Patent Publication Number: US-2021173069-A1

Title: Method and System for Frequency Offset Modulation Range Division MIMO Automotive Radar Using I-Channel Only Modulation Mixer

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     U.S. patent application Ser. No. ______, entitled “Method and System for Frequency Offset Modulation Range Division MIMO Automotive Radar,” by inventors Ryan Haoyun Wu, Douglas Alan Garrity, and Maik Brett, Attorney Docket No. 82155185US01, filed on even date herewith, describes exemplary methods and systems and is incorporated by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention is directed in general to radar systems and associated methods of operation. In one aspect, the present invention relates to an automotive radar system formed with multiple-input, multiple-output (MIMO) mono-static (co-located) and multi-static (distributed) radar arrays. 
     Description of the Related Art 
     Radar systems may be used to detect the range, velocity, and angle of nearby targets. With advances in technology, radar systems may now be applied in many different applications, such as automotive radar safety systems, but not every radar system is suitable for every application. For example, 77 GHz Frequency Modulation Continuous Wave (FMCW) Fast Chirp Modulation (FCM) radars are used as with very large MIMO arrays as sensors in Advanced Driver Assistance System (ADAS) and autonomous driving (AD) systems. Since the number of virtual antennas constructed with the MIMO approach (which equals the product of the number of physical transmit and receiver antenna elements) is larger than the total number of physical elements, the resulting MIMO array can form a larger aperture, resulting in improved angular resolution. However, MIMO systems can have difficulty distinguishing between Linear Frequency Modulation (LFM) waveforms transmitted by different transmit antennas. 
     Existing radar systems have attempted to address these challenges by using time-division (TD) multiplexing techniques to separate LFM waveforms from different transmitters in time, thereby separating signals originated from distinct transmitters at each receiving channel for constructing a virtual MIMO array. In particular, existing TD MIMO implementations are configured to schedule a sequence of transmit chirps (LFM waveforms) by individual transmit antennas one element or subarray at a time, meaning that the amount of time required to transmit all chirps is increased as the number of transmit antennas is increased. Unfortunately, because the coherent dwell time (i.e., the time duration an echo signal of a target can be coherently integrated on a moving target) is usually limited, the number of transmitters that can be used with TD-MIMO systems is limited. Another drawback with convention al TD-MIMO systems is that longer frame or chirp sequence durations may lead to multiple-times decrease in the maximum Doppler shift (or effectively, radial velocity of a target) that can be measured without ambiguity, again limiting the number of transmitters that may be used for TD-MIMO systems. As a result, TD-MIMO systems are typically confined to using a small number of transmitters (e.g., 3) to construct a relatively small MIMO virtual array. As seen from the foregoing, the existing radar system solutions are extremely difficult at a practical level by virtue of the challenges with achieving the performance benefits of larger size radars within the performance, design, complexity and cost constraints of existing radar system applications. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention may be understood, and its numerous objects, features and advantages obtained, when the following detailed description of a preferred embodiment is considered in conjunction with the following drawings. 
         FIG. 1  is a simplified schematic block diagram of a conventional LFM TD-MIMO automotive radar system. 
         FIG. 2  is a timing diagram illustrating a chirp transmission schedule for an LFM TD-MIMO automotive radar system. 
         FIG. 3A  is a simplified schematic block diagram of a frequency offset modulation LFM range division MIMO automotive radar system implemented with FOM modulation mixers in accordance with selected first embodiments of the present disclosure. 
         FIG. 3B  is a simplified schematic block diagram of a frequency offset modulation LFM range division MIMO automotive radar system implemented with FOM modulation mixers in accordance with selected second embodiments of the present disclosure. 
         FIGS. 4A-B  are simplified diagrams of the design and operation of a frequency offset modulation mixer in accordance with selected embodiments of the present disclosure. 
         FIG. 5  is a simplified schematic block diagram of frequency offset modulation generator in accordance with a first selected embodiment of the present disclosure. 
         FIG. 6  is simplified schematic block diagram of frequency offset modulation generator in accordance with a second selected embodiment of the present disclosure. 
         FIG. 7  depicts a fast-time range FFT spectrum of an I-sample only receiver channel of a conventional LFM automotive radar. 
         FIG. 8  depicts a fast-time range FFT spectrum of a receiver channel of an I-sample only for an 8-transmitter frequency offset modulated LFM range-division MIMO automotive radar in accordance with selected embodiments of the present disclosure. 
         FIG. 9  depicts a fast-time range FFT spectrum of a receiver channel of an I-sample only for a 16-transmitter frequency offset modulated LFM range-division MIMO automotive radar in accordance with selected embodiments of the present disclosure. 
         FIG. 10  depicts a fast-time range FFT spectrum of a receiver channel of an I/Q sample for a 16-transmitter frequency offset modulated LFM range-division MIMO automotive radar in accordance with selected embodiments of the present disclosure. 
         FIG. 11  is a simplified diagram of an I-branch only frequency offset modulation mixer in accordance with selected embodiments of the present disclosure. 
         FIG. 12A  depicts a fast-time range FFT spectrum of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3A  which uses I-branch only FOM mixers with insufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver. 
         FIG. 12B  depicts a fast-time range FFT spectrum of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixers with insufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver. 
         FIG. 13A  depicts a fast-time range FFT spectrum of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3A  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. 
         FIG. 13B  depicts a fast-time range FFT spectrum of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure with the exception that additional offset is required to prevent cancellation of a first transmitter&#39;s signal. 
         FIG. 13C  depicts a fast-time range FFT spectrum of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixer range spectrum with a first frequency offset for the first transmitter and a second, doubled frequency offset for the remaining transmitters in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. 
         FIG. 14A  diagrammatically depicts a coherent integration of the sum and delta components of the range spectrums of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3A  which uses I-branch only FOM mixers in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. 
         FIG. 14B  diagrammatically depicts a coherent integration of the sum and delta components of the range spectrums of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixers in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. 
         FIG. 15  diagrammatically depicts a coherent integration of the sum and delta components of the range spectrums of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixers in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. 
         FIG. 16A  depicts a fast-time range FFT spectrum of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3A  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with PQ-channel analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. 
         FIG. 16B  depicts a fast-time range FFT spectrum of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixer range spectrum with insufficient frequency offset for the first transmitter in combination with PQ-channel analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. 
         FIG. 16C  depicts a fast-time range FFT spectrum of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset for the first transmitter in combination with PQ-channel analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. 
         FIG. 17  is a simplified schematic block diagram of a frequency offset modulation LFM range division MIMO automotive radar system implemented with fast-time phase shifters in accordance with selected embodiments of the present disclosure. 
         FIG. 18  depicts a fast-time range FFT spectrum for two time slots of a receiver channel of an PQ sample for an 8-transmitter MIMO automotive radar which employs both time-division and frequency offset modulated LFM range-division radar techniques in accordance with selected embodiments of the present disclosure. 
         FIG. 19  illustrates a simplified flow chart showing the logic for using frequency offset modulation techniques to form a virtually large MIMO radar arrays. 
     
    
    
     DETAILED DESCRIPTION 
     A frequency offset modulation range and time division MIMO radar system, hardware circuit, system, architecture, and methodology are described for combining linear frequency modulation (LFM) time-division (TD) MIMO with frequency offset modulation 
     (FOM) range division MIMO to construct very large MIMO arrays for use with frequency modulation continuous wave (FMCW) radars. In selected embodiments, a signal processing methodology and apparatus are disclosed for mixing the LFM waveform (transmit chirp) at each transmit channel with different frequency offset signals (e.g., Δf, 2Δf, etc.) using a frequency offset mixer with increased ADC sampling rate to allow the separation of transmitters&#39; signals on receive in the range spectrum, thereby enabling very large MIMO array formation at the receiver. With each transmit channel transmitting a different frequency offset modulation LFM signal, the receiver can process and separate the transmit channel signals in the fast-time Fourier or the range domain, thereby defining an LFM range-division (RD) MIMO approach for differentiating between transmit channel signals. In selected embodiments, the frequency offset mixer may be implemented with an I/Q channel modulation mixer, an I-channel only modulation mixer, or a Q-channel only modulation mixer to implement a spectrum-coherent integration approach. In embodiments where the FOM mixer is implemented with an I-channel only modulation mixer or a Q-channel only modulation mixer with a spectrum domain coherent integration approach, the complexity of the hardware implementations is greatly reduced. In other embodiments, a signal processing methodology and apparatus are disclosed for frequency shifting the LFM waveform (transmit chirp) at each transmit channel with different fast-time phase shifters prior to transmit filtering and amplification, thereby enabling very large MIMO array formation at the receiver. With each transmit channel transmitting a different frequency offset modulation LFM signal that is generated with a fast-time phase shifter, there is no requirement of a frequency offset mixer at each transmit channel, and a high speed analog-to-digital converter at the receiver can process and separate the transmit channel signals in the fast-time Fourier or the range domain, thereby defining an LFM range-division (RD) MIMO approach for differentiating between transmit channel signals. Because of the simultaneous transmissions of FOM RD MIMO, the frame duration can be kept short, thereby avoiding the problem associated with prolonged frame duration of TD MIMO systems. The resulting FOM RD MIMO virtual array is much larger than the conventional TD-MIMO approach, and can provide high angular resolution performance. In selected embodiments, a signal processing methodology and apparatus are disclosed for combining the FOM RD MIMO approach with TD MIMO approach, such as by defining multiple transmit time slots such that alternating transmit channels (e.g., even number transmitter) are active in a first time slot and are suppressed in a second time slot. In this configuration, for each transmitter, its adjacent range spectrum segment is vacant, thereby enabling strong beyond-the-range targets to be correctly detected without imposing target interference. By providing hardware and software solutions for using frequency offset modulation in combination with time-division techniques to transmit LFM waveforms from multiple transmit channels, the disclosed frequency offset modulation range and time division MIMO radar system and methodology efficiently provide a MIMO virtual array having an aperture that is many times larger than the total physical apertures combined, thereby achieving better sensitivity, finer angular resolution, and low false detection rate. 
     In the context of the present disclosure, it will be appreciated that radar systems may be used as sensors in a variety of different applications, including but not limited to automotive radar sensors for road safety systems, such as advanced driver-assistance systems (ADAS) and autonomous driving (AD) systems. In such applications, the radar systems are used to measure the radial distance to a reflecting object, its relative radial velocity, and angle information, and are characterized by performance criteria, such as the angular resolution (the minimum distance between two equal large targets at the same range and range rate (or radial velocity) resolution cell which a radar is able to distinguish and separate to each other), sensitivity, false detection rate, and the like. Typically, frequency modulated continuous wave (FMCW) modulation radars are used to identify the distance, velocity, and/or angle of a radar target, such as a car or pedestrian, by transmitting Linear Frequency Modulation (LFM) waveforms from multiple transmit antennas so that reflected signals from the radar target are received at multiple receive antennas and processed to determine the radial distance, relative radial velocity, and angle (or direction) for the radar target. However, with current automotive designs, a vehicle can include multiple radar transmitters which can operate independently from one another. As a result, the LFM waveform transceivers may be configured to implement time-division (TD) MIMO operations to temporally separate signals originated from distinct transmitters so that a receiving channel can distinctly detect each signal and thereby construct a virtual MIMO array. 
