Cognitive waveform design for spectral coexistence
3.2 System model and problem formulation
joint design of the transmit code and receive filter in the presence of signal- independent disturbance is addressed, and the performance of the described algo- rithm analyzed. In Section 3.4, the signal-dependent interference environment is considered, and the effectiveness of the described procedure assessed. Finally, Section 3.5 is devoted to conclusions and proposals for possible future research tracks.
is the energy spectral density (ESD) of the fast-time codecand RkIðm;lÞ ¼
f2kf1k m¼l ej2pf2kðmlÞej2pf1kðmlÞ
j2pðmlÞ m6¼l 8>
<
>: ðm;lÞ 2f1;. . .;Ng2 (3.4)
Thus, denoting byEI, the amount of allowed interference, to overlay the radar with K coexisting telecommunication networks, the transmitted waveform has to fulfil the constraint
cyRIcEI (3.5)
where
RI ¼XK
k¼1
wkRkI (3.6)
Significantly, different weights and importance can be given to the coexisting wireless networks, for instance based on their distance from the radar, their relative angular positions with respect to the actual radar boresight, and their tactical importance (i.e., navigation systems, military communications, public services, etc.), by suitably choosing the coefficientswk0;k¼1;. . .;K.
3.2.1 Code design optimization problem
In this subsection, a waveform design approach that attempts to enhance the target detection probability while controlling both the amount of interfering energy produced in the licensed bands and some desirable features of the transmitted waveform is introduced. To this end, recall that in a Gaussian interference environ- ments, the detection probability is maximized by jointly designing the radar codec and the receive filterw2CN so as to optimize the SINR;defined as
SINRðc;wÞ ¼jaTj2jwycj2
wyM cð Þw (3.7)
To control some relevant features of the probing signal, other than an energy constraint, a similarity constraint is enforced on the transmit sequence, kcc0k2 e, where the parameter 0e2 rules the size of the trust hypervo- lume andc0 is a suitable reference code. There are several reasons that motivate the use of this constraint. In a nutshell, an unconstrained optimization can lead to signals with significant modulus variations, poor range resolution, high PSL and more generally with an undesired ambiguity function response. These drawbacks can be partially circumvented forcing the solution to be similar to a known codec0
ðkc0k2 ¼1Þ, which shares some nice properties such as constant modulus and a reasonable PSL.
Summarizing, leveraging on the aforementioned guidelines, the waveform design problem of interest can be formulated as the following non-convex opti- mization problem
P
maxc;w SINRðc;wÞ s:t: kck2¼1
cyRIcEI kcc0k2e 8>
>>
>>
<
>>
>>
>:
(3.8)
3.2.2 Cognitive spectrum awareness
To quantify and control the amount of interference induced on coexisting tele- communication networks, the radar needs to know the number K of coexisting licensed systems, their bandwidth (referred to as stop-band in the following and defined by the lower and upper normalized frequenciesf1kandf2k), and the penalty weightswk’s to assign to each competing system [see Equation (3.6)]. It is thus of paramount importance for the sensing radar to have an accurate, reliable and comprehensive radio environment awareness. REM [50] represents the key to gain the aforementioned spectrum cognizance that is at the base of an intelligent and agile spectrum management. First introduced by the Virginia Tech team [51] as the main foundation for a novel approach to CR networking, REM can be considered as anabstractionof real-world radio scenarios and can be considered as an inte- grated database digitizing and indexing the available e.m. information.
Figure 3.1 illustrates some REM multidomain knowledge sources represented by geographical features, available services and spectral regulations, locations and activities of telecommunication networks and previous sensing acquisitions (radio experiences and measurements) [52,53]. Indeed, the idea behind REM is to store and process a variety of data, so as to make possible the inference of a mul- titude of environmental characteristics, such as locations of transmitters, prevailing propagation conditions and estimates of spectrum usage over time and space.
Thus, REM offers a suitable vehicle of Cognitive Radio (CR) system support, which can be exploited by cognitive engines for most cognitive functionalities, such as situation awareness, learning, reasoning, planning and decision support.
