The advent of phased array radars and space-time adaptive processing has given radar designers the ability make radars adaptable on receive. The current state of radar technology allows the transmission of wavefields that vary across space, time, and frequency and that can be changed in rapid succession. The ability to exploit space-time adaptive processing is limited by the computational power available at the receiver, and increased flexibility on transmission only exacerbates this problem unless the waveforms are properly designed to simplify processing at the receiver.

相控阵雷达的出现和空时自适应处理使雷达设计人员能够让雷达适应接收。当前的雷达技术允许波场传输的时候在空间，时间和频率上变化，并且可以接连不断的变化。利用空时自适应处理的能力受到接收器处可用的计算能力的限制，并且增加的传输灵活性仅加剧了这个问题，除非波形被适当地设计以简化接收器处的处理。

Sixty years ago, efforts by Marcel Golay to improve the sensitivity of far infrared spectrometry led to the discovery of pairs of complementary sequences. Shortly thereafter, Welti proposed to use Golay sequences in radar, but they have found very limited application to date. This article shows that suitably transmitted and processed, radar waveforms based on Golay sequences provide new primitives for adaptive transmission that enable better detection and finer resolution, while managing computational complexity at the receiver.

六十年前，Marcel Golay努力提高远红外光谱的灵敏度，从而发现了互补序列对。 此后不久，Welti提出在雷达中使用Golay序列，但他们发现迄今为止应用非常有限。 本文表明，基于Golay序列的适当传输和处理的雷达波形为自适应传输提供了新的基元，可以实现更好的检测和更精细的分辨率，同时设法控制接收器的计算复杂性。

DEGREES OF FREEDOM AND RADAR SIGNAL PROCESSING

Advances in active sensing are enabled by the ability to control new degrees of freedom, and each new generation of radar platforms requires fundamental advances in radar signal processing. Later generations are distinguished by the increased dimensionality of the illumination pattern across the elements of the array (whether distributed or collocated), across available polarizations, and over time.

通过控制新自由度的能力实现了主动传感的进步，每一代新一代雷达平台都需要在雷达信号处理方面取得基本进展。

The simplest radars scan the antenna beam in azimuth and form an image of the environment by integrating one-dimensional views. Variation of pulse-repetition intervals (PRIs) resolves ambiguities, and processing of all ranges and Doppler shifts is simultaneous. Space-time adaptive processing (STAP) retains the single transmit beam direction but is electronically steerable, and digitization on receive enables adaptive beamforming to eliminate interference [30]. Advanced phased arrays introduce broad waveform adaptability (time, space, frequency,and polarization) leading to full distributed aperture functionality.These radars are able to transmit simultaneously in all directions, collect returns at multiple locations, and employ waveform adaptation to simplify signal processing.

最简单的雷达在方位角上扫描天线波束，并通过整合一维视图形成环境图像。脉冲重复间隔（PRI）的变化解决了模糊，并且所有距离和多普勒频移的处理是同时的。空时自适应处理（STAP）保留单个发射波束方向但是电子可操纵，接收数字化使能够自适应波束成形以消除干扰。先进的相控阵列引入了广泛的波形适应性（时间，空间，频率和极化），从而实现了完整的分布式孔径功能。这些雷达能够在所有方向上同时传输，在多个位置收集返回，并采用波形自适应来简化信号处理。

PHYSICAL DIVERSITY: SPACE AND POLARIZATION

fundamental objective of radar engineers is the design of waveforms that effectively utilize radar resources (transmitters and receivers) that are distributed spatially in polarization, time,and frequency. To comprehend the physical picture, assume N fully polarimetric transmit and M fully polarimetric receive antennas. Also assume narrowband transmission, where the waveforms take the form of relatively slow modulations on a carrier frequency at each transmitter, so that the scattering cross section is constant in frequency across the bandwidth of the waveform.
雷达工程师的一个基本目标是设计波形。该波形可以有效利用在极化，时间和频率空间分布的雷达资源（发射器和接收器）。为了理解物理场景，假设N个完全偏振发射天线和M个完全偏振接收天线。假设在每个发射机的远场中有一个散射体，所发射的信号以平面波的形式到达散射体，

