DSSS Sequence Even Acquisition Based on FFT

In direct sequence spread spectrum communication, the signal bandwidth is extended by multiplying the PN code and the signal, so that the signal cannot be recovered if the traditional receiver is still used. Therefore, at the receiving end, the same pseudo-random sequence used for spreading at the transmitting end performs correlation processing on the received spread spectrum signal to recover the original information. Since the interference signal is not related to the pseudo-random sequence, it is expanded at the receiving end, which greatly reduces the power of the interference signal falling within the signal frequency band, thereby improving the output signal-to-noise ratio of the system and achieving the purpose of anti-interference. It can be seen that the role of the spreading code in the direct spreading system is very important. In general, the selection of the PN code follows the receiving end and the transmitting end must use the same PN code (that is, the PN code requires synchronization) to complete the spreading Despread. However, the spreading codes can use different spreading codes at the transmitting end and the receiving end, and only need to satisfy certain conditions. Therefore, sequence pairs that meet the requirements of spread spectrum despreading can be used in direct-spread systems.

1 Sequence couple

Sequence pairs are one-dimensional arrays, assuming that a set of optimal sequence pairs X = (x0, x1, x2, ..., xN-1) and Y = (y0, y1, y2, ..., yN-1), N is Length, make up a set of optimal sequence pairs (X, Y), they are bipolar, so the value of X and Y is "+1" or "-1". The cross-correlation function of the two is:

If τ = 0, then R (X, Y) (τ) is the same-order autocorrelation or autocorrelation main lobe width. Similarly, if τ ≠ 0, then R (X, Y) (τ) is a different-order autocorrelation Correlation or autocorrelation sidelobe width. In the best sequence, the value of the autocorrelation function of the side lobe is 0. The correlation of the PN code is the key widely used in spread spectrum communication, and the best sequence pair is the autocorrelation with superior performance, so that it can be widely used in spread spectrum communication. For example: X = + 1 + 1 + 1-1-1-1 + 1 + 1 + 1-1-1-1-1 + 1 + 1 + 1-1-1-1-1, Y = + 1- 1 + 1 + 1-1 + 1 + 1-1 + 1-1-1 + 1-1-1 + 1-1-1 + 1-1-1. According to the formula, the correlation value of the best sequence pair is

, The main lobe value is 4, and the side lobe value is 0. The autocorrelation value of X is RX (0) = 20, the others are 13, 11, 10, 8, 7, 5, 4, 3, 2, 1, and 0; the autocorrelation function value of Y is the same as that of x. Although the correlation of (X, Y) is not ideal, its correlation performance has been greatly improved. However, in the DS system, if the second-largest correlation value of the spreading code is relatively large, it will affect the acquisition of the correlation peak, which will result in the PN code being out of synchronization. Therefore, the autocorrelation with superior performance plays an important role in the DS system . In order to study and compare the autocorrelation characteristics of the best sequence pair and the GOLD code and m sequence, suppose (X, Y) = (4E23E944, 4623E944), the GOLD code is (74FAB3AA), the m sequence is (483E3750), and the sequences are all 16 Hexadecimal, after conversion to binary, "1" stands for "1" and "0" stands for "-1". When the autocorrelation value is negative, it will also affect the judgment of the maximum correlation value, so it must be taken into account. It can be seen from Figure 1 that when the sequence length is the same, the m-sequence has the best auto-correlation, and the best sequence pair has a better auto-correlation than the GOLD code. Not only is the maximum correlation value less than the GOLD code, but also the second largest value Less than the GOLD code, the ratio of the maximum correlation value of the best sequence pair to the next-largest correlation value is 6/29 = 0.206 9, and the ratio of GOLD is 9/31 = 0.290 3, so this paper believes that the best sequence pair autocorrelation performance is better than GOLD code. The sequence pair is to weaken the main peak in exchange for the suppression of the side lobe, so the order of autocorrelation performance is m sequence, sequence pair, and GOLD code.

Since the autocorrelation of the sequence pair is better than that of the GOLD code, it can be applied to the DSSS, but unlike the general DSSS, the sequence pair X is used for spreading and Y is used for despreading at the receiving end.

The process of using sequence pairs for spreading can be analyzed mathematically. Let the transmission signal be:

u (t) = Acd (t) X (t) cos (2Ï€fct)

Where: d (t) is the baseband signal; Ac and fc are the amplitude and frequency of the modulated carrier. Received signal r (t) = Acd (t) X (t) cos (2Ï€fct) + i (t) + n (t), where i (t) = Acos (2Ï€fIt) is sine wave interference signal; n (t) For noise, demodulate and despread the signal:

When the system is in an environment with sinusoidal interference, the bit error rate performance of using sequence pairs is better than m-sequence and GOLD codes. Without sinusoidal interference, the performance of the sequence couple is the worst.

In the following, the relatively new theory of sequence pairs will be used in burst DS systems.