     To illustrate the design and operation of a conventional TD MIMO radar system, reference is now made to  FIG. 1  which depicts a simplified schematic block diagram of a conventional LFM TD-MIMO automotive radar system  100  which includes an LFM TD-MIMO radar device  10  connected to a radar controller processor  20 . In selected embodiments, the LFM TD-MIMO radar device  10  may be embodied as a line-replaceable unit (LRU) or modular component that is designed to be replaced quickly at an operating location. Similarly, the radar controller processor  20  may be embodied as a line-replaceable unit (LRU) or modular component. Although a single or mono-static LFM TD-MIMO radar device  10  is shown, it will be appreciated that additional distributed radar devices may be used to form a distributed or multi-static radar. In addition, the depicted radar system  100  may be implemented in integrated circuit form with the LFM TD-MIMO radar device  10  and the radar controller processor  20  formed with separate integrated circuits (chips) or with a single chip, depending on the application. 
     Each radar device  10  includes one or more transmitting antenna elements TX&#39; and receiving antenna elements RX j  connected, respectively, to one or more radio-frequency (RF) transmitter (TX) units  11  and receiver (RX) units  12 . For example, each radar device (e.g.,  10 ) is shown as including individual antenna elements (e.g., TX 1,i , RX 1,j ) connected, respectively, to three transmitter modules (e.g.,  11 ) and four receiver modules (e.g.,  12 ), but these numbers are not limiting and other numbers are also possible, such as four transmitter modules  11  and six receiver modules  12 , or a single transmitter module  11  and/or a single receiver modules  12 . Each radar device  10  also includes a chirp generator  112  which is configured and connected to supply a chirp input signal to the transmitter modules  11 . To this end, the chirp generator  112  is connected to receive a separate and independent local oscillator (LO) signal  110  and a chirp start trigger signal  111 , though delays are likely to be different due to the signal path differences and programmable digital delay elements in the signal paths. Chirp signals  113  are generated and transmitted to multiple transmitters  11 , usually following a pre-defined transmission schedule, where they are filtered at the RF conditioning module  114  and amplified at the power amplifier  115  before being fed to the corresponding transmit antenna TX 1,i  and radiated. By sequentially using each transmit antenna TX 1,i  to transmit successive pulses in the chirp signal  113 , each transmitter element  11  operates in a time-multiplexed fashion in relation to other transmitter elements because they are programmed to transmit identical waveforms on a temporally separated schedule. 
     The radar signal transmitted by the transmitter antenna unit TX 1,i , TX 2,i  may by reflected by an object, and part of the reflected radar signal reaches the receiver antenna units RX 1,i  at the radar device  10 . At each receiver module  12 , the received (radio frequency) antenna signal is amplified by a low noise amplifier (LNA)  120  and then fed to a mixer  121  where it is mixed with the transmitted chirp signal generated by the RF conditioning unit  113 . The resulting intermediate frequency signal is fed to a first high-pass filter (HPF)  122 . The resulting filtered signal is fed to a first variable gain amplifier  123  which amplifies the signal before feeding it to a first low pass filter (LPF)  124 . This re-filtered signal is fed to an analog/digital converter (ADC)  125  and is output by each receiver module  12  as a digital signal D 1 . The receiver module compresses target echo of various delays into multiple sinusoidal tones whose frequencies correspond to the round-trip delay of the echo. 
     The radar system  100  also includes a radar controller processing unit  20  that is connected to supply input control signals to the radar device  10  and to receive therefrom digital output signals generated by the receiver modules  12 . In selected embodiments, the radar controller processing unit  20  may be embodied as a micro-controller unit (MCU) or other processing unit that is configured and arranged for signal processing tasks such as, but not limited to, target identification, computation of target distance, target velocity, and target direction, and generating control signals. The radar controller processing unit  20  may, for example, be configured to generate calibration signals, receive data signals, receive sensor signals, generate frequency spectrum shaping signals (such as ramp generation in the case of FMCW radar) and/or register programming or state machine signals for RF (radio frequency) circuit enablement sequences. In addition, the radar controller processor  20  may be configured to program the modules  11  to operate in a time-division fashion by sequentially transmitting LFM chirps for coordinated communication between the transmit antennas TX 1,i , RX 1,j . The result of the digital processing at the radar controller processing unit  20  is that the digital domain signals D 1  are processed for the subsequent fast-time range FFT  21 , slow-time Doppler FFT  22 , constant false alarm rate (CFAR) target detection  23 , spatial angle estimation  24 , and target tracking processes  25 , with the result being output  26  to other automotive computing or user interfacing devices for further process or display. 
     To illustrate an example of time division transmission of radar transmit signals, reference is now made to  FIG. 2  which depicts a timing diagram illustration  200  of a chirp transmission schedule for an LFM TD-MIMO automotive radar system. As depicted, each transmitter (e.g., TX 1 , etc.) is programed to take turns transmitting one chirp (e.g.,  201 ) of a sequence of chirps  201 - 206 . This temporal separation of chirp transmission by each transmit antenna allows the separation of transmitters at the receiving end by simply associating the received signal with the scheduled transmitter. The ability to separate transmitters in the received signal is a prerequisite of the MIMO radar approach, which is routinely used in automotive radars for constructing a virtually large antenna array aperture compared to the physical aperture of the transmit and receive antennas. The larger aperture constructed virtually via MIMO provides better angular resolution performance which is required by many advanced driver assistance system (ADAS) and autonomous driving (AD) applications. The use of a transmitter schedule to divide the time-domain resources amongst the transmitters when forming a virtual MIMO array is referred to as a time division (TD) MIMO approach. 
     Since the TD-MIMO approach provides a relatively straightforward way to separate transmitters with little or no leakage, it is routinely used in automotive radar applications. However, the requirement of dividing time between resources means that a much longer frame duration is required to complete the transmission of all chirps for each transmitter. If the prolonged frame duration is longer than the duration a target stays within a single range resolution cell, any range migration by the target can degrade the subsequent digital Doppler coherent integration processing and angle estimation, thereby adversely impacting measurement performance. 
     Another drawback with conventional TD-MIMO approaches is the increase in the duration of the pulse repetition intervals (PRI) between adjacent pulses of the same transmitter. In particular, with each transmitter (e.g., TX 1 -TX N ) being scheduled to take its turn to transmit their first pulses (e.g.,  201 - 202 ) before beginning the sequential transmission of the second pulses (e.g.,  203 - 204 ), and so on until the last pulses (e.g.,  205 - 206 ) are transmitted, the pulse repetition interval (PRI)  202  between two adjacent pulses of the same transmitter is also prolonged. Because the maximum unambiguous Doppler shift measurable by the chirp sequence is inversely related to the PM, a lengthened PM results in reduced maximum unambiguous Doppler performance. As a result, the maximum number of transmitters that can be used for TD-MIMO operation is limited. For typical road use, up to  3  transmitters may be used for TD MIMO without unacceptable performance degradation. 
     To address these limitations from conventional solutions and others known to those skilled in the art, reference is now made to  FIG. 3A  which depicts a simplified schematic block diagram of a frequency offset modulation LFM range division MIMO automotive radar system  300 A which includes an LFM RD-MIMO radar device  330 A having a transmit module  310 A and receiver module  320  which are connected and configured to transmit and receive LFM waveforms  302 A,  303 A for reflection by a target  301  under control of a radar controller processor (not shown). In selected embodiments, the LFM RD-MIMO radar device  330 A and/or radar controller processor may be embodied as a line-replaceable unit (LRU) or modular component that is designed to be replaced quickly at an operating location. In addition and as described hereinbelow, the LFM RD-MIMO radar device  330 A may also be configured to perform time-division multiplexing of the transmitted LFM waveforms  302 A,  303 A to implement a combined time-division and range-division MIMO scheme to separate the transmitters not only in the range domain, but also in the time domain. 
     Each radar device  330 A includes one or more transmitting antenna elements TX i  and at least a first receiving antenna element RX connected, respectively, to one or more radio-frequency (RF) transmit modules  310 A and receive module  320 . At each transmit module  310 A, a transmit channel circuit is provided for each transmit antenna. For example, a first transmit channel circuit includes a first RF conditioning module  311  and power amplifier  312  connected to a first transmit antenna TX 1 , a second transmit channel circuit includes a second RF conditioning module  314  and power amplifier  315  connected to a second transmit antenna TX 2 , and so on with the Nth transmit channel circuit including an Nth RF conditioning module  317  and power amplifier  318  connected to the Nth transmit antenna TX N . 
     In addition, each radar device  330 A includes a chirp generator  304  which is configured and connected to supply a chirp input signal  305  to the different transmit channel circuits  311 / 312 ,  314 / 315 ,  317 / 318  in the transmitter module(s)  310 A. However, instead of providing the chirp input signal  305  directly to all of the transmit channel circuits, the radar device  330 A also includes a frequency offset generator  306 A and frequency offset modulator (FOM) mixers  313 ,  316  which are connected to shift or offset the frequency of each transmitted LFM waveform  302 A by a different integer multiple of a frequency offset (Δf). To this end, the first transmit channel circuit  311 / 312  may be connected to directly receive the chirp input signal  305 . However, the second transmit channel circuit  314 / 315  may include an FOM mixer  313  which is connected as an I/Q mixer to apply a first frequency offset signal Δf to the chirp input signal  305  before being filtered and amplified by the second transmit channel circuit  314 / 315  for transmission over the antenna TX 2 . In similar fashion, the remaining transmit channel circuits (e.g.,  317 / 318 ) may include an FOM mixer (e.g.,  316 ) which is connected as an I/Q mixer to apply a unique frequency offset signal (e.g., (N−1)Δf) to the chirp input signal  305  before being filtered, amplified, and radiated by the antenna (e.g., TX N ). 
     With the frequency offset generator  306 A connected to receive the reference local oscillator signal LO, a plurality of predefined frequency offset signals  307 A may be generated, such as by generating a different integer multiple of a frequency offset (Δf) for each transmitter channel circuit which is connected to receive a frequency offset. By shifting the center frequency of LFM waveform at each transmitter TX i  according to a predefined offset frequency unique to each transmitter, frame durations can be reduced (as compared to TD schemes) to prevent range migration effect from degrading the Doppler and angle processing. In selected embodiments, the amount of frequency offsets should be sufficient such that no targets within the maximum detection range of the radar from any two transmitters overlaps in the range domain. Thus, the amount of range shift corresponds to the amount of frequency offset imposed on each transmitter and is at least the amount of the maximum detection range of the radar. 