All three of the situations fall under the umbrella of MIMO radar (although spatial separation without transmit waveform diversity is traditionally referred to a multistatic radar), but each presents a very different waveform design/adaptation challenge. For example, the effect of waveforms on performance for phased arrays can be understood in terms of ambiguity functions and array manifolds. Most of the literature on MIMO radar falls into this category although this is often not made clear.
所有这三种情况都属于MIMO雷达的范畴（尽管没有发射波形分集的空间分离传统上称为多基地雷达），但每种情况都呈现出非常不同的波形设计/适应挑战。 例如，可以根据模糊函数和阵列流形来理解波形对相控阵列性能的影响。 关于MIMO雷达的大多数文献都属于这一类，尽管这一点往往不明确。

WAVEFORM DIVERSITY

Modern radars are increasingly being equipped with arbitrary waveform generators that enable simultaneous transmission of different waveforms from different polarimetric antennas, even on a pulse-to-pulse basis. The available design space encompasses spatial location, polarization, time, and frequency. Thus, although we must respect time and bandwidth constraints, the number of possibilities is vast.
现代雷达越来越多地配备有任意波形发生器，即使在脉冲到脉冲的基础上，也可以同时传输来自不同极化天线的不同波形。 可用的设计空间包括空间位置，极化，时间和频率。 因此，尽管我们必须尊重时间和带宽限制，但可能性的数量是巨大的。
The complexity of the design problem motivates synthesis of waveforms from components having smaller time-bandwidth product and complementary properties. A waveform is assembled by sequencing the components in time and/or stacking them in frequency in such a way that they have negligible overlap. With this approach, the waveform design problem splits into two simpler pieces: the design of components that complement each other, and the design of time-frequency combinations of these components with desirable properties. Another advantage of modularity is that the time-frequency combinations can be varied in time to enable adaptive control of the radar’s operation.Examples of this approach include pulse trains of orthogonal waveforms (separation in time) and what is often referred to as orthogonal frequency division multiplexing (OFDM) radar,where waveforms are separated in frequency.
设计问题的复杂性促使从具有较小时间带宽积和互补特性的组件合成波形。 通过及时对组件进行排序和/或以频率堆叠它们以使它们具有可忽略的重叠来组装波形。 采用这种方法，波形设计问题分为两个较简单的部分：相互补充的组件设计，以及具有所需特性的这些组件的时频组合设计。 模块化的另一个优点是时频组合可以及时变化以实现对雷达操作的自适应控制。该方法的示例包括正交波形的脉冲序列（时间上的分离）和通常被称为正交频分多路复用（OFDM）雷达，波形在频率上分开。

THE RADAR AMBIGUITY FUNCTION

For simplicity, we postpone consideration of the spatial and polarization degrees of freedom and focus on time/frequency aspects (collocated transmitter and receiver). The radar ambiguity function is the standard and convenient device to express blurriness of a scene as a result of illumination by a radar waveform and processing of the return by correlating with the transmitted waveform—matched filtering [2], [13], [29]. This optimizes the post-processing signal-to-noise ratio (SNR). The ambiguity function is, in a very real sense, the point-spread function for the range-velocity plane. Provided the transmitter and receiver are collocated, the ambiguity function for a waveform w is
为简单起见，我们把考虑空间和极化自由度放在次要地位，并主要关注时间/频率方面（发射器和接收器同时考虑）。 雷达模糊函数是通过雷达波形照射表示场景模糊度的标准方便装置，通过与发射波形匹配滤波相关联来处理返回[2]，[13]，[29]。 这优化了后处理信噪比（SNR）。 在非常真实的意义上，模糊函数是范围 - 速度平面的点扩散函数。 如果发射器和接收器同时考虑，则波形w的模糊函数为