[1] In a coding system that uses complementary codes, the decoding process favors the geophysical signal and other radar returns which have been coded by the radar system, while interference signals may be attenuated. The attenuation is relative to the geophysical signal and is dependent on the spectral characteristics of the interference signal and the code used. An interference suppression factor (ISF) is defined as the ratio (in dB) of the power gains of the interference to that of the geophysical signals, as both traverse the coherent integration and decoding stages of the radar signal processor. ISF values of codes, in and around the zero Doppler frequency band, are obtained analytically, while the corresponding values for other frequency bands are estimated from simulations performed using the sinusoidal interference signal. The results show that codes having an equal number of opposite elements have superior performances over other codes as they have better values of ISF in and around the zero Doppler frequency band, a segment of the spectrum where the geophysical signal is expected. This is confirmed by the observations made using the middle and upper atmosphere radar in Japan, where other experiments intended to study the effectiveness of different codes have also been performed, and the results are reported.

[2] Complementary codes have been used in pulse coding techniques for clear-air radar systems for over 20 years [e.g., Schmidt et al., 1979; Woodman, 1980; Farley, 1985; Wakasugi and Fukao, 1985]. They are used to enhance range resolution performances of radar systems by maintaining the duty cycle of the transmitter at its optimum value despite demanding requirements that would otherwise reduce it to lower levels.

[3] The decoding process inherently favors the returned signals that have been coded, and has the potential to suppress interference signals that have not been coded by the radar system. The degree of suppression is relative to the geophysical signal and is dependent on the spectral characteristics of the interference signal and also on the code used. This aspect of complementary codes has been considered by Ghebrebrhan and Crochet [1992], Spano [1994], and Spano and Ghebrebrhan [1996a].

[4] In this paper, the interference suppression characteristics of complementary codes are studied quantitatively. For this, an interference suppression factor (ISF) is defined as the ratio of the power gains of the interference to that of the geophysical signals, as both traverse the coherent integration and decoding stages of the radar signal processor. ISF values of codes, in and around the zero Doppler frequency band, are obtained analytically, while the corresponding values at other frequency bands are estimated from simulations obtained using the sinusoidal interference signal. This is done by computing the ISF values of a sinusoidal signal for various frequencies corresponding to a desired frequency range within the receiver pass-band.

[5] Experimental observations were conducted with the MU radar using both generated and “natural” interference, and the results obtained are consistent with the corresponding results obtained from theoretical considerations.

2. Complementary Codes and the Decoding Process

[6] Although poly-phase complementary codes exist, bi-phase complementary codes are the most widely used types in ST/MST radar systems, which are also the ones considered here. A complementary code pair consists of two finite and equally long code sequences C_{0} and C_{1} which may be represented as [Golay, 1961], C_{0} = {c_{1}, c_{2}, …c_{N}} and, C_{1} = {c′_{1}, c′_{2}, …c′_{N}} such that c_{i}, c′_{i} ∈ {1, −1}, i = 1, 2, …N where N is the number of elements of each sequence and is termed the code length.

[7] Complementary code pairs have the important property that the sum of the auto correlation functions (ACF) of each of the two code sequences of the pair is equal to zero for all lags, except for the zero lag, where it becomes 2N [Golay, 1961].

[8] The sequences C_{0} and C_{1} are used to code two consecutive pulses P_{0} and P_{1}, where the coding process involves phase modulating (0, π) the pulses in accordance with the elements of the code sequences.

[9] The returned signals are sampled, with sample spacing of τ (which is equal to the subpulse width), and decoded using their respective codes. That is, the returns from pulse P_{0} are decoded using code sequence C_{0} and similarly the returns from P_{1} are decoded using C_{1}. The details are given next.

[10] Detailed treatment of the signals and processes at the various stages of the transmitting/receiving and processing channels of ST/MST radar systems is given by Spano and Ghebrebrhan [1996a]. Using notations similar to those of Ghebrebrhan [1990] and Ghebrebrhan and Crochet [1992], the returns due to pulse P_{0} are sampled at time instants t_{1}, t_{2}, …t_{R}, where R is the number of heights (or ranges) that are sampled. Similarly, the returns due to P_{1} are sampled at time instants t_{1} + T, t_{2} + T, …t_{R} + T, where T is the interpulse period (IPP). The sampled signal consists of the geophysical signal, and various types of interference as elaborated below. In order to simplify the analysis, we will consider first the geophysical signal. This is expressed in terms of the code elements and the contributions from the atmospheric range cells of interest. Thus the complex sampled voltage at the kth range gate, due to pulse P_{0}, may be expressed as

Similarly, the sampled voltage due to P_{1} is given by

The sign at the top of a variable indicates that the variable is complex valued, and the variable _{k} represents the effective contribution of range cell r_{k}, and contains the phase and amplitude information about the cell that we are seeking to extract through the decoding process.