     For each transmit channel circuit except the first transmit channel circuit  311 / 312 , the frequency offset generator  306 A generates a frequency offset tone based on a fundamental offset frequency Δf that is derived from the LO signal and multiplied by an integer (e.g., 1, 2, 3, 4, . . . N−1), with a different integer value being used for each transmit channel circuit. For example, the frequency offset generator  306 A generates a first frequency offset tone 1×Δf that is supplied to the FOM mixer  313  for the second transmit channel circuit  314 / 315 . Likewise, the frequency offset generator  306 A generates a second frequency offset tone 2×Δf that is supplied to the FOM mixer for the third transmit channel circuit, and so on, with the frequency offset generator  306 A generating a last frequency offset tone (N−1)×Δf that is supplied to the FOM mixer  316  for the last transmit channel circuit  317 / 318 . In this way, the frequency offset generator  306 A provides N−1 offset tones for the transmit channel circuits. If desired, an additional 2NΔf Hz component can be generated to drive the ADC if the sampling rate if f s =2NΔf. 
     As will be appreciated, a variety of different configurations may be used to deploy the frequency offset generator and FOM mixers for purposes of frequency-shifting each transmit channel. For example, reference is now made to  FIG. 3B  which depicts a simplified schematic block diagram of a frequency offset modulation LFM range division MIMO automotive radar system  300 B which includes an LFM RD-MIMO radar device  330 B having a transmit module  310 B and receive module  320  which are connected and configured to transmit and receive LFM waveforms  302 B,  303 B for reflection by a target  301  under control of a radar controller processor (not shown). As depicted, the LFM RD-MIMO radar device  330 B is similar to the LFM RD-MIMO radar device  330 A shown in  FIG. 3B , except that the chirp input signal  305  is not directly provided to any of the transmit channel circuits. Instead, the frequency offset generator  306 B and frequency offset modulator (FOM) mixers  313 ,  316  are connected to shift or offset the frequency of the chirp input signal  305  by a different integer multiple of a frequency offset (Δf) before being provided to any transmit channel circuit. In particular, the first transmit channel circuit  314 / 315  includes an FOM mixer  313  which is connected as an I/Q mixer to apply a first frequency offset signal Δf to the chirp input signal  305  before being filtered and amplified by the first transmit channel circuit  314 / 315  for transmission over the antenna TX 1 . In similar fashion, the remaining transmit channel circuits (e.g.,  317 / 318 ) include an FOM mixer (e.g.,  316 ) which is connected as an I/Q mixer to apply a unique frequency offset signal (e.g., (N)Δf) to the chirp input signal  305  before being filtered and amplified by the antenna (e.g., TX N ). With this configuration, the frequency offset generator  306 B is connected to receive the reference local oscillator signal LO and to generate therefrom a plurality of predefined frequency offset signals  307 B as a different integer multiple of a frequency offset (Δf) for each corresponding transmitter channel circuit. By shifting the center frequency of LFM waveform  302 B at each transmitter TX i  according to a predefined offset frequency unique to each transmitter, the combined reflected LFM waveforms  303 B are received and processed by the receiver module  320  in the substantially the same way as described hereinbelow. 
     To ensure sufficient range space is available for division amongst all transmitters, a much longer system-describable unambiguous range extent must be provided by the fast-time sampling. Because the maximum unambiguous range extent is inversely related to the fast-time sampling interval, a faster analog-to-digital converter (ADC) is employed at each receive channel. For example, a conventional TD-MIMO FCM radar may use a 40 mega-samples-per-second (Msps) ADC, but an LFM MIMO radar device using frequency offset modulation to enable N-transmitter MIMO operation should use an ADC sampling rate that is increased to N×40 Msps. Note also that depending on the radar system requirements and also upon the actual performance of the low-pass filter that directly precedes the ADC, the sample rate of the ADC may need to be increased beyond N×40 Msps. As a result, the fast-time FFT processing can divide the spectrum into N consecutive segments, with each being associated with a corresponding transmitter. Because the transmitters are separated or divided in the range domain and the waveform is based on LFM, the approach can also be referred to as the LFM range-division (RD) MIMO approach. 
     With the frequency offset signals  307 A,  307 B applied to the chirp input signal  305  by a bank of FOM mixers  313 ,  316  at the transmitter channel circuits before transmission on the transmit antennas TX 1 -TX N , the combined reflected LFM waveforms  303 A,  303 B are received and processed by the receiver module  320 . In particular, the receive antenna RX receives the combined reflected LFM waveforms  303 A,  303 B which are then amplified by the low noise amplifier (LNA)  321 . At the I/Q mixer  322 , the amplified receive signal is mixed with the reference chirp signal  305  before being conditioned for digital conversion by the high pass filter  323 , variable gain amplifier  324 , low pass filter  325 , and analog-to-digital converter  326 . 
     In some cases, the signal radiated from the transmitters TX 1 -TX N  is not sufficiently isolated from the receiver which can result in undesirable interference that presents itself as an artificial target at near-zero range. This is known as transmitter-to-receiver spill-over interference. In selected embodiments of the present disclosure, an analog-domain tunable and configurable notch filter bank circuit may be substituted for the high pass filter  323  for filtering out the zero-range interference in the fast-time spectrum of each transmitter. Because it is not a target return, its presence interferes with the detection of valid targets that are close in distance due the spectral skirts caused by the phase noise of the system. In addition, reflective structures (e.g., the bumper) of the car around the radar result in a close-in echo (with nearly zero range) which interferes with the detection of valid targets. Such interference can be suppressed by applying analogue filters and/or digital filters. In FMCW radar designs where an analog high-pass filter (HPF) with a tunable pass-band frequency is employed after the chirp mixer  322  to suppress the zero-range interference signals, such a single high-pass filter cannot filter out all of the multiple zero-range signals in the received FOM signal occurring at multiple non-zero frequencies. To suppress these interference signals, a bank of notch filters (also known as a comb filter) is employed where each notch filter is tuned to a corresponding zero-range frequency, thereby providing a FOM LFM RD MIMO radar with spill-over interference cancellation using a notch filter in the receive path. 
     To provide an improved understanding of how the FOM mixers  313 ,  316  shift the frequency of the reference chirp, reference is now made to  FIG. 4A  which is a simplified diagram  400  of the design and operation of a frequency offset modulation mixer  401  which shifts the frequency of the offset tone mixed with the reference chirp signal. Denoting the reference chirp signal as s b (t)sin(2πf 0  t), it will be understood that sin(2πf 0  t) represents the carrier with a center frequency of f 0 , and s b  (t) denotes the baseband chirp waveform that is modulated by the carrier tone. Since the chirp bandwidth is much smaller than the carrier frequency, it can be treated as a narrow band signal. To shift the reference chirp&#39;s carrier frequency by f Δ , an offset tone signal sin(2πf Δ t) is generated for input to the FOM mixer  401 . As indicated by the cascaded mixer symbol, the FOM mixer  401  is a I/Q mixer for mixing the LFM waveform of the reference chirp signal (s b (t)sin(2πf 0  t)) with a fixed frequency of the offset tone (sin(2πf Δ t)). 
     To provide additional details for an improved understanding of selected embodiments of the present disclosure, reference is now made to  FIG. 4B  which is a simplified diagram of the design and operation of a frequency offset modulation mixer  451 . As depicted, the reference chirp input signal (sin(2πf 0  t)) is first split into I and Q component branches, with one branch shifted by 90 degrees (at shifter  454 ) to generate the Q component (cos(2πf 0  t))) for mixing with the I component of the offset tone (sin(2πf Δ t)) at the I/Q mixer  453  to produce the mixer output x 2 (t). In similar fashion, the I component of the reference chirp input signal (sin(2πf 0  t)) is mixed with the 90-degree phase-shifted offset tone signal (cos(2πf Δ t)) which is generated by the 90 degree shifter  452  at the I/Q mixer  455  to produce the mixer output x 1 (t). Finally, the I/Q mixer circuit  456  combines the outputs x 1 (t), x 2 (t) of the two mixers  453 ,  455  to form the final frequency offset modulated chirp signal (sin(2π(f 0 +f Δ )t)). 
     To demonstrate that the sum of the two branches is the frequency-offset modulated chirp signal, the following derivation may be established: 
         x   1 ( t )=sin(2π f   0    t )cos(2 πf   Δ   t )=0.5(sin(2π( f   0   +f   Δ ) t )+sin(2π( f   0   −f   Δ ) t ))
 
         x   2 ( t )=cos(2π f   0    t )sin(2π f   Δ   t )=0.5(sin(2π( f   0   +f   Δ ) t )−sin(2π( f   0   −f   Δ ) t ))
 
         x   1 ( t )+ x   2 ( t )=sin(2π( f+f   Δ ) t )
 
     For each transmit channel circuit, the frequency offset generator  306  generates a frequency offset tone based on a fundamental offset frequency Δf that is derived from the LO signal and multiplied by an integer (e.g., 1, 2, 3, 4, . . . N−1), with a different integer value being used for each transmit channel circuit. For example, the frequency offset generator  306 A generates a first frequency offset tone 1×Δf that is supplied to the FOM mixer  313  for the second transmit channel circuit  314 / 315 . Likewise, the frequency offset generator  306 A generates a second frequency offset tone 2×Δf that is supplied to the FOM mixer for the third transmit channel circuit, and so on, with the frequency offset generator  306 A generating a last frequency offset tone (N−1)×Δf that is supplied to the FOM mixer  316  for the last transmit channel circuit  317 / 318 . In this way, the frequency offset generator  306 A provides N−1 offset tones for the transmit channel circuits. If desired, an additional 2NΔf Hz component can be generated to drive the ADC if the sampling rate if f s =2NΔf. Note also that depending on the radar system requirements and also upon the actual performance of the low-pass filter  325  that directly precedes the ADC, the sample rate of the ADC may need to be increased beyond f s =2NΔf. 
     While any suitable frequency offset generator circuit arrangement may be used, reference is now made to  FIG. 5  which depicts a simplified schematic block diagram of frequency offset modulation generator  500  in accordance with a first selected embodiment of the present disclosure. As depicted, the frequency offset modulation generator  500  is connected to receive the fundamental offset frequency tone (sin(2πf Δ t)) as an input, and to output the received frequency tone as a first output offset frequency tone (sin(2πf Δ t)). The frequency offset modulation generator  500  also includes a plurality of frequency multiplier circuits  502 - 506 , each providing a different integer multiplier function to generate a corresponding output. For example, a first frequency multiplier circuit  502  provides a 2× multiplier function to generate a second output offset frequency tone (sin(2π2f Δ t)). In addition, a second frequency multiplier circuit  503  provides a 3× multiplier function to generate a third output offset frequency tone (sin(2π3f Δ t)), a third frequency multiplier circuit  504  provides a 4× multiplier function to generate a third output offset frequency tone (sin(2π4f Δ t)), and so on, with the a (N−1)th frequency multiplier circuit  505  providing an (N−1)× multiplier function to generate the (N−1)th output offset frequency tone (sin((N−1)π2f Δ t)). In selected embodiments, the frequency offset modulation generator  500  may also include an additional frequency multiplier  506  that provides a 2N multiplier function to the generate the sampling output offset frequency tone (sin(2π2Nf Δ t)) for driving the ADC in the receiver module if the sampling rate if f s =2NΔf. Note also that depending on the radar system requirements and also upon the actual performance of the low-pass filter  325  that directly precedes the ADC, the sample rate of the ADC may need to be increased beyond f s =2NΔf. 
