Pulse compression is known as a technique to raise the signal to maximum sidelobe (signal-to-sidelobe) ratio to improve the target detection and range resolution abilities of the radar system. This technique allows a radar to simultaneously achieve the energy of a long pulse and the resolution of a short pulse without the high peak power which is required by a high energy short duration pulse [1]. One of the waveform designs suitable for pulse compression is phase-coded waveform design. The phase-coded waveform design is that a long pulse of duration
is divided into
subpulses each of width
. Each subpulse has a particular phase, which is selected in accordance with a given code sequence. The pulse compression ratio equals the number of subpulses
, where the bandwidth is
. In general, a phase-coded waveform with longer code word, in other words, higher pulse compression ratio, can have lower sidelobe of autocorrelation, relative to the mainlobe peak, so its main peak can be better distinguished. The relative lower sidelobe of autocorrelation is very important since range sidelobes are so harmful that they can mask main peaks caused by small targets situated near large targets. In addition, the cross-correlation property of the pulse compression codes should be considered in order to reduce the interference among radars when we choose a set of pulse compression codes to work in a Radar Sensor Network (RSN).

Much time and effort was put for designing sequences with impulsive autocorrelation functions (ACFs) and cross-correlation functions (CCFs) for radar target ranging and target detection. On one hand, for aperiodic sequences, it is known that for most binary sequences of length
the attainable sidelobe levels are approximately
[2, 3] and the mutual peak cross-correlations of the same-length sequences are much larger and are usually in the order of
to
. Later, set of binary sequences of length
with autocorrelation sidelobes and cross-correlation peak values of approximately
are studied in paper [4]. Besides, the small set of Kasami sequences and the Bent sequences could achieve maximum correlation values of approximately
. In addition to binary sequences, polyphase codes, with better Doppler tolerance and lower range sidelobes such as the Frank and P1 codes, the Butler-matrix derived P2 code, the linear-frequency-derived P3 and P4 codes were provided and intensively analyzed in [5–7]. Quadiphase [8] code could also reduce poor fall-off of the radiated spectrum and mismatch loss in the receiver pulse compression filter of biphase codes. Nevertheless, the range sidelobe of the polyphase codes can not be low enough to avoid masking returns from targets. Hence, considerable work has been done to reduce range sidelobes for the radar system. By suffering a small
loss, the authors in [9] present several binary pulse compression codes to greatly reduce sidelobes. In the previous paper [10], pulse compression using a digital-analog hybrid technique is studied to achieve very low range sidelobes for potential application to spaceborne rain radar. In the paper [11], time-domain weighting of the transmitted pulse is used and is able to achieve a range sidelobe level of
55 dB or better in flight tests. These sidelobe suppression methods, however, degrade the receiving resolution because of wider mainlobe.

On the other hand, for periodic sequences, the lowest periodic ACF that could be achieved for binary sequences, as in the case of
-sequences [12, 13] or Legendre sequences, is
. GMW [14] has the same periodic ACF properties, but posses larger linear complexity. Considering the nonbinary case, it is possible to find perfect sequences, such as two valued Golomb sequences, Ipatov ternary sequences, Frank sequences, Chu sequences, and modulatable sequences. However, it should be noted that for both binary and non-binary cases, it is impossible for the sequences to have perfect ACF and CCF simultaneously although ideal CCFs could be achieved alone. One can synthesize a set of non-binary sequences with impulsive ACF and the lower bound of CCF:
,
[15, 16], which is governed by Welch bound and Sidelnikov bound.

So far in the previous work, range sidelobes could hardly reach as low as zero. In addition, it has also been well proven that it is impossible to design a set of codes with ideal impulsive autocorrelation function and ideal zero cross-correlation functions, since the corresponding parameters have to be limited by certain bounds, such as Welch bound [15], Sidelnikov bound [16], Sarwate bound [17], and Levenshtein bound [18]. To overcome these difficulties, the new concepts, generalized orthogonality (GO), also called Zero Correlation Zone (ZCZ) is introduced. Based on ZCZ [19–21] concept, we propose a set of ternary codes, ZCZ sequence-pair set, which can reach zero autocorrelation sidelobe zero mutual cross-correlation peaks during Zero Correlation Zone. We also present and analyze a method to construct such ternary codes and subsequently apply them to a radar detection system. The method is that optimized punctured sequence-pair joins together with Hadamard matrix to construct optimized punctured ZCZ sequence-pairs set. An example is presented, investigated, and studied in the radar targets detection simulation system for the performance evaluation of the proposed ternary codes. Because of the outstanding property performance and well target detection performance in simulation system, the newly proposed codes can be useful candidates for pulse compression application in radar system.

The rest of the paper is organized as follows. Section 2 introduces the definitions and properties of ZCZPS. In Section 3, the optimized punctured ZCZPS is introduced, and a method using optimized punctured sequence-pair and Hadamard matrix to construct such codes is given and proved. In Section 4, the properties and ambiguity function of optimized punctured ZCZPS are simulated and analyzed. The performance of optimized punctured ZCZPS is investigated in radar targets detection system by comparing with P4 code in Section 5. In Section 6, conclusions are drawn on optimized punctured ZCZPS.