[11] The decoded value for the kth range gate due to P_{0} is given by

The corresponding values due to P_{1} may be obtained similarly.

[12] Finally, the fully decoded value for the kth range gate is given by

[13] As is implied, expression (5) is not applicable to the first N − 1 range gates. These are the truncated ranges. The operations for the truncated ranges corresponding to those represented by expressions (3)–(5) for the untruncated ranges are given by Ghebrebrhan [1990].

[14] On the other hand, it is possible to get rid of the operation of full decoding of truncated ranges applicable to single code pairs by using appropriately chosen complementary code sequences. Spano and Ghebrebrhan [1996b] have shown that for complementary code lengths which can be expressed as a power of two (N = 4, 8, 16, 32, …), N/2 appropriately chosen complementary code pairs may be used. These are called optimal complementary code sequences. They have the important property that the truncated ranges can be normally decoded without the need to resort to special decoding procedures. In addition, optimal codes offer superior signal-to-noise ratio in the truncated ranges [Spano and Ghebrebrhan, 1996b].

3. Interference Suppression Factor (ISF)

[15] In general, the decoding process is expected to favor the signals that have been coded by the radar. These are the ones which have been transmitted by the radar and have been scattered by various targets. In this category is the geophysical signal, which is the desired one. The other signals include: (1) echoes from birds, airplanes, etc., (2) echoes from fixed targets (hills, sea, etc.), and (3) interference signals from the radar itself (coupling and associated phenomena). On the other hand, the radar system also receives signals that have not been coded by the radar system. In this category we find the following: (1) noise, both internal (electronic or receiver noise) and external (cosmic noise), (2) electromagnetic noise (noise from electric switches, power lines, etc.), and (3) various types of radio interference signals (radio, TV, other radar systems, etc.). Other forms of interference include d-c biases and also offsets which may not affect equally the in-phase and quadrature channels of the system.

[16] The decoding process may be compared to constructive and destructive interference in wave phenomena. It may be said that the decoding process enables the received radar echoes to add up constructively, while the uncoded interference signals are destructively integrated. Before elaborating these characteristics of the decoding process, we give the definition of the ISF.

3.1. Definition of the ISF

[17] The received and sampled radar signal is assumed to be composed of the geophysical and the interference signals. For the purpose of the present definition, the powers at each range gate of the interference signal, P_{ii}, and that of the geophysical signal, P_{ig}, are arbitrarily assumed to be equal, without loss of generality. The corresponding powers of the interference and geophysical signals after the coherent integration and decoding processes are P_{oi} and P_{og}, respectively. The ISF is then defined as [Ghebrebrhan and Crochet, 1992; Spano, 1994]

[18] In order to have a better view of this definition, it may be useful to consider the output interference power as a product of the interference input power and a variable k_{1} representing the effects of the coherent integration and the decoding processes. Similarly, the output power of the geophysical signal may be represented as a product of the geophysical signal input power and a variable k_{2}. As the input powers are assumed to be equal, ISF is essentially the ratio of k_{1} to k_{2} and gives a measure of the effect of the system on the output powers of the two signals. Both k_{1} and k_{2} may further be expressed as products of two variables each, with the first ones taking into account the effect of the coherent integration process and the other ones the effect of the code.

3.2. Computing the ISF

[19] In this subsection a very low frequency geophysical signal and three well known interference signals are considered, and the corresponding expressions for computing the ISF are derived. In the case of the geophysical signal, the assumption made is intended to simplify computations without loss of generality. In all cases, a complementary code pair of length N is used. To simplify the analysis further, only the decoding process is considered first. The effect of coherent integration is addressed later.

3.2.1. Very Low Frequency Interference

[20] Consider first a slowly varying geophysical signal which remains constant in amplitude (for at least two IPPs) and changes in phase in accordance with the code it has been coded with. The complex amplitude of this signal is denoted by . In practice, the geophysical signal has indeed a very low frequency, as compared to the signals that could possibly exist within the pass-band of the receiver filter, and the example given here is reasonable. Under this condition, and following the procedures of sampling and decoding of the preceding section, the expression of the power at the kth range gate becomes

with

where the asterisk sign denotes complex conjugation.