     While the frequency offset tones can be generated from the fundamental offset frequency using a plurality of multipliers, it will be appreciated that other approaches for generating the offset frequencies may be used. For example, reference is now made to  FIG. 6  which depicts a simplified schematic block diagram of frequency offset modulation generator  600  in accordance with a second selected embodiment of the present disclosure wherein the FOM tones are generated from the sampling frequency of the ADC LO at f s  Hz. As depicted the frequency offset modulation generator  600  is connected to receive the ADC sampling frequency tone (sin(2πf s t)) as an input to a first frequency divider circuit  601  which divides the input frequency by a factor of 2N for output as a first output offset frequency tone (sin(2πf Δ t)). The frequency offset modulation generator  600  also includes a plurality of frequency multiplier circuits  602 - 605 , each providing a different integer multiplier function to generate a corresponding output. For example, a first frequency multiplier circuit  602  provides a 2× multiplier function to the output from the first frequency divider circuit  601 , thereby generating a second output offset frequency tone (sin(2π2f Δ t)). In addition, a second frequency multiplier circuit  603  provides a 3× multiplier function to the output from the first frequency divider circuit  601 , thereby generating a third output offset frequency tone (sin(2π3f Δ t)), and a third frequency multiplier circuit  604  provides a 4× multiplier function to the output from the first frequency divider circuit  601 , thereby generating a third output offset frequency tone (sin(2π4f Δ t)), and so on, with the a (N−1)th frequency multiplier circuit  605  providing an (N−1)× multiplier function to generate the (N−1)th output offset frequency tone (sin((N−1)π2f Δ t)). 
     For a contextual understanding of the design and arrangement of a range-divided transmitter signal spectrum produced by a frequency offset modulation LFM range division MIMO automotive radar system, reference is now made to  FIG. 7  which depicts an example fast-time range FFT spectrum  700  of an I-sample only receiver channel of a conventional LFM automotive radar having a designed 2π range of 400 m which corresponds to a 2π IF frequency of 40 MHz. In the example, the potential range spectrum  700  of such a radar is generated from a single transmit antenna Tx 1  by sampling only the real part (I samples) of the mixer output at the receiver for use in producing the spectrum. Given real samples only, it can be seen that the spectrum is conjugate symmetric around the zero frequency, in which case the usable range extent is between 0 and 200 m, and the maximum unambiguous range of this radar is designed to be 200 m. It will also be appreciated that any simultaneous transmission from multiple transmit antennas of the same of LFM waveforms will result in overlapping signals in the same range FFT spectrum segment, making it impossible to extract individual transmit channel information. While this information extraction problem can be addressed by temporally separating the LFM waveform transmissions from each transmit antenna, such a time-division scheme by itself has the performance limitations and drawbacks noted hereinabove. 
     To address these limitations and others known to those skilled in the art, there is disclosed herein a frequency offset modulation (FOM) approach for use with LFM automotive radar systems to separate individual transmit channel information within the fast-time range FFT spectrum at the receiver by having the transmitter mix a unique frequency offset signal with the chirp signal of each transmit channel. To illustrate the resulting transmit signal spectrum, reference is now made to  FIG. 8  which depicts a fast-time range FFT spectrum  800  of a receiver channel of an I-sample only mixer which receives an 8-transmitter frequency offset modulated LFM range-division MIMO automotive radar in accordance with selected embodiments of the present disclosure. Based on the waveform configuration shown in  FIG. 7 , the application of frequency offset modulation to support 8 transmitters for RD-MIMO will require that the sampling rate be increased to at least 320 MHz so that each transmitter occupies a portion of the spectrum without overlapping each other. As depicted with the darker lines, the transmitter channels Tx 1 -Tx 8  occupy consecutive 20 MHz spectrum segments between 0 and 160 MHz, and as indicated with the gray lines, the rest of the spectrum  800  is conjugate symmetrically redundant due to the use of real sample only data. In this case, the offset frequency f Δ  between two adjacent transmitters is 20 MHz. Again, the use of only real samples means that the spectrum is conjugate symmetric around the zero frequency, and the usable range extent for each transmitter Tx 1 -Tx 8  is between 0 and 200 m, with each transmitter&#39;s range extent being shifted or offset from one another in the range FFT spectrum  800  (e.g., 0 m≤Tx 1 &lt;200 m, 200 m≤Tx 2 &lt;400 m, 400 m≤Tx 3 &lt;600 m, etc.). Based on the range-spectrum division arrangement whereby individual transmitters occupy distinct portions of the spectrum  800 , the fast-time samples associated with distinct transmitters may be recovered at the receiver module for subsequent processing to construct the MIMO virtual array. 
     To provide another example transmitter signal spectrum for an LFM range division MIMO automotive radar system, reference is now made to  FIG. 9  which depicts a fast-time range FFT spectrum  900  of a receiver channel of an I-sample only for a 16-transmitter frequency offset modulated LFM range-division MIMO automotive radar in accordance with selected embodiments of the present disclosure. Assuming the same waveform configuration as before, the ADC sampling rate must be increased to at least 640 MHz so that each transmitter occupies at least 20 MHz of the spectrum without overlapping each other. Note also that depending on the radar system requirements and also upon the actual performance of the low-pass filter  325  that directly precedes the ADC, the sample rate of the ADC may need to be increased beyond f s =2NΔf. As depicted with the darker lines, the transmitter channels Tx 1 -Tx 16  occupy consecutive 20 MHz spectrum segments between 0 and 320 MHz, and as indicated with the gray lines, the rest of the spectrum  900  is conjugate symmetrically redundant due to the use of real sample only data. 
     As will be appreciated, other sampling arrangements can be implemented with FOM LFM RD-MIMO automotive radar systems to provide a fast-time range division FFT spectrum. For example, both the real and imaginary (I and Q) samples may be used for producing the spectrum. To provide an example of transmitter signal spectrum generated from I and Q samples, reference is now made to  FIG. 10  which depicts a fast-time range FFT spectrum  1000  of a receiver channel of an I/Q sample for a 16-transmitter frequency offset modulated LFM range-division MIMO automotive radar in accordance with selected embodiments of the present disclosure. By virtue of using both I and Q samples, the sampling rate of each of the I and Q channel ADCs can be reduced to 320 MHz while still allowing the 16 transmitters to fit within the 320 MHz swath of spectrum while maintaining at least 20 MHz of the spectrum for each transmitter without overlapping each other. In particular, the transmitter channels Tx 1 -Tx 16  occupy consecutive 20 MHz spectrum segments between 0 and 320 MHz. However, this arrangement requires balanced I/Q mixers and two ADCs (one for I samples and one for Q samples) which may be costlier than the I-sample only implementation for achieving similar performance. 
     While selected embodiments of the FOM MIMO scheme are described with reference to using I/Q modulation mixers to combine offset frequency signals (f Δ , 2f Δ , 3f Δ , etc.) with the reference chirp signal, it will be appreciated that some I/Q modulators impose significant hardware costs and complexity, such as the requirement for implementing phase shifters and/or for avoiding unbalanced I/Q mixing that can arise when there is misalignment between the amplitude and phase of the I and Q channels. To provide additional details for an improved understanding of selected single channel modulation mixer embodiments of the present disclosure, reference is now made to  FIG. 11  which depicts a simplified diagram of an I-branch only frequency offset modulation mixer  1100  which shifts the carrier frequency of the reference chirp signal sin(2πf 0  t) by the offset tone signal sin(2πf Δ t) which are both input to the I-channel only FOM mixer  1101 . In this example, the frequency f 0  represents the chirp signal&#39;s instantaneous frequency, and the frequency f Δ  represents a constant offset frequency. As indicated by the single mixer symbol, the FOM mixer  1101  is a single channel (e.g., I-channel only) mixer for mixing the LFM waveform of the reference chirp signal carrier sin(2πf 0  t)) with a fixed frequency of the offset tone (sin(2πf Δ t)). As will be appreciated, the same operative principles may be used to implement a Q-branch only frequency offset modulation mixer (not shown) for shifting the carrier frequency of the reference chirp signal sin(2πf 0  t) by the offset tone signal sin(2πf Δ t). 
     In the depicted example of an I-channel only FOM mixer  1101 , the reference chirp input signal carrier (sin(2πf 0  t)) is provided as an I-channel for mixing with the I component of the offset tone (sin(2πf Δ t)) at the I-channel only mixer  1102  to produce the mixer output x 1 (t) which includes a first down-shifted delta component (e.g., 0.5(cos(2π(f 0 −f Δ )t)) and a second up-shifted sum component (e.g., −0.5(cos(2π(f 0 +f Δ )t)). To demonstrate that the sum of the two components is the frequency-offset modulated chirp signal, the following derivation of the mixer output x 1 (t) may be established based upon established trigonometric identities: 
         x   1 ( t )=0.5 cos(2π( f   0   −f   Δ ) t )−0.5 cos(2π( f   0   +f   Δ ) t )=0.5 sin(2π( f   0   −f   Δ ) t+π/ 2)+0.5 sin(2π( f   0   +f   Δ ) t−π/ 2).
 
     With this derivation, it is seen that the I-channel only mixer output x 1 (t) includes a first down-shifted delta component (e.g., 0.5(sin(2π(f 0 −f Δ )t+π/2)) and a second up-shifted sum component (e.g., 0.5 sin(2π(f 0 +f Δ )t−π/2)). The sum component shifts the range spectrum of a transmitter by the amount of offset frequency to the positive range direction. The delta component shifts the range spectrum of a transmitter by the amount of offset frequency to the negative range direction. 
     As will be appreciated, the mixer output x 1 (t) value when the frequency offset f Δ =0 will depend on the configuration of the frequency offset generator (e.g.,  FIG. 3A, 306A  or  FIG. 3B, 306B ) and the FOM mixers in the transmit modules (e.g.,  FIG. 3A, 310A  or  FIG. 3B, 310B ). For example, with the transmit module configuration shown in  FIG. 3A  where the first transmit channel  311 ,  312  has no mixer, the mixer output x 1 (t)=sin(2πf 0 t), which is out-of-phase with the other channel&#39;s up-shifted sum component by π/2 and therefore requires proper handling at the receiver. In contrast, with the transmit module configuration shown in  FIG. 3B  where the each transmit channel includes a mixer, the mixer output x 1 (t)=0 when the frequency offset f Δ =0. 
