	US 7,538,720 B2
	Simultaneous savings in bandwidth and energy using waveform design in presence of interference and noise
Unnikrishna Sreedharan Pillai, Harrington Park, N.J. (US)
Assigned to C & P Technologies, Inc., Closter, N.J. (US)
Filed on May 11, 2007, as Appl. No. 11/747,365.
Application 11/747365 is a continuation in part of application No. 11/623965, filed on Jan. 17, 2007.
Prior Publication US 2008/0169971 A1, Jul. 17, 2008
Int. Cl. G01S 7/28 (2006.01); G01S 7/35 (2006.01); G01S 13/02 (2006.01); G01S 13/00 (2006.01); G01S 7/00 (2006.01)

U.S. Cl. 342—196 [367/87; 342/82; 342/89; 342/159; 342/175; 342/195; 375/316; 375/346; 375/350]

22 Claims

16. An apparatus comprising

a transmitter;

a receiver; and

a computer processor;

wherein the computer processor is programmed to cause the transmitter to output a first transmit signal having a first transmit signal waveform;

wherein the computer processor is programmed to cause the transmitter to output a second transmit signal having a second transmit signal waveform;

wherein the first transmit signal is different from the second transmit signal and the first transmit signal waveform is different from the second transmit signal waveform;

wherein the first transmit signal has a prescribed bandwidth which is B_o;

wherein the first transmit signal has a prescribed energy which is E_o;

wherein the second transmit signal has a smaller bandwidth which is B_C;

wherein the second transmit signal has a smaller energy level which is E_c;

wherein the first transmit signal has a transform F_o(ω) which is determined by a user input into the computer processor;

wherein the second transmit signal has transform F₁(ω) whose magnitude function is given by

and wherein the first and second transmit signals have the same performance index SINR_ogiven by

in terms of target detection in interference and noise, when used in conjunction with a receiver filter for the receiver such that the receiver filter has a Fourier transform H_opt(ω) given by

wherein t_ois a decision instant at which the target signal is to be detected, and either F₁(ω) or F_o(ω) are substituted for F(ω) above accordingly.