[21] The interference signal is now considered, and is also assumed to be similar to the geophysical signal except that it is not coded by the radar and is designated here by , with ∣∣ = ∣∣.

[22] Following similar procedures as above and setting

the interference power for the kth range gate after full decoding becomes

[23] By recognizing that is equal to P_{a} and using expression (6), the expression of the ISF for the kth range gate becomes

[24] As an example, if we consider the code pair of length 16 and having the sequences C_{0} = 166742 and C_{1} = 166435 in octal representation (chosen to save space, and obtained from the binary values of the sequences that result when −1 is replaced by zero), then N_{s} = 8 and ISF = −12.04 dB. This means that an interference signal having the same power as the geophysical signal before decoding is attenuated after decoding by 12.04 dB relative to the geophysical signal.

[25] It is important to note here that in order to perform decoding for one range gate, the decoding process is operating on N range gates, each having samples consisting of the geophysical and interference signal components. In a way it may be viewed as an “integration” process. The integration is coherent (only adds up) for the geophysical signal but incoherent (adds/subtracts) for the interference signal. Accordingly, the geophysical signal is amplified by a factor of 4N^{2} while the corresponding value for the interference signal is N_{s}^{2}. It is therefore clear that in absolute terms both the geophysical and the interference signals are amplified in this case by the decoding process. However, since N_{s} < N, the interference signal is always attenuated relative to the geophysical signal.

3.2.2. Noise Interference

[26] Consider a geophysical signal as described above, and white Gaussian noise interference signal denoted by _{n}. This interference signal has the same power as the geophysical signal before decoding and possesses the normal noise statistics. It can be shown that the noise power for the kth range gate after decoding is given by

where E{x} represents the mathematical expectation of x. By recognizing that E is the noise power before decoding, the expression for the ISF becomes

ISF is only a function of N, and is independent of the type of code used. For N = 16, the value of ISF is −15.05 dB. It is important to note here that in the case of white noise, the decoding process is equivalent to 2N coherent integrations.

3.2.3. Sinusoidal Interference

[27] The geophysical signal is assumed to be as in the previous cases, while the interference signal is assumed to be sinusoidal having peak amplitude equal to that of the geophysical signal. However, although the interference signal is uncoded, the geophysical signal is coded with the transmitted code. It is also to be recalled that, whereas the interference signal may have any value of frequency that is within the pass-band of the receiver filter, the geophysical signal is assumed to have very low frequency. Accordingly, the expression for the interference signal is given by

[28] Applying the procedures for sampling and decoding given above for the sinusoidal interference signal, the expression of the power for the decoded value corresponding to the kth range gate is given by

where β(ω, C_{0}, C_{1}) represents the degree of amplification of the interference power and C_{0} and C_{1} are the sequences of the code pair. Accordingly,

[29] The analytical expression for the function β(ω, C_{0}, C_{1}) has been derived by Spano and Ghebrebrhan [1996a, equation (94), p. 313] and is rather complicated, which limits its practical utility. Better insight is obtained through numerical simulation which is given next.

3.3. Numerical Simulations

[30] Due to the complexity of the expression of the decoded sinusoidal interference signal, it is instructive to use numerical simulation of the ISF, in order to have a good picture of the interference suppression characteristics of complementary codes. This approach was first used by Spano [1994]. The simulation program that has been developed for this purpose simulates the operations performed by the radar signal processing system.

3.3.1. Simulation of Complementary Code Pairs

[31] In order to make the simulations more general, the ISF values are given as a normalized value of fT, where f is the frequency and T is the interpulse period. Two complementary code pairs of length 16 are considered. The first code pair is the most popular code, possibly due to the ease with which it is generated [Rabiner and Gold, 1975], and it has already been studied by Wakasugi and Fukao [1985] using the MU radar system. For ease of reference, it is given the code name AB and has the sequences C_{0} = 166742 and C_{1} = 166435 in octal representation. Figure 1a shows the ISF for this code pair. The ISF for the second code pair, with code name of CD, is shown in Figure 1b. The two sequences of code CD are C_{0} = 051637 and C_{1} = 003312. To avoid confusion, the values of the number of coherent integrations (NCI) are represented in this paper as NCI1 and NCI2, where NCI1 has a value of 1 for codes AB and CD and a value of 2 for the uncoded pulse NC (to be considered later); and NCI2 equals 19 for codes AB and CD and equals 38 for NC. The number of pulses involved in both the coded and uncoded modes are identical and are equal to 2 and 38 for NCI1 and NCI2, respectively.