     In this simplified FOM transmit mixer implementation  1101 , circuit complexity is reduced by eliminating the Q channel processing circuits and phase shifters, such as the phase shifters  452 ,  454  and summing circuits  456  shown in  FIG. 4B . In addition to reducing the required hardware, the I-branch only FOM mixer  1101  eliminates the magnitude and phase mismatch problem that can arise from unbalanced I/Q mixing (that is, misaligned amplitude and phase between I and Q channels). However, a drawback with such single-channel mixer is that the mixer output signal x 1 (t) contains an undesirable down-shifted delta component which has to be properly handled at the receiver. 
     To illustrate this issue, reference is now made to  FIG. 12A  which depicts a fast-time range FFT spectrum  1200  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3A  which uses I-branch only FOM mixers with insufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver. In this example, the transmitter uses I-channel only FOM mixers connected to all but the first transmit channel circuit to provide integer multiples of a frequency offset f Δ =20 Mhz to generate transmit channel offsets at 0 MHz, 20 MHz, 40 MHz, 60 MHz, 80 MHz, 100 MHz, 120 MHz, and 140 MHz. At the receiver, the I-channel only ADC having a sampling rate of 320 MHz creates, for each transmitter (Txi), a sum component  1201  (shown with the black solid line and normal font), a delta component  1202  (shown with the black dotted line and bold-faced font), a sum component&#39;s complex-conjugate image  1203  (shown with the gray solid line and italic font), and a delta component&#39;s complex-conjugate image  1204  (shown with the gray dotted line and bold-faced italic font). In an example scenario where a 20 MHz IF spectrum is assumed to be sufficient to cover the maximum range, the I-only FOM mixing results in the delta components whose spectral image aliases with the sum component, causing significant interference. In particular, this is illustrated with the images of the delta component  1204  (shown with gray dotted line) for each transmitter (e.g., Tx 2 ) which alias into the designated range spectrum for detecting the sum component  1201  (shown with black solid line) of a different transmitter (e.g., Tx 1 ), thereby causing severe ambiguity in terms of what is being detected in the range spectrum segments for each transmit channel. In addition, the downshifted delta component  1202  (shown with black dotted line) for each transmitter (e.g., Tx 2 ) aliases into the image of the sum component  1203  (shown with gray solid line) of a different transmitter (e.g., Tx 1 ), thereby impairing correct detection. This happens when the transmit channel offset is no greater than twice of the instrumented range spectrum extent of an individual transmitter&#39;s instrumented range-spectrum bandwidth. 
     To provide another illustration of this issue, reference is now made to  FIG. 12B  which depicts a fast-time range FFT spectrum  1210  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixers with insufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver. In this example, the transmitter uses I-channel only FOM mixers connected to each transmit channel circuit to provide integer multiples of a frequency offset f Δ =20 Mhz to generate transmit channel offsets at 0 MHz, 20 MHz, 40 MHz, 60 MHz, 80 MHz, 100 MHz, 120 MHz, and 140 MHz. At the receiver, the I-channel only ADC having a sampling rate of 320 MHz creates, for each transmitter (Txi), a sum component  1211  (shown with the black solid line and normal font), a delta component  1212  (shown with the dotted black line and bold-faced font), a sum component&#39;s complex-conjugate image  1213  (shown with the gray solid line and italic font), and a delta component&#39;s complex-conjugate image  1214  (shown with the gray dotted line and bold-faced italic font). As illustrated, the upshifted sum component from the first transmitter Tx 1  is cancelled by the downshifted delta component from the first transmitter Tx 1 , and the image of the sum component from the first transmitter Tx 1  cancels the image of the delta component from the first transmitter Tx 1 . In addition, the images of the delta component  1214  (shown with gray dotted line) for one transmitter (e.g., Tx 2 ) alias into the designated range spectrum for detecting the sum component  1211  (shown with black solid line) for a different transmitter (e.g., Tx 1 ), thereby causing severe ambiguity in terms of what is being detected in the range spectrum segments for each transmit channel. Likewise, the downshifted delta component  1212  (shown with black dotted line) for each transmitter (e.g., Tx 2 ) aliases into the image of the sum component  1213  (shown with gray solid line) of a different transmitter (e.g., Tx 1 ), thereby impairing correct detection. Again, this happens when the transmit channel offset is no greater than twice of the instrumented range spectrum extent of an individual transmitter&#39;s instrumented range-spectrum bandwidth. 
     To prevent spectrum aliasing interactions between the images of the delta component (e.g.,  1204 ) of a first I-channel only mixer and an adjacent channel&#39;s sum component (e.g.,  1201 ), the amount of offset frequency f Δ  should be doubled or increased by at least 100 percent, with a corresponding increase in the ADC sampling rate at the receiver module  320  in order to maintain number of supported transmitters. As a result of these adjustments to the amount of frequency offset and ADC sampling rate, the final range spectrum may be derived from the sum and delta components by means of coherently integrating the range spectrums. By at least doubling the offset frequency f Δ , much of the aliasing effect is eliminated. With the up-shifted sum component and down-shifted delta component range spectrum both available, they can be combined to achieve better signal-to-noise ratio (SNR). 
     To illustrate a first example solution, reference is now made to  FIG. 13A  which depicts a fast-time range FFT spectrum  1300  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3A  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. In this first example solution, the transmitter uses I-channel only FOM mixers connected to all but the first transmit channel circuit to provide integer multiples of a frequency offset f Δ =40 Mhz to generate transmit channel offsets at 0 MHz, 40 MHz, 80 MHz, and 120 MHz. At the receiver, the I-channel only ADC having a sampling rate of 320 MHz creates, for each transmitter (Txi), an upshifted sum component  1301  (shown with the black solid line and normal font), a downshifted delta component  1302  (shown with the dotted black line and bold-faced font), a sum component&#39;s complex-conjugate image  1303  (shown with the gray solid line and italic font), and a delta component&#39;s complex-conjugate image  1304  (shown with the gray dotted line and bold-faced italic font). As illustrated, the upshifted sum component  1301  for a first transmitter (e.g., from the first transmitter Tx 1 ) has no interfering aliasing from the image of the delta component  1304  from an adjacent transmitter (e.g., from the second transmitter Tx 2 ). In addition, there is no aliasing interference between images of the delta component  1302  (shown with black dotted line) for a first transmitter (e.g., a first transmitter Tx 1 ) and the image of the sum component  1303  (shown with gray solid line) for an adjacent transmitter (e.g., a second transmitter Tx 2 ). As a result, the sum and delta components of the first transmitter Tx 1  are both available and can be combined in the first IF bandwidth segment (0-20 MHz) to achieve better SNR performance. 
     As illustrated with the first example solution shown in  FIG. 13A , the ADC sampling rate of 320 MHz supports four transmitters, each consuming 40 MHz except for the first transmitter Tx 1 , which consumes only 20 MHz. Thus, the number of supported transmitters is halved in comparison to the example shown in  FIG. 12A , given the same ADC sampling rate (namely 320 MHz). However,  FIG. 13A  shows that there is unused spectrum between 140 MHz and 160 MHz and −140 MHz and −160 MHz, indicating that the ADC rate may be reduced by 40 MHz to 280 MHz and still support 4 transmitters. Alternatively, the receiver module (e.g.,  320 ) may be configured to support additional transmitters by increasing the ADC sampling rate by 80 MHz to fit each additional transmitter (in the given example). For example, to fit 8 transmitters, the ADC sampling rate should be increased to at least 600 MHz. Similarly, to support 16 transmitters, the ADC sampling rate must be at least 1240 MHz. 
     To illustrate a second example solution, reference is now made to  FIG. 13B  which depicts a fast-time range FFT spectrum  1310  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3A  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. In this second example, the transmitter uses I-channel only FOM mixers connected to all transmit channel circuits to provide integer multiples of a frequency offset f Δ =40 Mhz to generate transmit channel offsets at 0 MHz, 40 MHz, 80 MHz, and 120 MHz. At the receiver, the I-channel only ADC having a sampling rate of 320 MHz creates, for each transmitter (Txi), an upshifted sum component  1311  (shown with the black solid line and normal font), a downshifted delta component  1312  (shown with the dotted black line and bold-faced font), a sum component&#39;s complex-conjugate image  1313  (shown with the gray solid line and italic font), and a delta component&#39;s complex-conjugate image  1314  (shown with the gray dotted line and bold-faced italic font). As illustrated, if a frequency offset f Δ  is not applied to the first transmitter, the upshifted sum component  1311  for the first transmitter Tx 1  is cancelled by the image of the delta component  1314  for the first transmitter Tx 1 , and the image of the delta component  1314  for the first transmitter Tx 1  is cancelled by the image of the sum component  1313  for the first transmitter Tx 1 . To avoid aliasing and cancellation of the signal from the first transmitter Tx 1 , the first transmitter Tx 1  needs to be offset, but only by the regular amount which is at least the instrumented range spectrum extent of a transmitter. 
     To illustrate an adjustment for avoiding cancellation of the first transmitter signal, reference is now made to  FIG. 13C  which depicts a fast-time range FFT spectrum  1320  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixer range spectrum with a first frequency offset for the first transmitter and a second, doubled frequency offset for the remaining transmitters in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. In this example solution, the transmitter uses I-channel only FOM mixers connected to all transmit channel circuits to generate transmit channel offsets at 20 MHz, 60 MHz, 100 MHz, and 120 MHz. In this example, a first frequency offset (e.g., f Δ =20 Mhz) is applied to the first transmitter which is at least the instrumented range spectrum extent of a transmitter, and a second frequency offset (e.g., f Δ =40 Mhz) is applied to the remaining transmitters to avoid signal overlap and cancellation of the first transmitter Tx 1 . At the receiver, the I-channel only ADC having a sampling rate of 320 MHz creates, for each transmitter (Txi), an upshifted sum component  1321  (shown with the black solid line and normal font), a downshifted delta component  1322  (shown with the dotted black line and bold-faced font), a sum component&#39;s complex-conjugate image  1323  (shown with the gray solid line and italic font), and a delta component&#39;s complex-conjugate image  1324  (shown with the gray dotted line and bold-faced italic font). As illustrated, the “Tx 1 ” delta component&#39;s target echo component  1325  is phase-shifted 180° from the “Tx 1 ” sum component&#39;s target echo component  1321 . In addition, the corresponding noise components for the first transmitter (e.g., image of the sum component for Tx 1  and the image of the delta component for Tx 1 ) are independent of one another. As a result, the delta component of Tx 1   1322  may be phase-shifted by 180° and combined with the sum component of the Tx 1   1321  to double the target echo component&#39;s amplitude, quadruple its power, thereby doubling the noise component&#39;s variance (power) and the SNR. As will be appreciated, a similar improvement in the SNR gain can also be achieved by combining the images of the sum and delta components  1323 ,  1324 . However, SNR gains cannot be achieved by combining a sum or delta component with its image because the noise values are not independent. 
