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For the purpose of target localization, Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing (MIMO-OFDM) radar has been proposed. OFDM technique has been adopted in order to a simultaneous transmission and reception of a set of multiple narrowband orthogonal signals at orthogonal frequencies. Although multi-carrier systems such as OFDM support high data rate applications, they do not only require linear amplification but also they complicate the power amplifiers design and increase power consumption. This is because of high peak-to-average power ratio (PAPR). In this work, a new proposition has been made based on the Pulse Width Modulation (PWM) to enhance the MIMO-OFDM radar systems’ performance. In order to check the proposed systems performance and its validity, a numerical analysis and a MATLAB simulation have been conducted. Nevertheless of the system characteristics and under same bandwidth occupancy and system’s specifications, the simulation results show that this work can reduce the PAPR values clearly and show capable results over the ones in the literature.

Many researchers have turned their attentions toward the Orthogonal Frequency Division Multiplexing (OFDM) scheme in order to provide high data rate applications under maintaining the spectral efficiency. Therefore, its clearly deployed in many broadband communication systems and protocols such as WiFi, WiMax, 4G and advanced LTE, Bluetooth-2. However, due to a high Peak-to-Average Power Ratio (PAPR), linear amplifiers suffer from low power efficiency under the utilization with multicarrier systems [

In order to enhance the MIMO radar, which is adopting the OFDM technique, a new work has been proposed in this paper based on hard decision-based PWM technique to tackle one of the main deficiencies found in OFDM; namely PAPR.

This deficiency appears due to the addition process with different frequencies and phases of numerous waves, which leads to the need of high dynamic ranges transmitters. The predicted PAPR values in OFDM signal can be formed as [

Here,

which results from the modulation process of an

Such deficiency causes transmission amplification and other circuitry limitations. Therefore, to overcome this problem, average signal power must be kept low to allow the transmission process of the higher average power to be in a fixed level. Then an improvement of the reception process will be attained based on improving the signal to noise ratio.

There are several propositions and techniques that either tackle the PAPR effects or address the linearity and power efficiency issues, such as filtering and clipping techniques; coding based techniques; artificial intelligence based techniques; and signal representation techniques as the envelope elimination and restoration techniques and the phase shifted sequence ones. This is in order to optimize a solution at the expense of several challenges, such as the degradation of the Bit Error Rate (BER); the decrement of the spectral efficiency due to the side information (SI) transmission; and the computational complexity [

This paper addresses the proposition of a new technique based on using the pulse width modulation (PWM) to overcome the PAPR problem effect. Consequently, the overall performance will be enhanced for the MIMO radar, which adopting the OFDM technique. As a result of considering the use of PWM, a basis of controlling the power electronics [

PWM signal is easily generated by comparing the reference signal with a carrier one. Mainly, the input signal is used to determine the width of the generated PWM signal. This is clearly shown in the following mathematical representation

where the generated PWM signal depends on the sign function of the subtraction process between the compared reference signal;

As basic PWM signal generation, there are two methods that help in producing the variable pulses widths; direct digital generation and uniformly sampled PWM. They can be distinguished by the focusing on the controlling criteria. In this paper, the second technique will be chosen, where a triangle clock signal is used to generate the uniformly sampled PWM signal. This is due to that it does not need high frequency clock signal. Moreover, the triangle clock signal is chosen over the other two types, Sawtooth or the inverted Sawtooth, due to that it has low number of dominant higher harmonics. The achieved benefit here concluded in reducing the needed system bandwidth [

The rest of this work is introduced as follows: Section 2 describes the model of MIMO-OFDM radar signals based on PWM along with the analytical formulation in addition to the computational complexity. Section 3 presents simulation results and hardware implementations; finally, the conclusion is represented in Section 4.

In [

The baseband MIMO-OFDM transmitted matrix is defined in (1) by

Here, the IFFT of _{i,j}(k), and 0_{1×(L}_{ }_{−}_{ }_{k}_{)} for zero padding when L ≥ k. Accordingly, the produced i-th OFDM symbol will be processed and transmitted from the i-th antenna.

The next step after generating the OFDM baseband waveforms is the imposing of a guard interval process at the beginning of each OFDM symbol. This is attained by attaching a copy of the later OFDM symbol part at the beginning; namely a cyclic prefix process, which is introduced in order to maintain the orthogonality between the used sub-bands by MIMO operation and will be accomplished by making use of windowing techniques. Moreover, the MIMO-OFDM radar will make use of it in order to compensate for the shifts in time. This is clearly shown under the case of multiple targets at different ranges, where it guarantees the existence of the needed phase delay information inside the used window. This is true under a predefined separation range, which is based on the antenna array dimension and the used lengths for the transmitted symbol period and the cyclic prefix length. Therefore, the final transmitted baseband matrix is given as

Here,

Moreover, in order to maintain the orthogonality condition, the antenna elements displacement should satisfy curtain threshold. In this work, to detect and estimate a target within 180˚, the displacement; D should satisfy

where,

The imposing process of the cyclic prefix is clearly described in

In this work, and after the imposing of the guard interval; i.e. the cyclic prefix, a new processing block has been inserted to analyze the PAPR performance. This is to free the channel from the inter symbol interference (ISI) drawback. Moreover, this choice will reduce the hardware area under the consideration of hardware implementation.