[32] It is to be noted that for code pair CD, N_{s} = 0. Spano [1994] has shown that such complementary codes exist only for N = x^{2}, where x is an even integer greater than zero (for N of 4, 16, 64, etc. as complementary code pairs do not exist for N of 36). For such codes, d-c interference signals are completely annihilated. This code pair has the advantage over the other pair in that it heavily attenuates interference signals in and around zero Doppler frequencies, where the geophysical signal is most likely to be found. In the other frequency bands, the two code pairs have similar performance, although the positions of their minimum and maximum values are different. It is seen that the minimum values of ∣ISF∣ for both of them are identical, namely 12.04 dB. It is interesting to note that the ISF value for code AB for very low frequency range agrees with the result obtained previously in 3.2.1.

3.3.2. Simulation of Complementary Code Sequences

[33] We consider here an optimal code sequence for N = 16, which consists of 8 code pairs. As stated above, optimal code sequences have the important property that, for the truncated ranges, the sum of all the partially decoded values of the individual code pairs results in the full decoding for those ranges. The sequences of the code pairs are given in Table 1. The ISF for these code sets is given in Figure 2a.

Table 1. Sequences Used in the Simulation of the Optimal Codes^{a}

Number

1

2

3

4

5

6

7

8

a

For ease of presentation, they are given here in octal format (see text for details of octal representation).

C_{0}

001632

123300

115003

140246

054700

001545

140131

062404

C_{1}

053317

171625

147526

112763

171552

124717

065363

147651

[34] It is interesting to plot the ISF for the truncated ranges. For this we need to calculate the corresponding powers for the desired and interference signals. Normally, the optimal codes have N sequences. That is, if we take N of 16 as an example, the optimal codes consist of 8 code pairs or 16 code sequences. Taking this into consideration, it is not difficult to see that for the geophysical signal, relation (7) is modified as

[35]Figure 2b gives the plot of the ISF for the 14th gate of the truncated ranges. The ISF value close to the zero Doppler frequency (for fT = 0.001) of the truncated range gates, along with one gate of the untruncated ranges, is given in Figure 3, in order to indicate the situation in the other truncated ranges.

3.3.3. Other Simulations

[36] It is interesting to present results of simulations of some well known pulse combinations. The plot for an uncoded pulse (NC mode) is shown in Figure 4a. In some ST/MST radar systems, 180 degree phase flipping is done on every other pulse to minimize d-c offset biases. The plot for this configuration is shown in Figure 4b. A similar configuration with phase flipping applied to code pair AB results in the plot shown in Figure 4c. The flipped version of AB has sequences whose elements are the inverse of the corresponding elements of the corresponding sequences of AB. That is, the transmitted sequences consist of 4 pulses, namely C_{0} and C_{1} of AB followed by their corresponding inverses.

3.4. Comparison of ISFs

[37] When comparing ISF performances of codes, it is useful to realize that ISF is negative and high suppression corresponds to high negative value of ISF. For the purpose of this paper, when comparisons are involved, the absolute values are implied even if it is not explicitly stated. In this context, CD has a higher value of ISF than AB in and around the zero Doppler frequency band (Figure 1).

[38] In order to see the ISF characteristics of the codes better, we compare the ISF values for the case of white noise and the sinusoidal interference signals. In the case of white noise, relation (13) gives the result. On the other hand, for the case of the sinusoidal interference signal, we should some how try to get an analytic expression that may help in comparing performances. As an approximate expression, we take it to be equal to the rather conservative value of ISF_{min}, which for the case of Figure 1 is 12 dB. This can be shown to be given by

where

with

and

[39] It is explained next that all code pairs of the same length have identical N_{pq}. This is also reflected in the simulated cases. This may be elaborated as follows.

[40] The complementary property may be stated in another way [see Ghebrebrhan et al., 1992]. Let p and q represent the number of 1's in C_{0} and C_{1}, respectively. By considering complementarity arguments, Golay [1961] has derived an equation relating N, p, and q given as

[41] The values of p and q for code lengths from 4 to 32 are given in Table 2. It is implied from Table 2 that for a given N, N_{pq} is the same for all code pairs of the same length.

Table 2. A List of the Number of 1's in the Two Sequences of Complementary Code Pairs for the Various Code Lengths^{a}

N

4

8

10

16

20

26

32

a

Note that the complement values are not shown here, but they could easily be obtained. As an example, for the case of length 10, 4 could be used in place of 6 and 3 could be used in place of 7.

p

3

4

6

6

7

11

16

q

1

6

7

10

9

16

20

[42] The ISF values for the noise and the sinusoidal interference signals are then computed for various values of N. The result is shown in Figure 5. It can be concluded from this that the decoding process discriminates almost equally the noise and the sinusoidal interference signals.