     As illustrated with the example solution shown in  FIG. 13C , the ADC sampling rate of 320 MHz supports four transmitters, which is half the number of transmitters from the example shown in  FIG. 12B  given the same ADC sampling rate (namely 320 MHz). However, the receiver module (e.g.,  320 ) may be configured to support additional transmitters by increasing the ADC sampling rate by 80 MHz to fit each additional transmitter (in the given example). For example, to fit 8 transmitters, the ADC sampling rate should be increased to at least 600 MHz. Similarly, to support 16 transmitters, the ADC sampling rate must be at least 1240 MHz. 
     To illustrate a first example solution for coherently integrating the sum and delta components, reference is now made to  FIG. 14A  which diagrammatically depicts a coherent integration of the sum and delta components in a fast-time range FFT spectrum  1400  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3A  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. In the depicted example solution, the transmitter uses I-channel only FOM mixers connected to all but the first transmit channel circuit to generate transmit channel offsets at 0 MHz, 40 MHz, 80 MHz, and 120 MHz. At the receiver, the I-channel only ADC having a sampling rate of 320 MHz creates, for each transmitter (Txi), an upshifted sum component (shown with the black solid line and normal font), a downshifted delta component (shown with the dotted black line and bold-faced font), a sum component&#39;s complex-conjugate image (shown with the gray solid line and italic font), and a delta component&#39;s complex-conjugate image (shown with the gray dotted line and bold-faced italic font). Since the I-only FOM mixers on transmit module divide the transmit power into the sum and delta components, the received signal power is also halved if only the sum or delta component is processed at the receiver (except for the first transmit channel). This is illustrated in  FIG. 14A  which shows that the transmitter&#39;s sum and delta spectral segments are separated by applying the appropriate frequency offset values to each transmitter channel. 
     Once the separation of transmitters and the sum and delta spectral segments are done, a final spectrum can be produced for each transmitter by using a combination of phase shifter and summing circuits  1401 - 1407  to coherently combine the sum and delta spectrums in the digital domain. In this example, it is noted that the first transmitter Tx 1  does not undergo the FOM mixing, so it is ahead of the sum component outputs by 90 degrees in phase. As a result, a first phase shifter circuit  1401  applies a −90° phase shift to the first transmitter&#39;s spectrum to align all outputs (e.g., by multiplying with e −jπ/2 ) into an output Tx 1  signal  1410 . For the remaining transmitters, it is noted that the sum component for a given transmitter (e.g., Tx 2 ) lags the corresponding delta component by a phase shift of 180°, so coherent combination is implemented simply by reversing the sign of the delta component before summing the two extracted spectrum segments. For example, a second phase shifter circuit  1402  applies a 180° phase shift to the second transmitter&#39;s delta component for combination with the second transmitter&#39;s sum component at the summing circuit  1403  to generate a coherently combined output Tx 2  signal  1411 . In addition, a third phase shifter circuit  1404  applies a 180° phase shift to the third transmitter&#39;s delta component for combination with the third transmitter&#39;s sum component at the summing circuit  1405  to generate a coherently combined output Tx 3  signal  1412 . And finally, a fourth phase shifter circuit  1406  applies a 180° phase shift to the fourth transmitter&#39;s delta component for combination with the fourth transmitter&#39;s sum component at the summing circuit  1407  to generate a coherently combined output Tx 4  signal  1413 . As a result, the coherently combined delta and sum components for the transmitters  1410 - 1413  result in a quadrupled target echo signal power, a doubled noise power, and a doubled SNR. 
     As illustrated with the example solution shown in  FIG. 14A , the ADC sampling rate of 320 MHz supports four transmitters. Thus, the number of supported transmitters is halved in comparison to the example shown in  FIG. 12A , given the same ADC sampling rate (namely 320 MHz). However,  FIG. 14A  shows that there is unused spectrum between 140 MHz and 160 MHz and between −140 MHz and −160 MHz, indicating that the ADC rate may be reduced by 40 MHz to 280 MHz and still support 4 transmitters. Alternatively, the receiver module may be configured to support additional transmitters by increasing the ADC sampling rate to fit each additional transmitter. 
     To illustrate a second example solution for coherently integrating the sum and delta components, reference is now made to  FIG. 14B  which diagrammatically depicts a coherent integration of the sum and delta components in a fast-time range FFT spectrum  1420  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. In the depicted solution, the transmitter uses I-channel only FOM mixers connected to all transmit channel circuits to generate transmit channel offsets at 20 MHz, 60 MHz, 100 MHz, and 140 MHz. At the receiver, the I-channel only ADC having a sampling rate of 320 MHz creates, for each transmitter (Txi), an upshifted sum component  1421  (shown with the black solid line and normal font), a downshifted delta component  1422  (shown with the dotted black line and bold-faced font), a sum component&#39;s complex-conjugate image  1423  (shown with the gray solid line and italic font), and a delta component&#39;s complex-conjugate image  1424  (shown with the gray dotted line and bold-faced italic font). Since the I-only FOM mixers on transmit module divide the transmit power into the sum and delta components, the received signal power is also halved if only the sum or delta component is processed at the receiver. This is illustrated in  FIG. 14B  which shows that the transmitter&#39;s the sum and delta spectral segments are separated by applying the appropriate frequency offset values to each transmitter channel. 
     Once the separation of transmitters and the sum and delta spectral segments are done, a final spectrum can be produced for each transmitter by using a combination of phase shifter and summing circuits  1425 - 1432  to coherently combine the sum and delta spectrums in the digital domain. In this example, each of the transmitters generates a sum component that lags the corresponding delta component by a phase shift of 180°, so coherent combination is implemented simply by reversing the sign of the delta component before summing the two extracted spectrum segments. For example, a first phase shifter circuit  1425  applies a 180° phase shift to the first transmitter&#39;s delta component for combination with the first transmitter&#39;s sum component at the summing circuit  1426  to generate a coherently combined output Tx 2  signal  1432 . In addition, a second phase shifter circuit  1427  applies a 180° phase shift to the second transmitter&#39;s delta component for combination with the second transmitter&#39;s sum component at the summing circuit  1428  to generate a coherently combined output Tx 2  signal  1433 . In addition, a third phase shifter circuit  1429  applies a 180° phase shift to the third transmitter&#39;s delta component for combination with the third transmitter&#39;s sum component at the summing circuit  1430  to generate a coherently combined output Tx 3  signal  1434 . And finally, a fourth phase shifter circuit  1431  applies a 180° phase shift to the fourth transmitter&#39;s delta component for combination with the fourth transmitter&#39;s sum component at the summing circuit  1432  to generate a coherently combined output Tx 4  signal  1435 . As a result, the coherently combined delta and sum components for the transmitters  1432 - 1435  result in a quadrupled target echo signal power, a doubled noise power, and a doubled SNR. 
     As illustrated with the example solution shown in  FIG. 14B , the ADC sampling rate of 320 MHz supports four transmitters. Thus, the number of supported transmitters is halved in comparison to the example shown in  FIG. 12B , given the same ADC sampling rate (namely 320 MHz). However, the receiver module may be configured to support additional transmitters by increasing the ADC sampling rate to fit each additional transmitter. 
     To illustrate a third example solution for coherently integrating the sum and delta image components, reference is now made to  FIG. 15  which diagrammatically depicts a coherent integration of the sum and delta image components in a fast-time range FFT spectrum  1500  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with I-channel only analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. In the depicted solution, the transmitter uses I-channel only FOM mixers connected to all transmit channel circuits to generate transmit channel offsets at 20 MHz, 60 MHz, 100 MHz, and 140 MHz. At the receiver, the I-channel only ADC having a sampling rate of 320 MHz creates, for each transmitter (Txi), an upshifted sum component  1501  (shown with the black solid line and normal font), a downshifted delta component  1502  (shown with the dotted black line and bold-faced font), a sum component&#39;s complex-conjugate image  1503  (shown with the gray solid line and italic font), and a delta component&#39;s complex-conjugate image  1504  (shown with the gray dotted line and bold-faced italic font). Since the I-only FOM mixers on transmit module divide the transmit power into the sum and delta components, the received signal power is also halved if only the sum or delta component is processed at the receiver. This is illustrated in  FIG. 15  which shows that the transmitter&#39;s the sum and delta spectral segments are separated by applying the appropriate frequency offset values to each transmitter channel. 
     Once the separation of transmitters and the sum and delta image spectral segments are done, a final spectrum can be produced for each transmitter by using a combination of phase shifter, summing, and index reversal circuits  1505 - 1516  to coherently combine the sum and delta image spectrums in the digital domain. In this example, each of the transmitters generates a sum image component that lags the corresponding delta image component by a phase shift of 180°, so coherent combination is implemented simply by reversing the sign of the sum image component segment before summing with the delta image component segment. For example, a first phase shifter circuit  1505  applies a 180° phase shift to the first transmitter&#39;s sum image component for combination with the first transmitter&#39;s delta image component at the summing circuit  1506  to generate a coherently combined signal which has sample indices reversed at the index reversal circuit  1513  to generate the output Tx 2  signal  1520 . In addition, a second phase shifter circuit  1507  applies a 180° phase shift to the second transmitter&#39;s sum image component for combination with the second transmitter&#39;s delta image component at the summing circuit  1508  to generate a coherently combined signal which has sample indices reversed at the index reversal circuit  1514  to generate the output Tx 2  signal  1521 . In addition, a third phase shifter circuit  1509  applies a 180° phase shift to the third transmitter&#39;s sum image component for combination with the third transmitter&#39;s delta image component at the summing circuit  1510  to generate a coherently combined signal which has sample indices reversed at the index reversal circuit  1515  to generate the output Tx 3  signal  1522 . And finally, a fourth phase shifter circuit  1511  applies a 180° phase shift to the fourth transmitter&#39;s sum image component for combination with the fourth transmitter&#39;s delta image component at the summing circuit  1512  to generate a coherently combined signal which has sample indices reversed at the index reversal circuit  1516  to generate the output Tx 4  signal  1523 . As a result, the coherently combined delta and sum image components for the transmitters  1520 - 1523  result in a quadrupled target echo signal power, a doubled noise power, and a doubled SNR. 
     As illustrated with the example solution shown in  FIG. 15 , the ADC sampling rate of 320 MHz supports four transmitters. Thus, the number of supported transmitters is halved in comparison to the example shown in  FIG. 12B , given the same ADC sampling rate (namely 320 MHz). However, the receiver module may be configured to support additional transmitters by increasing the ADC sampling rate to fit each additional transmitter. 
