tailieunhanh - Fundamentals of Spread Spectrum Modulation phần 7

Điều này có thể được phân biệt đối với ρ và thiết lập bằng số không đến, về nguyên tắc, giải quyết cho ρopt, (từ quan điểm của jammer) tối ưu phần nhỏ của băng thông lây lan bị kẹt. Sau đó ρopt có thể được thay thế vào () để tạo ra một kết quả xác suất lỗi bit trường hợp xấu nhất. | FUNDAMENTALS OF SPREAD SPECTRUM MODULATION 55 the spread bandwidth being jammed the average probability of bit error is P 1 Pb 1 - p Pb 0 J p Pb Nữ Eb J P 1 p R W J 6-7 where M M - 1 -1 1 k log2 M Eb b 2 M - 1 k k 1 p k 1 N0 . . k 1 x This can be differentiated with respect to p and set equal to zero to in principle solve for popt which is the optimum from the standpoint of the jammer fraction of the spread bandwidth being jammed. Then popt can be substituted into to produce a result for the worst-case bit error probability. The mathematics is somewhat complex since transcendental equations must be solved. Details are given in 2 15 where it is shown that the worst-case bit error probability is kk _ . P max . Eb NJ - 2 kk for M 2 k for M 4 kk for M 8 kk for M 16. Typical performance results are plotted in Fig. 26. Instead of the exponential decrease of bit error probability with Eb Nj as in the case for Gaussian noise backgrounds the optimum jammer imposes a decrease as the inverse of Eb Nj . Note that the jammer must have knowledge of the communicator s signal-to-jamming energy ratio in order to impose this severe penalty. DPSK Data Modulation We again assume that the jammer concentrates its power in a fraction p of the FH DPSK bandwidth. When not jammed the noise power spectral density is Nt N . When jammed the noise power spectral density is Nt N0 Nj p. Thus since Pb exp -Eb Nt for binary DPSK the average probability of error for the FH DPSK system is Pb 2 1 - p exp E N 1 p exp -- N J P R W 1 p J . W Following the previous procedure of finding the optimum p by differentiation of and setting the result equal to zero we find that 1 popt P J W R . 56 FUNDAMENTALS OF SPREAD SPECTRUM MODULATION FIGURE 26 Performance of FH MFSK noncoherent in worst-case partial band jamming. When this value for p is substituted into the worst-case optimum from the jammer s standpoint bit error probability is found to be .Pi .