3.5. Subcomplementary Codes

[43] The range of high ∣ISF∣ values around the radar center frequency, associated with codes of type CD, may be extended substantially by using codes having N_{p} = N_{q} = 0. Such codes are close to, but not strictly, complementary, and are called subcomplementary codes. They have the property that the sum of the autocorrelation functions of the two codes is equal to zero, except for the 0 and 1 lags, where it is equal to 2N and −N, respectively.

[44] The presence of the sidelobes at lag 1 is the price that one has to pay for the advantage gained by the interference suppression capacity of the codes. Sulzer and Woodman [1984] have also relaxed the constraints on complementarity to obtain quasi-complementary codes which are good at minimizing the effects of instrumental imperfections. Details of subcomplementary codes and their interference characteristics are given by Ghebrebrhan et al. [2003].

3.6. Effects of the Coherent Integration Process

[45] The coherent integration process may be viewed as a digital low-pass filter having a transfer function given by [Schmidt et al., 1979]

[46] The ISF plot for the uncoded pulse is shown for NCI = 38 in Figure 6a. Similarly, the ISF plots of the complementary code pairs considered when both the coherent integration and the decoding processes are included are shown for NCI = 19 in Figures 6b and 6c. We recall that the total number of pulses is the same in both cases.

[47] Reference to the simulation results indicates that the ISF_{min} values of Figure 1, which were of the order of 12 dB, have jumped to about 40 dB on the average (see Figures 6b and 6c) when the effect of coherent integration is taken into account. In this case, the coherent integration process is the main contributor to the ISF. By way of elaborating on the variables k_{1} and k_{2} (see 3.1 above), and using the computational tools developed so far, the effects of the coherent integration and the decoding processes are summarized in Table 3.

Table 3. The Expressions of the Powers of the Three Signals After the Operations of Coherent Integration (NCI), and Decoding (DECOD), and the Corresponding Expressions for the ISF^{a}

Signal

Power in

NCI

DECOD

ISF

a

Note that the expression for K could be obtained as a function of the frequency of the interference and the number of coherent integrations NCI by realizing the effect of the coherent integration process.

Geophysical

P_{a}

N_{CI}^{2}P_{a}

4N_{CI}^{2}N^{2}P_{a}

0

Interference

P_{a}

KP_{a}

KN_{pq}^{2}P_{a}

10 log_{10}

Noise

P_{a}

N_{CI}P_{a}

2N_{CI}NP_{a}

−10 log_{10}(2NN_{CI})

4. Experimental Observations

[48] The interference suppression characteristics of complementary codes have been experimentally investigated using the Japanese 46.5 MHz MU radar [Fukao et al., 1985a, 1985b, 1990; Yamamoto et al., 1996]. The set of observation parameters used are given in Table 4. Code pairs AB and CD, as well as the uncoded pulse NC, have been tested in the presence of generated and “natural” interferences. First, we present results for the case of generated interference. Since their frequencies are selected as needed, this experiment permitted us to check quantitatively the theoretical and simulation results. Next, “natural” interferences are considered. Results of analyses are shown for two interesting periods during which “strong” and “mild” interferences of unknown frequencies occurred. The mild interference signal appeared as a single frequency mainly at the edges of the displayed Doppler frequency spectra while the strong interference signal appeared to have multiple frequencies. The interference signals did not appear all the time, but it was possible to get several hours of observations when they were present.

Table 4. Parameters Used During the Radar Experiment^{a}

Mode

IPP, μs

NFFT

N_{CI1}/2

N_{II}

a

The three modes were run in a cyclic mode, one after the other, as NC, AB, CD, first with NCI = NCI2 and then with NCI = NCI1. N_{II} represents the value of the number of incoherent spectral averaging.