To populate and update the REM, botha prioriknowledge as well as spectral sensing techniques (like feature-based signal detectors) can be used [53]. Further- more, as depicted in Figure 3.1, a dedicated sensor network could be also employed to improve the quality of the scenario monitoring. Obviously, the better the characterization and modelling of the radio environment, the more the system can benefit bya prioriinformation and past experiences and adapt to the operational environment. Summarizing, exploiting the REM, the radar can become aware of the surrounding e.m. environment; hence, it can intelligently use the available data/
information/knowledge sources to make an agile transmission suitably diversifying the probing waveform [29]. In addition, a prediction of the overlaid networks
coverage can be obtained and used together with the radar antenna pointing direction, to select a suitable weightwk for each stop-band.
3.2.3 Feasibility issues
The similarity and the spectral compatibility constraints are generally competing requirements that may lead to an unfeasible design problem. For instance, assuming e¼0 Problem P is infeasible wheneverc0yRIc0>EI. This motivates the study of the I/S achievable region for any fixed similarity codec0, namely, the set of the admissible interference and similarity levels. It is defined as
F¼fðEI;eÞ:EI lminðRIÞ;0e2; problem P is feasibleg (3.9) and represents the set of pairsðEI;eÞdefining a feasible Problem P. As shown in [47],Fshares some important features, reported below for completeness:
● Each point on the boundary ofFcan be computed in a polynomial time;
● Fis a convex set. From a practical point of view, this allows to control its accuracy description. In fact, the convex hull of the I/S levels ðEIi;eiÞ i¼1;. . .;Na, associated to an arbitrary set of Na admissible radar codes, is contained in the I/S region;
GIS
Service &
regulations Activity profile of telecommunication
networks Experience
Sensing fusion centre
Sensing module
Sensing module
Sensing module
Spectral characterization
Waveform adaptation
Cognitive radar adaptation Cognitive radar adaptation
REM
Figure 3.1 A pictorial representation of the REM and its usage in a cognitive radar
● Each point on the boundary ofF(withEI >lðRIÞ) is uniquely associated to a radar code (under some mild technical conditions). Hence, it is possible to associate to the boundary of the feasible region some important radar performance metrics, such as ISL, PSL and, obviously, the produced interference power.
A graphical example of I/S achievable region is given in Figure 3.2. Therein, it is assumed that the overlaid licensed radiating systems, spectrally coexisting with the radar of interest, are working over the following normalized (according to the sampling frequencyfs¼810 kHz) frequency bands [54]:
W1¼½0:0000;0:0617; W2¼½0:0988;0:2469; W3¼½0:2593;0:2840; W4¼½0:3086;0:3827; W5¼½0:4074;0:4938; W6¼½0:5185;0:5556; W7¼½0:9383;1:0000
(3.10) As reference waveformc0, a unitary norm complex linear frequency modulated (LFM) pulse with a duration of 200ms and a chirp rateKs¼ ð750103Þ=200106Þ
Hz/s is considered; moreover, wk¼1 for k¼1;. . .;7. Further details about the considered simulation setup can be found in Section 3.3.
Before concluding this section, it is worth pointing out that the radar designer can choose the pairðEI;eÞ, referred to in the sequel as operative point, to reasonably trade off spectral coexistence, desirable radar waveform characteristics and achievable SINR of the system. For instance, with respect to Figure 3.2, consideringðEI;eÞequal to the point A, the frequency coexistence of the radar with
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
ε
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
EI A
B
I/S achievable region boundary (EI, ε) = (0.066, 0.264) (EI, ε) = (0.066, 0.444) (EI, ε) = (0.066, 0.654) (EI, ε) = (0.235, 0.066)
Figure 3.2 I/S achievable region for chirp similarity code and K¼7 overlaid licensed wireless systems
the overlaid telecommunication networks is emphasized, with respect to choosing EI;e
ð Þequal to the point B. In the last case, other radar features, such as low PSL and/or ISL, are privileged.
The interested reader may refer to Appendix 3.6.1 for all the analytical details concerning the study of the I/S achievable region.