     To provide additional details for an improved understanding of selected embodiments of the present disclosure, reference is now made to  FIG. 16A  which depicts a fast-time range FFT spectrum  1600  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3A  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with I/Q-channel analog-to-digital converter in the receiver. In the depicted embodiment, the transmitter uses I-channel only FOM mixers connected to all but the first transmit channel circuit to generate transmit channel offsets at 0 MHz, 20 MHz, 40 MHz, 60 MHz, 80 MHz, 100 MHz, 120 MHz, and 140 MHz. At the receiver, an I/Q channel ADC is provided with a sampling rate of 320 MHz to create, for each transmitter (Txi), an upshifted sum component  1601  (shown with the black solid line and normal font) and a downshifted delta component  1602  (shown with the dotted black line and bold-faced font). Since the I-only FOM mixers on transmit module divide the transmit power into the sum and delta components, the received signal power is also halved if only the sum or delta component is processed at the receiver (except for the first transmit channel). When I-channel only FOM mixers are used at the transmitter and the I/Q ADC is used at the receiver, the delta components may alias into sum components if sampling frequency is not sufficiently high, causing cancelation or interference.  FIG. 16A  shows the case of the minimally required sampling frequency for the I/Q ADC. 
     Once the separation of transmitters and the sum and delta spectral segments are done, a final spectrum can be produced for each transmitter by using a combination of phase shifter and summing circuits to coherently combine the sum and delta spectrums in the digital domain. In this example, it is noted that the first transmitter Tx 1  does not undergo the FOM mixing, so it is ahead of the sum component outputs by 90 degrees in phase. As a result, the sum and delta components of the transmitters Tx 2 -Tx 8  can be coherently combined after applying the 180° phase shift to the delta component, while the sum component of the first transmitter Tx 1  is phase shifted by −90° to be in phase with other channels. As illustrated with the example solution shown in  FIG. 16A , the ADC sampling rate of 320 MHz supports eight transmitters. 
     To provide additional details for an improved understanding of selected embodiments of the present disclosure, reference is now made to  FIG. 16B  which depicts a fast-time range FFT spectrum  1610  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixer range spectrum with insufficient frequency offset in combination with I/Q-channel analog-to-digital converter in the receiver. In the depicted embodiment, the transmitter uses I-channel only FOM mixers connected to all but the first transmit channel circuit to generate transmit channel offsets at 0 MHz, 20 MHz, 40 MHz, 60 MHz, 80 MHz, 100 MHz, 120 MHz, and 140 MHz. At the receiver, an I/Q channel ADC is provided with a sampling rate of 320 MHz to create, for each transmitter (Txi), an upshifted sum component  1611  (shown with the black solid line and normal font) and a downshifted delta component  1612  (shown with the dotted black line and bold-faced font). Since the I-only FOM mixers on transmit module divide the transmit power into the sum and delta components, the received signal power is also halved if only the sum or delta component is processed at the receiver (except for the first transmit channel). When I-channel only FOM mixers are used at the transmitter and the I/Q ADC is used at the receiver, the delta components may alias into sum components if sampling frequency is not sufficiently high, causing cancelation or interference.  FIG. 16B  shows the case where the upshifted sum component from the first transmitter Tx 1  is cancelled by the downshifted delta component from the first transmitter Tx 1 . 
     To avoid interference or cancellation of the first transmitter Tx 1 , a carrier frequency offset should also be applied to the first transmitter Tx 1  and the sampling frequency should be increased to fit all transmitters unambiguously. An example embodiment of such a solution is illustrated in  FIG. 16C  which depicts a fast-time range FFT spectrum  1620  of a frequency offset modulation LFM range division MIMO automotive radar system such as shown in  FIG. 3B  which uses I-branch only FOM mixer range spectrum with sufficient frequency offset in combination with I/Q-channel analog-to-digital converter in the receiver in accordance with selected embodiments of the present disclosure. In the depicted embodiment, the transmitter uses I-channel only FOM mixers connected to all transmit channel circuits to generate transmit channel offsets at 20 MHz, 40 MHz, 60 MHz, 80 MHz, 100 MHz, 120 MHz, 140 MHz, and 160 MHz. At the receiver, an I/Q channel ADC is provided with a sampling rate of 320 MHz to create, for each transmitter (Txi), an upshifted sum component  1611  (shown with the black solid line and normal font) and a downshifted delta component  1612  (shown with the dotted black line and bold-faced font). Since the I-only FOM mixers on transmit module divide the transmit power into the sum and delta components, the received signal power is also halved if only the sum or delta component is processed at the receiver (except for the first transmit channel). When I-channel only FOM mixers at the transmitter (including the first transmitter Tx 1 ) are each offset by an integer multiple of the frequency offset f Δ  and the I/Q ADC at the receiver uses a sufficiently high sampling frequency, the delta components do not alias into the sum components, thereby avoiding cancelation or interference. 
     Once the separation of transmitters and the sum and delta spectral segments are done, a final spectrum can be produced for each transmitter by using a combination of phase shifter and summing circuits to coherently combine the sum and delta spectrums in the digital domain, provided that the ADC sampling frequency is increased to fit all transmitters unambiguously. In this example, it is noted that the first transmitter Tx 1  undergoes FOM mixing along with the rest of the transmitters. As a result, the sum and delta components of the transmitters Tx 1 -Tx 8  can be coherently combined after applying the 180° phase shift to the respective delta components. As illustrated with the example solution shown in  FIG. 16C , the ADC sampling rate of 360 MHz supports eight transmitters. 
     While selected embodiments of the FOM MIMO scheme are described with reference to using an offset frequency generator to generate unique frequency offset tones for each transmit channel, it will be appreciated that other frequency offset modulation schemes may also be used. For example, selected FOM implementations may use a fast-time phase shifter at each transmit channel circuit of the transmit module in combination with a high speed ADC at the receiver module, thereby eliminating the need for I/Q modulation mixers at the transmit module. 
     To provide additional details for an improved understanding of selected phase shifter embodiments of the present disclosure, reference is now made to  FIG. 17  which depicts a simplified schematic block diagram of a frequency offset modulation LFM range division MIMO automotive radar system  1700  which includes an LFM RD-MIMO radar device  1730  having fast-time phase shifters in the transmit module  1710  which are connected and configured to transmit and receive LFM waveforms  1702 ,  1703  for reflection by a target  1701  to the receive module  1720  under control of a radar controller processor (not shown). In selected embodiments, the LFM RD-MIMO radar device  1730  and/or radar controller processor may be embodied as a line-replaceable unit (LRU) or modular component that is designed to be replaced quickly at an operating location. In addition and as described hereinbelow, the LFM RD-MIMO radar device  1730  may also be configured to perform time-division multiplexing of the transmitted LFM waveforms  1702 ,  1703  to implement a combined time-division and range-division MIMO scheme to separate the transmitters not only in the range domain, but also in the time domain. 
     As depicted, each radar device  1730  includes one or more transmitting antenna elements TXi and at least a first receiving antenna element RX connected, respectively, to one or more radio-frequency (RF) transmit modules  1710  and receive module  1720 . At each transmit module  1710 , a transmit channel circuit is provided for each transmit antenna. For example, a first transmit channel circuit includes a first RF conditioning module  1711  and power amplifier  1712  connected to a first transmit antenna TX 1 , a second transmit channel circuit includes a second RF conditioning module  1714  and power amplifier  1715  connected to a second transmit antenna TX 2 , and so on with the Nth transmit channel circuit including an Nth RF conditioning module  1717  and power amplifier  1718  connected to the Nth transmit antenna TX N . 
     In addition, each radar device  1730  includes a chirp generator  1704  which is configured and connected to supply a chirp input signal  1705  to the different transmit channel circuits  1711 / 1712 ,  1714 / 1715 ,  1717 / 1718  in the transmitter module(s)  1710 . However, instead of providing the chirp input signal  1705  directly to all of the transmit channel circuits, the radar device  1730  also includes a programmable fast-time phase shifter circuits which are connected to phase shift the chirp input signal  1705 , thereby creating progressive phase shifts which mimic the effects of a frequency offset for the transmit antennas (TX 1 -TX N ). To this end, the first transmit channel circuit  1711 / 1712  may be connected to directly receive the chirp input signal  1705 . However, the second transmit channel circuit  1714 / 1715  may include a first fast-time phase shifter  1713  which is connected to apply a first phase shift to the chirp input signal  1705  before being filtered and amplified by the second transmit channel circuit  1714 / 1715  for transmission over the antenna TX 2 . In similar fashion, the remaining transmit channel circuits (e.g.,  1717 / 1718 ) may include a fast-time phase shifter (e.g.,  1716 ) which is connected to apply a unique phase shift to the chirp input signal  1705  before being filtered and amplified by the antenna (e.g., TX N ). 
     As disclosed herein, each of the phase shifters  1713 ,  1717  may be implemented with a programable phase shifter having a fast switching time or response time. For example, phase shift control signals  1706  can be applied to programmable K-bit phase shifters  1713 ,  1716  to create progressive phase shifts at the transmitter module  1710 , thereby mimicking the effects of frequency offset for 2 (K−1)  transmitters. In selected embodiments, the phase shifters  1713 ,  1716  are used to introduce regular progressive phase shift at fast-time sampling intervals. For example, a 1-bit phase shifter with switching positions {0°, 180°} can cause frequency offsets of {0,1/(2T s )} [Hz], where T s  is fast-time sampling interval as well as the switching interval of the phase shifter in seconds. For another example, a 4-bit phase shifter with switching positions {0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, 157.5°, 180°, 202.5°, 225°, 247.5°, 270°, 292.5°, 315°, 337.5°} can cause frequency offsets of {0, 1/(32T s ), 2/(32T s ), 3/(32T s ) , 4/(32T s ), 5/(32T s ), 6/(32T s ), 7/(32T s )} [Hz]. In this case, a T s  corresponding to a switching frequency of 320 MHz allows for 8 transmitters to share a total of 320 MHz of fast-time spectrum, each occupying a segment of 40 MHz, whose integer {0, 1, 2 . . . 7} multiples are the amount of frequency offsets applied to the transmitters. 
     In principle, a K-bit phase shifter can support up to 2 (K−1)  transmitters. In addition, a frequency offset of f Δ  Hz is equivalent to imposing a progressive phase shift in time by a rate of 2πf Δ  radians per second. At a sampling rate of f Δ  Hz (or sampling interval of T s  which equals to 1/f s ), the amount of progressive (or additive) phase shift per T s  interval is then 2πf Δ /f s  radians. To comply with the Nyquist sampling theorem, the phase shifter switched at fast-time sampling rate can support a maximum frequency offset of 1/(2T s ) Hz. 