NC

400

128

2/38

5

AB

400

128

1/19

5

CD

400

128

1/19

5

4.1. Observations With Generated Interference

[49] For this experiment, we used a synchronized signal generator feeding a dipole antenna placed near the MU radar antenna array. The transmitted power (1 W) did not saturate the radar receiver. The transmitted frequencies were f_{c} + f where f_{c} is the carrier frequency of the MU radar (46.5 MHz) and f values are small frequency shifts introduced for simulating electromagnetic interferences near the center of the receiver bandwidth. The normalized frequency shifts fT (T = IPP = 400 μs) are shown in Table 5. For each fT value, the radar was operated sequentially in three modes: (1) the uncoded 1 μs pulse (NC); (2) the 16-bit complementary code pair AB; and (3) the second 16-bit complementary code pair CD (with its present configuration, the MU radar is not able to use optimal complementary code sequences). A subcomplementary code pair was also used but the results are not shown here since this code is not discussed in the present paper. The radar was not in transmission mode (but in reception only) in order to avoid the undesired geophysical signals and other perturbations resulting from airplanes for example. The number of coherent integrations used for this experiment is NCI1.

Table 5. Sequences of fT Values at Three Frequency Bands That Were Used in the Generated Interference Observations

fT

fT

fT

0.0

10.0

100.0

0.01

10.01

100.01

0.05

10.05

100.05

0.1

10.1

100.1

0.5

10.5

100.5

1.0

11.0

101.0

[50] The noise and interference powers are computed by first determining the noise level using the Hildebrand and Sekhon [1974] method. The noise power is obtained as a product of the noise level and the number of FFT points. The interference power is computed by summing up the net interference powers above the noise level for the spectral points around the selected peak. Three successive spectra for each configuration were recorded in order to calculate the noise and interference power averages. The spectra were also averaged in altitude, i.e., an average spectrum corresponding to the 128 sampled gates was calculated. This data processing permitted us to get very reliable estimates of the noise and interference powers. We then calculated the interference to noise ratio (INR) as the ratio of the interference to noise powers, for the three modes and for each fT value and compared (in relative values) with the theoretical ISF for each of these configurations. The result is shown in Figure 7 for the fT band [0.01–1.0]. Unfortunately, the values for fT = 0.01 are missing due to a manipulation error. Excellent agreement is found between the experimental and theoretical values validating the ISF plots in Figures 1a and 1b for AB and CD and Figure 4a for NC. It also confirms that noncoded interference of frequencies within the Doppler range of geophysical signals are more attenuated by CD than by AB or NC.

4.2. Observations With “Natural” Interference

[51] For the two observation periods for which “natural” interference occured, the radar was operated in a cyclic sequence using NC, AB, and CD. The set of observation parameters used are given in Table 4 for NCI1 and NCI2. NCI2 is the one used in routine observations with the MU radar, and NCI1 was used in order to reduce the frequency aliasing of the interference signal as much as possible and get a better view of its frequency spectrum. In all observations, 128 ranges were sampled, and the antenna was pointing in the vertical direction.

4.2.1. Performance in the Case of Strong Interference

[52] Nature of the interference: The strong interference was observed during the time period of 2 to 5 April 2001 and manifested itself as multipeaks filling the entire width of the displayed Doppler spectrum masking the geophysical signal even at lower altitudes (where it is expected to be strong). The nature and characteristics of this interference signal have not changed throughout the observation period, and representative figures are chosen and presented. A typical averaged set of Doppler spectra for the three modes of operation is shown in Figure 8. All the peaks in this figure are interference signals and the crosses at the bottom represent the locations (in frequency) of the peaks, while the noise level is indicated by the horizontal line towards the bottom of the peaks.

[53] Data processing: The data were processed with two objectives in mind. The first objective was to estimate the noise and interference powers in order to get the interference-to-noise power ratio (INR), while the second objective aims at estimating the geophysical signal power for determining the signal-to-noise power ratio (SNR). In order to get a good measure (smoothed) of the interference and noise powers, the last 32 of the 128 range gates of the profiles were averaged to obtain the mean noise and interference powers of each profile (the averaging consists in adding the values of corresponding spectral points of the last 32 range gates and dividing by 32). Since the radar was in transmission mode the lower altitudes were left out to minimize the effects of the geophysical signal. To estimate the geophysical signal power, the first 40 altitudes were considered as it was felt that the signal may only be expected with a high degree of reliability in those altitude ranges.

[54] The INR is computed from the averaged spectra in the following manner. First the noise power density is determined using the Hildebrand and Sekhon [1974] method, and the noise power is obtained as a product of the noise level and the number of FFT points. Then, the interference power is obtained by first identifying the spectral points with values exceeding the noise level, and then adding the corresponding values above this level. This means that all interference peaks are added up. Finally, the INR is obtained as the ratio of the interference to noise powers. The process was applied to the experimental data in an automatic manner. Representative plots of the INR values (in dB) for the three modes (NC, AB, and CD) are shown in Figure 9 for 5 April 2001. The results corresponding to NCI2 are shown in Figure 9a, and those for NCI1 are shown in Figure 9b. Comparing Figures 9a and 9b, the smoothing effect of the coherent integration process is recognizable, as this process is indeed a form of low-pass digital filtering process. The mean values of the interference and noise powers for the entire data of Figure 9 are tabulated in Table 6. In determining these values, very large entries such as those of the airplane echoes shown in Figure 9a have been rejected.