Returning to the implementation of the baseband OFDM signal; i.e.

The proposed PWM work starts with reshaping the signal,

Here, m stands for the block index as defined in (7), and N(m) denotes the block length.

The reshaped result from (6) has been used to be processed in the production of a constant amplitude signal based on the PWM technique. This is clearly depicted and shown in

As shown in

・ In order to distinguish each symbol after the conversion process an extra zero sample has been added at the beginning of each OFDM symbol.

・ The sampling rate has been increased in order to enhance the accuracy of the conversion process;

where i stands for the sample value;

In this stage, the oversampled version of the OFDM symbol will be processed in order to produce a constant envelope version. For simplicity, the slope between two consecutive samples has been chosen as a comparison criterion. This criterion is depicted as follows in (9).

These two stages are clearly described in

As described earlier,

This is clearly found in

The variation has been reduced and the peaks values have been diminished, consequently the PAPR values will be reduced. In addition, to simplify the proposed work, the hermitian structure of the OFDM systems could be exploited [

The transmitter stages are shown in

In the receiver side, the signal modelling will be determined based on the sent and received signals between/ among the transmitter and the object(s), which will help in determining the objects specifications. The issues of determining the objects directions and locations are considered out of scope of this work and will be discussed in another work. Thus, it is focusing on how to overcome the rise problem due to the use of the FFT and its inverse in modelling the OFDM system.

After the transmission through a channel from different transmitting antennas, in the receiver side, the main task of the receiver is to recover the original OFDM signal from the modified one. Accordingly, the used recovering

procedure will be divided into two main stages; firstly, proposing an algorithm to recover the OFDM symbol from the constant enveloped received symbols, and secondly, a signal processing stage based on removing the extra imposed samples. This procedure is clearly shown and described in

The reproduction process of regenerating OFDM signal from the received is clearly depicted in

The given procedure in

Furthermore, in

The next section describes the results from the proposed work simulation against the conventional techniques; they are based on both of CCDF and SER curves. These two criteria are used to validate the OFDM systems performance, where the lower the values the higher the system performance.

The proposed MIMO-OFDM radar system that has been described in

At this stage, the performed MATLAB simulation has the following specifications:

・ Carrier frequency of 3 GHz,

・ Extra 9 samples have been added between the consecutive samples; N′(m) = 9,

・ IFFT length of 1024 point,

・ T_{p} = 0.25 × T_{s},

・ Carrier spacing = (1/32) GHz,

・ 64-QAM modulation technique,

・ Vertical-Bell Laboratories Layered Space-Time (V-BLAST) MIMO system will be used for the four-element array transmission. This is in order to boost the system performance in terms of bits/symbol.

To imitate a real scenario, the shown proposed work in _{o}. It is expressed by:

As depicted in

CCDF (2%) | Additional reduction (%) | ||||
---|---|---|---|---|---|

Modulation technique | PAPR without coding (dB) | MIMO-OFDM radar based PWM (dB) | Clipping | SLM | PTS |

64 QAM | 20 | 11.5 | 72.1 | 44.5 | 11 |

time. This modification enhances the SER from 9.3 × 10^{−}^{4} to 8.7 × 10^{−}^{4}.

Furthermore, the second part of the systems performance checking is shown in ^{−}^{3} to 2 × 10^{−}^{4}. Furthermore, a comparison has been made between our proposed work and the work that found in the literature. This comparison is shown in

The proposed system performance improvement has bean clearly shown in

MIMO-OFDM radar work is different from the conventional ones in the literature, where this work has built the comparison stage making use of the slope between the two consecutive samples. Additionally, this work enhances the use of the PWM techniques, where the conventional PWM links the comparison performance to the inserted number of extra samples. In the MIMO-OFDM radar, the performance has been improved without overloading the systems with extra samples since the comparison stage has been linked to the slope between the samples.

This work takes high PAPR effect into consideration when proposing the OFDM technique to the conventional MIMO radar systems. High PAPR values could reduce the system performance especially when using nonlinear devices. A new work has been proposed to overcome this deficiency making use of the conventional PWM with some modifications.

A MATLAB simulation has been conducted to validate the analytical model of the proposed work. It consists of two parts: one to check the sample error rate (SER) after the recovery process, while the other one to describe the probability of the PAPR to exceed a certain threshold. Moreover, a comparison with the literature has been made in order to confirm the expected performance modification.

Under same environmental conditions and system specifications, a SER of 8.7 × 10^{−}^{4} has been achieved compared with the transmission of conventional OFDM signals. This is in addition to enhancing the probability of the PAPR that exceeds 20 dB from 2.1 × 10^{−}^{2} to 1.7 × 10^{−}^{4}. The work validity has been checked based on a comparison with the ones in the literature, such as PTS, SLM or Clipping techniques, the proposed work gives an additional PAPR reduction percentage between 11% and 72% over the achieved 11.5 dB value. As a consequence, the transmission throughput will improve.