Joint optimization of PAPR reduction based on modified TR scheme for MIMO-OFDM radar

Abstract

In this paper, we propose a joint optimization method to reduce peak-to-average power ratio (PAPR) for multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) radar systems, based on the modified tone-reservation (TR) scheme which has sufficient degree of freedom to satisfy some special and meaningful waveform design criteria. In terms of applying independent or concurrent reserved subcarrier weights for transmit antennas, we provide two PAPR reduction schemes respectively, i.e., independent TR (ITR) and concurrent TR (CTR). It is demonstrated that the proposed joint optimization method can effectively reduce the PAPR to an acceptable threshold and is superior to the conventional methods. Note that the optimized OFDM waveforms for MIMO radar can avoid the grating-lobes in distance domain. Simulation results are presented to verify the derivations.

Introduction

Recently, multiple-input multiple-output (MIMO) radar with multiple transmit and receive antennas has attracted considerable interests [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. MIMO radar transmits multiple independent waveforms via multiple transmit antennas, unlike the conventional phased-array radar which is considered as a single-input single-output (SISO) radar [11], [12]. Generally, MIMO radars are categorized into two types: distributed MIMO radar and colocated MIMO radar. Distributed MIMO radar applies widely separated transmit/receive antennas to gain the spatial diversity, while colocated MIMO radar allows transmit and receive antennas to have colocated elements to improve the spatial resolution. In this paper, we are only interested in colocated MIMO radar and consider the corresponding waveform design at the stage of target search. The waveform design criteria for MIMO radar can be typically given as follows:

C1) To reduce inter-signal interference, the transmitting waveforms for multiple antennas should be orthogonal to each other or as orthogonal to each other as possible.

C2) To obtain a maximum work efficiency of the power amplifier, the transmitted waveforms should have constant envelope or low peak-to-average power ratio (PAPR) in time domain.

C3) To keep the range resolution compared to phased-array radar with single transmitting waveform, multiple transmitting waveforms should share the same frequency band with the same bandwidth.

Orthogonal frequency-division multiplexing (OFDM) has been successfully used in broadband communication systems for high speed data transmission. To preserve the orthogonal of subcarriers, time and frequency synchronization is crucial in OFDM communications systems. However, sensitivity to synchronization is beneficial since the radar receiver uses a stored version of the transmitted signal to measure time-delay (range) and frequency (Doppler) offsets between the transmitted signal and the received echo to achieve target detection. Therefore, OFDM waveform has been introduced into radar field in recent years, some practical applications see, e.g., [13], [14], [15], [16], [17]. Furthermore, OFDM waveform is naturally regarded as the suitable shared-signal for joint radar-communication system. Some fundamental researches of exploiting OFDM waveform to be a bridge between radar and communication systems can be seen in [18], [19]. As far as we know, MIMO-OFDM radar concepts firstly have been proposed in [20], [21], and then OFDM waveforms have been studied for the MIMO radar applications [22], [23], [24].

Criterion C2 is one of the most important waveform design issues for MIMO-OFDM radar system. Due to generated by a sum of subcarriers spacing special frequency, OFDM waveform has an inherent drawback of having very large envelope fluctuations in time domain. The variation in instantaneous signal power results in large power back-off and reduces the efficiency of the power amplifier, even brings nonlinear distortion. Therefore, OFDM waveform should reduce its PAPR before practical applications. An overview and taxonomy PAPR reduction for OFDM systems can be seen in [25], [26], [27]. Typically, PAPR reduction methods are categorized into three types: coding (precoding [28]), signal distortion (companding transform [29], [30]) and multiple signaling & probabilistic (active constellation extension (ACE) [31], selected mapping (SLM) [32], partial transmit sequences (PTS) [33], [34] and tone-reservation (TR) [35], [36], [37], [38]). However, the coding method has high complexity in code and decoding, and the signal distortion method always results in inter-carrier interference and frequency spectrum leakage. By comparison, probabilistic method brings no distortion to original OFDM signal because its operation in PAPR reduction is a linear procedure.

It is worthy to note that the waveform design for MIMO-OFDM radar in [20] has met the forementioned three criteria. However, using Zadoff–Chu (ZC) sequences for nearly 0 dB PAPR waveform design is limited in extension to diverse applications such as data transmission and target detection. In practice, we hope to have sufficient flexibility in waveform design for MIMO-OFDM radar system or joint radar-communication system. From this viewpoint, TR technique draws our special interests since it uses partial subcarriers to reduce the PAPR of OFDM waveform meanwhile enables the available subcarriers to provide flexibility for waveform selection. Although there are some researches on the PAPR reduction for MIMO-OFDM communication systems [39], [40], the PAPR reduction for MIMO-OFDM radar systems, as far as we know, is still rare, especially based on the TR technique. In the conventional TR technique extended for MIMO-OFDM communication, the reserved subcarriers occupy the same positions in OFDM block for all transmit antennas. Moreover, the PAPR reduction is performed independently in each transmit antenna. However, it is not suitable to reduce PAPR in this way for MIMO-OFDM radar systems any more because it has difficulty in satisfying the waveform design criteria. To cope with this issue, we modify TR scheme for MIMO-OFDM radar waveform design and propose a joint optimization method for PAPR reduction.

The contributions of this paper are as follows: 1) based on the colocated MIMO radar, we have adjusted TR scheme to the typical waveform design criteria and particularly discussed the joint optimization PAPR reduction method; 2) with regard to the subcarrier interleaving for MIMO-OFDM radar system, we have proposed a grouping optimization algorithm to lower the PAPR without influence on radar performance (such as range resolution) as much as possible; 3) the distance–velocity estimation for MIMO radar using compensating phase-offset method has been developed for the optimized OFDM waveforms.

The rest of this paper is organized as follows. Section 2 introduces the signal model for colocated MIMO radar. Section 3 discusses MIMO-OFDM radar waveform design for the typical criteria in detail. Section 4 proposes a joint optimization PAPR reduction method for MIMO-OFDM radar based on the modified TR scheme and then gives the ITR and CTR schemes for practical applications. Section 5 develops the distance–velocity estimation with compensating phase-offset process for MIMO-OFDM radar. Section 6 presents some simulation results to verify the effectiveness of the proposed method. Finally the conclusions are given in Section 7.