Table 6. Mean Values of the Noise and Interference Powers of the Three Modes Corresponding to the Data of Figures 9 and 10^{a}

Units are in dB. The averaging is done over all records shown in the figures. However, very large values, essentially those originating from airplane echoes, have been rejected.

b

Values obtained with NCI2.

c

Values obtained with NCI1.

NC

56.77

54.55

50.62

44.31

49.71

AB

69.05

66.62

74.35

56.07

60.20

CD

68.68

67.23

74.00

55.80

62.70

[55] As stated earlier, the geophysical signal power is estimated from the averaged spectra (averaging done as above), of the first 40 range gates, where the geophysical signal is expected most. In computing the powers of the geophysical signal, the mean noise levels in Table 6 were used for the corresponding modes. As the antenna was pointing in the vertical direction, the geophysical signal is expected to be close to the zero Doppler frequency band, and the peak within this band is attributed to the geophysical signal. Once the peak is identified, the power of the geophysical signal is obtained by summing the values above the noise level of the spectral points around the peak. As most of the interference signal was falling outside the frequency area of the geophysical signal, the estimated value is believed to be reasonable (large values have been rejected as they are suspected to be due to interference signals). The SNR is then obtained as the ratio of the signal to noise powers. Figure 10 shows plots of the SNR of the data set of Figure 9, for the three modes of observations for the case of NCI2. The corresponding mean values are also tabulated in Table 6 along with the other values mentioned earlier. Due to the low value of coherent integration, it was not feasible to determine the mean powers of the geophysical signal for the case of NCI1. It would be appropriate to remark here that in estimating the geophysical signal power, the objective is to obtain reasonable estimates for comparison purposes.

[56] Noise power comparisons: Reference is made to Table 6 (where the noise powers are tabulated with other values) and considering the case for NCI2, modes AB and CD have similar powers, which is expected. The difference between NC and AB or CD is also close to what is expected (about 12 dB, see Table 3). Considering the case of NCI1, it is observed that the results of the corresponding comparisons are similar to those of NCI2.

[57] Interference power comparisons: The comparison of interference powers is made along similar lines as for the noise. The difference between the powers corresponding to NC and AB or CD for the case of NCI1 is more or less equal to what is expected (about 12 dB, see Table 3). The discrepancy is attributed to the intensity fluctuation of the interference signal. The results of the corresponding comparisons for the case of NCI2 is similar. It is important to emphasize here that the noise and the interference signals have been scaled (affected) almost equally by the decoding process.

[58] Geophysical signal power comparisons: Reference is again made to Table 6, where in this case only the geophysical signal powers for the case of NCI2 are available. The difference in the geophysical signal powers in the case of modes NC and that of AB or CD is close to 24 dB, which is expected (see Table 3). It is interesting to note that, while the increase in the geophysical signal from mode NC to mode AB or CD is of the order of 24 dB, the corresponding increase in the noise and the interference signals are of the order of 12 dB. It may be said then, that the decoding process attenuates the interference or noise signals, relative to the geophysical signal, by about 12 dB. This is the component of the ISF attributed to the decoding process. This is also reflected in the SNR plots of Figure 10.

4.2.2. Performances in the Case of “Mild” Interference

[59] During the observations of 06 April 2001, a mild interference appeared in the spectral profiles of NC and AB, but it was absent in CD. In an attempt to quantify performance, the presentation shown in Figure 11 is opted. The three dimentional plots shown have been obtained from the observations consisting of 127 records of spectral profiles of each configuration (NC, AB, and CD). Every spectral profile consists of 128 sampled altitudes. As shown in the figure, the vertical axis indicates the number of times a point (in the altitude-frequency plane) has been in the position of the selected peak.

[60] For the case of CD, the selected peaks were mostly near the zero Doppler frequency range, indicating that the selected peaks were due to the geophysical signal. On the other hand, for modes NC and AB, a number of peaks are selected far from the zero Doppler frequency band pointing that these are due to interference signals. The profiles show significant interference for the cases of NC and AB, but the interference is completely suppressed in the case of CD. The superiority of CD over NC and AB, in this case, is evident indicating that the frequency of the interference is within the range of suppression effectiveness of CD.

