the same transmission rate

for 128 SPA-OFDM. For example, when the number of sub-

channels occupied by the licensed users is equal to the

SPA-OFDM system requires approximately 3 dB more trans-

mitted power per bit compared to the system with no interfering

licensed users for the same BER level of . Also as the

number of subchannels occupied by the licensed users increases

beyond 36 the BER curve levels off. This is the point when theallocated SINRs are very close to the limits imposed by admis-

sibility condition (17).

VII. CONCLUSION

In this paper, we introduced and analyzed a novel

SPA-OFDM system for unlicensed users in cognitive radio

operation. The system can adapt its rate according to the

upper layer applications and the presence of other licensed

transmissions. In order to improve the system rate flexibility

and preserve the spectrum usage, the distributed processing

algorithm is derived defining individual bit cost functions. The

SPA-OFDM system optimizes the bit spectrum patterns, while

the powers are adapted subject to SINR constraints. It is shown

that algorithm converges to an optimal solution even though

this solution is not unique.

We define an admissibility condition where the control layers

decide what applications can be run according to the maximum

allowed transmitted bits, . The algorithm is implemented

using the normalized gradient method that is an appropriate tool

to solve this constraint optimization problems. In all cases, the

optimal set of bit spectrum patterns and powers form a WBE set

for which the correlator implemented at the receiver behaves as

a MMSE filter. In this sense, both receivers maximize the user

SINR in the presence of MAI plus AWGN and active licensed

users. Also, for the optimal point, the system capacity is max-imized for the minimum power allocation. The incremental

bit spectrum pattern adaptation allows the transmitter to deal

with the dynamic behavior of the licensed users, removing the

mutual interference, while continuing to transmit and detect

information. The numerical examples and the 128 SPA-OFDM

system simulations proved the abilities of unlicensed users to

successfully coexist with other licensed and unlicensed users.

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Cătălin Lăcătuş received the Ph.D. degree from theUniversity of Texas at San Antonio in 2008 and theelectrical engineering diploma (withspecializationinradarsystems)from the Military Technical Academy,Bucharest, Romania, in 1994.

He was Head of Technical Staff for EasternRomanian Air Traffic Management Company and,starting in 1996, was a Senior Engineer at AerostarS.A. Romania, where he developed, tested, andvalidated telecommunication, air traffic manage-ment, avionics, and antenna systems. Currently,

he is a Radio Platform Development Engineer at Toyota-ITC. His researchinterest includes wideband sensing techniques, adaptive spectrum managementalgorithms for cognitive radio systems, navigation, and positioning systems.

David Akopian (M’00–SM’03) received the M.Sc.degree in radioelectronics from the Moscow Instituteof Physics and Technology, Moscow, USSR, in 1987and the Ph.D. degree in electrical engineering fromthe Tampere University of Technology, Tampere, Fin-land, in 1997.

He is an Associate Professor at the University of Texas at San Antonio. From 1999 to 2003, he was

a Senior Research Engineer and then Specialist withNokia Corporation. Prior to joining Nokia in 1999,he was a member of teaching and research staff of

Tampere University of Technology. His current research interests include digitalsignal processing algorithms for communication receivers, dedicated hardwarearchitectures, and positioning methods. He authored and co-authored more than20 patents and more than 90 publications.

Prasad Yaddanapudi received the B.E. degree fromthe University of Madra, Madra, India in 2000, theM.Sc. degree from University of Toledo, Toledo, OH,in 2002, and the Ph.D. degree from the University of Texas at San Antonio in 2007, all in electrical engi-neering.

His current area of research interests includedynamic spectrum allocation and co-existenceof OFDM-based cognitive radios and cross-layerdesign of wireless networks.

Mehdi Shadaram (S’83–M’84–SM’89) receivedthe Ph.D. degree in electrical engineering from theUniversity of Oklahoma in 1984.

He is the Briscoe Distinguished Professor in theDepartment of Electrical and Computer Engineeringand Associate Dean of Engineering at the Universityof Texas at San Antonio (UTSA). Prior to joiningUTSA in 2003,he wasthe Schellenger Endowed Pro-fessor and Chairman of the Department of Electrical

and Computer Engineering at the University of Texasat El Paso (UTEP). His main area of research activityis in the broadband analog and digital fiber optic and wireless communicationsystems. He has published more than 100 articles in refereed journals and con-ference proceedings. He has been either PI or Co-PI for numerous grants andcontracts, totaling more than $8 million in the past 15 years. NASA, Jet Propul-sion Laboratory, National Science Foundation, Office of Naval Research, De-partment of Defense, Department of Education, Texas Higher Education Co-ordinating Board, Texas Instruments and Lucent Technologies have funded hisresearch projects.

Dr. Shadaram is the recipient of the Best Teacher Award in the College of Engineering at UTEP in 1994 and a NASA monetary award for contributionsto space exploration. He has been the General Chair, Session Chair, TechnicalProgram Chair, and Panelist for several IEEE conferences. He is a Member of OSA, SPIE, ASEE, and HKN and a Professional Registered Engineer in theState of Texas.

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