5. Discussion

[61] Simulation using the sinusoidal interference signal is a powerful tool for the study of the ISF characteristics at any frequency band of interest. The simulation results shown above may be classified into two groups, namely, those having very high ISF values in and around the zero Doppler frequency band (like CD) and those having the opposite properties (like NC and AB). For reference purposes, we designate the first group as type 1 and the second group as type 2. The main difference between the two types is the difference in the positions of the peaks and nulls. Due to the presence of d-c biases and other interference signals in and around the zero Doppler frequency band, good ISF values at this frequency band are desired. Accordingly, type 1 group is preferred to type 2 group. For this reason, type 2 group is usually converted in practice to type 1 group using the scheme presented earlier (see Figure 4). However, a closer look at the ISF simulations for CD and the converted version for AB (Figure 4c) reveals that the region of good ISF values for CD (around the zero Doppler frequency band) is wider than the corresponding value for the inverted version of AB.

[62] Outside of the zero Doppler frequency band, the ISF characteristics of type 1 and type 2 groups are similar, although the peaks and nulls are at different positions. For interference occupying wider frequency bands, it becomes useful to consider mean ISF values, and the approach of section 3.4 is appropriate for this case.

[63] With reference to Figure 9, it is observed that the curves for the three modes are similar. This confirms that both noise and interference signals are attenuated similarly. This is in contrast to Figure 10, where the SNR of AB and CD are greater than the corresponding values for NC by about 12 dB, confirming that the decoding process has not attenuated the geophysical signal (see also Tables 3 and 6).

[64] On the other hand, a closer observation at Figure 9 reveals that the curve for CD is mostly above the other curves indicating that the interference signal in this mode has been relatively less attenuated. Further, it is observed that the curve for NC is mostly above that of AB. These observations are consistent with the simulation results of Figures 1 and 4, if the larger part of the interference signal falls in frequency segments where CD has lower suppression effects than AB and NC. In contrast, in the case of Figure 11, the interference signal is falling on a single frequency segment, which has a higher suppression for CD and a lower one for NC and AB. Whereas NC and AB are marginally performing better than CD in the former case, CD is performing much better than NC and AB in the latter case. Comparing Figures 9a and 9b, the smoothing effect of the coherent integration process is recognizable, as this process is indeed a form of low-pass digital filtering process.

6. Summary and Conclusion

[65] Using the sinusoidal interference signal, it was possible to investigate the ISF characteristics outside the zero Doppler frequency band and the results show that, overall, all complementary code pairs have similar ISF performances, although the positions of the peaks and nulls may be different. The results of experimental observations performed with the MU radar using generated interference signals are consistent with theoretical results. Likewise, the corresponding results obtained in the presence of “natural” interference signals are interpreted to be compatible with the theoretical results. The results also show that it is possible to suppress narrow band interference signals through the use of appropriate codes, while it becomes difficult (if not impossible) to handle wide band interference. For wide band interference, like the strong interference considered in this paper, choice of the most appropriate codes may only give marginal improvements.

[66] In addition to the desired geophysical signals, the frequency band close to the zero Doppler frequency also contains the unwanted biases and other interference originating from the system, some of which may be constant while others may be varying slowly with time. Although the effects of the constant components may be handled by ignoring the zero FFT point, the slowly varying components should also be dealt with. Type 1 complementary code pairs, whose ISF characteristics have been investigated in this paper together with other configurations, are good candidates for suppressing such interference. Of the type 1 family of codes, those of type CD have relatively wider frequency range of effectiveness of interference suppression. Accordingly, although specific cases may require specific solutions, in view of the importance of the zero Doppler frequency band, and given that all codes have similar mean ISF performances at other frequency bands, it is generally concluded that code pairs of type CD are the preferred codes in suppressing interference as they have better performances in the zero Doppler frequency band, a segment of the frequency band where the geophysical signal is expected most. In the event that there is a need for using type 2 codes, then it is important to effect phase flipping in order to suppress interference in and around the zero Doppler frequency band.

Acknowledgments

[67] Fruitful discussions with M. Crochet and E. Spano at the initial stages of this work are gratefully acknowledged. We also thank H. Hashiguchi for his support with computer facilities. Rudy Wiens read the entire manuscript and made useful comments. The research of the paper was accomplished while the first author (O.G.) was a visiting professor at RASC and H.L. was a Japan Society for Promotion of Science postdoctoral fellow at RASC. The MU radar belongs to and is operated by the RASC, Kyoto University.