     In one example, the transmitter module  1710  may be programmed with phase shift control signals  1716  so that the phase shifters  1713 ,  1716  provide a progressive phase shift of 45 degrees (e.g., {0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°, 0°, 45°, . . . }) at intervals of T sw  seconds. With this arrangement, a complete 2π phase shift is imposed on the reference chirp every 8 intervals such that an effective frequency offset of 1/8T s  Hz is imposed on the chirp signal. For another example, the transmitter module  1710  may be programmed with a 337.5° progress phase shift per switching interval, resulting in the application of the following progressive phase shift: {0°, 337.5°, 315°, 292.5°, 270°, 247.5°, 225°, 202.5°, 180°, 157.5°, 135°, 112.5°, 90°, 67.5°, 45°, 22.5°, 0°, . . . }. The resulting progressive phase shift has a step size of −22.5° to effectively apply a negative frequency offset. Based on Nyquist criteria, a progressive phase shift with a step size no more than 180° may be applied without incurring ambiguity. As a result, 4-bit phase shifters can be used to support up to 8 frequency offsets (including the zero offset). 
     To ensure sufficient range space on the transmit spectrum is available for division amongst all transmitters, a faster analog-to-digital converter (ADC)  1726  may be employed at each receive channel  1720 . For example, an LFM RD-MIMO radar device  1730  using fast-time phase shifters  1713 ,  1716  to implement frequency offset modulation should use an ADC sampling rate that is increased to N×40 Msps. As a result, the fast-time FFT processing can divide the spectrum into N consecutive segments, with each being associated with a corresponding transmitter. 
     With the fast-time phase shifters  1713 ,  1716  phase-shifting the chirp input signal  1705  under control of the phase shift control signals  1706  before transmission on the transmit antennas TX 1 -TX N , the combined reflected LFM waveforms  1703  are received and processed by the receiver module  1720 . In particular, the receive antenna RX receives the combined reflected LFM waveforms  1703  which are then amplified by the low noise amplifier (LNA)  1721 . At the I/Q mixer  1722 , the amplified receive signal is mixed with the reference chirp signal  1705  before being conditioned for digital conversion by the high pass filter  1723 , variable gain amplifier  1724 , low pass filter  1725 , and analog-to-digital converter  1726 . 
     Generally speaking, the implementation of frequency offset modulation using fast-time phase shifters differs from a phase-coded chirp system where the phase shift switching interval may not coincide with the fast-time sampling rate and where the phase shift usually follows an orthogonal code pattern which is not a progressive phase shift. In code-division MIMO systems, the transmitters are separated by transmitting a unique phase-coded waveform that is orthogonal to those of other transmitters, and the receivers require a receiver bank of correlators to decode the signals from individual transmitters. This differs from the range-division principle of the present invention. 
     As disclosed herein, the use of frequency offset modulation in an LFM automotive radar systems enables very large MIMO arrays to be formed by separating transmitter signals in the fast-time Fourier or the range domain. The resulting virtual array is much larger than the conventional TD-MIMO approach, thereby achieving high angular resolution performance. However, by combining the FOM RD MIMO approach with TD MIMO approach, even larger MIMO virtual arrays can be formed with the additional benefit of mitigating or reducing the problem of strong beyond-maximum-range target interference than an arise with FOM RD MIMO only systems. In particular, this combined approach allows the separation of the transmitters not only in the range domain, but also in the time domain to allow the detection of extremely large RCS targets that are beyond the maximum unambiguous range measurable for each transmitter. To implement the time-domain separation, the LFM RD-MIMO radar device  330 A may be implemented as a combination LFM RD-MIMO/TD-MIMO radar device  330 A which is configured to activate adjacent transmitters in an alternating fashion over time. With the time-domain modulation implemented at the transmit module  310 A, the received transmit spectrum includes, for each transmitter range spectrum segment, an adjacent range spectrum segment that is vacant, thereby allowing strong beyond-the-range targets to be freely present and correctly detected. 
     One of the benefits from combining the FOM and TD MIMO approaches arises from the detection distance limitations of the FOM MIMO approach alone. In particular, the FOM MIMO approach effectively divides, at each receive channel, the entire range spectrum into N segments, each containing the range spectrum of a corresponding individual transmitter. In some cases, the maximum range extent of an individual range spectrum is not large enough to contain all detectable targets (especially for targets with extremely large radar cross-sections) at a distance that is longer than the maximum range of the individual transmitter. In such cases, these strong beyond-the-range targets show up at the range spectrum of the next transmitter, causing false detections or at least ambiguous detections. To avoid this, a longer-range extent may be allocated to each transmitter by allocating more IF frequency spectrum for each transmitter. However, this results in higher ADC sampling rate requirements or fewer transmitters fitting into the total range spectrum for the same ADC sampling rate. This trade-off can be avoided by combining the time division MIMO principle with the FOM Range Division MIMO principle to allow larger range extent while not reducing the maximum number of transmitters that can be supported at the expense of increased frame duration. 
     As disclosed herein, the TD and RD MIMO approaches can be combined with a variety of different schemes. For example, a combined TD and RD MIMO scheme may separately transmit the odd-number transmitters and the even-number transmitters in two groups so that the transmission for each chirp is divided with the first group of odd-numbered transmitters being transmitted first, and with the second group of even-numbered transmitters being transmitted second. To illustrate an example grouping, reference is now made to  FIG. 18  which depicts first and second fast-time range FFT spectrums  1801 ,  1802  for two time slots of a receiver channel of an I/Q sample for an 8-transmitter MIMO automotive radar which employs both time-division and frequency offset modulated LFM range-division radar techniques. In this example, it is assumed that the range spectrum is divided by transmitters Tx 1 , Tx 2 , Tx 3 , . . . , TxN in a sequential fashion and adjacent-numbered transmitters&#39; range spectrum are also adjacent to each other. In the depicted arrangement, the first group is first transmitted from the odd-numbered transmitters (e.g., Tx 1 , Tx 3 , Tx 5 , Tx 7 ), followed by transmission from the even-numbered transmitters (e.g., Tx 2 , Tx 4 , Tx 6  Tx 8 ). In the range spectrum of time slot # 1   1801 , the even-numbered transmitters do not transmit so the corresponding range spectrum segments Tx 2 , Tx 4 , Tx 6 , Tx 8  are vacant, allowing strong beyond-the-range targets to be present and detected in these vacant segments in an unambiguous fashion. Likewise, in the range spectrum of time slot # 2   1802 , the odd-numbered transmitters Tx 1 , Tx 3 , Tx 5 , Tx 7  do not transmit which leaves the corresponding range spectrum segments vacant so that strong beyond-the-range targets can be freely present and detected. This approach effectively doubles the maximum range of the radar system. As seen from this example, the temporal separation of transmissions from the first group from the second group in the time domain, in combination with separation in the frequency or range domain, greatly reduces the chance of a strong beyond-the-range target interference between adjacent transmitters. While the combined TD and RD approach greatly reduces the risk of interference due to strong beyond-the-range targets, if such interference is not a practical concern, the combined TD and RD approach also increases the number of transmitters supported. 
     As will be noted, the last transmitter (e.g., Tx 8 ) does not have additional free room for ambiguous detection of the strong beyond-the-range targets due to the conjugate symmetric nature of the I-sample only spectrum. Such ambiguity may be tolerated because it does not occur in the rest of transmitters&#39; range spectrums. Because of such inconsistency in the range spectrum, the ambiguous target will not be coherently integrated in the subsequent Doppler and angle processing such that its impact is minimized. If such tolerance is not acceptable, the limitation may be addressed by increasing the ADC sampling rate by one transmitter&#39;s IF frequency extent. Alternatively, the maximum number of transmitters should be reduced by one without increased ADC sampling rate. In yet another alternative, the number of time slots can be increased (e.g., more than 2) to further reduce the chance of ambiguous detections. In such embodiments, the activated transmit antennas in any particular transmission time slot are separated from one another by two or more deactivated transmit antennas, depending on the number of time slots. 
     As disclosed herein, the FOM MIMO approach can be combined with other MIMO approaches besides TD MIMO schemes. For example, a combined Doppler Division and Range Division MIMO can be implemented to separate the transmitters in both the range domain (using FOM MIMO) and in the Doppler domain. Likewise, a combined Time Division, Doppler Division, and Range Division MIMO can be implemented to separate the transmitters not only in the range domain, but also in the Time and Doppler domains. 
     To provide additional details for an improved understanding of selected embodiments of the present disclosure, reference is now made to  FIG. 19  which depicts a simplified flow chart  1900  showing the logic for using frequency offset modulation techniques to form virtually large MIMO radar arrays. In an example embodiment, the control logic and methodology shown in  FIG. 19  may be implemented as hardware and/or software on a host computing system, processor, or microcontroller unit that includes processor and memory for storing programming control code for constructing and operating a large virtual MIMO radar arrays by introducing frequency offset modulations signals to reference chirp signals to enable separation of the transmitter signals in the fast-time Fourier or the range domain. 
     The process starts (step  1901 ), such as when the radar system begins the process of sensing the location and movement of one or more target objects using one or more transmit radar signals that are sent over a plurality of transmit antennas. To generate the transmit radar signals, the radar system first generates a reference chirp signal (step  1902 ), such as by periodically modulating a transmit radar signal with a frequency and/or phase shift. For example, with automotive Frequency Modulation Continuous Wave (FMCW) radars, the reference chirp signal may be generated as a Linear Frequency Modulation (LFM) waveform that is distributed to a plurality of transmit channel circuits which are respectively associated with a plurality of transmit antennas. 
     At step  1904 , the reference chirp signal is applied to a plurality of frequency offset modulation (FOM) mixers to generate frequency offset chirp signals for a plurality of transmit channels. In selected embodiments, the FOM mixing step may be implemented by applying the reference chirp signal to a plurality of FOM mixers which are each respectively connected to receive a plurality of defined frequency offset tones for mixing with the reference chirp signal, thereby generating a plurality of different frequency offset reference chirp signals for use with the plurality of transmit channel circuits. In addition, one of the transmit channel circuits may be connected to directly receive the reference chirp signal without any frequency offset modulation. In selected embodiments, the frequency offset mixer may be implemented with an I/Q channel modulation mixer, an I-channel only modulation mixer, or a Q-channel only modulation mixer to implement a spectrum-coherent integration approach. By using frequency offset modulation mixers to mix the reference chirp signal as an LFM waveform at each transmit channel with different frequency offset signals (e.g., Δf, 2Δf, etc.), the receiver may employ a high sampling rate ADC to allow separation of different transmitters&#39; transmit signals in the received range spectrum. 
     As an alternative step  1905 , the reference chirp signal is applied to a plurality of fast-time phase shifters to generate phase-shifted chirp signals for a plurality of transmit channels. In selected embodiments, the phase shifting step may be implemented by applying the reference chirp signal to a plurality of phase shifters which are respectively controlled by a phase shift control signal, thereby generating a plurality of different frequency offset reference chirp signals for use with the plurality of transmit channel circuits. In addition, one of the transmit channel circuits may be connected to directly receive the reference chirp signal without any phase shift modulation. By using phase shifters to introduce regular progressive phase shifts to the reference chirp signal at each transmit channel example, the phase shifters effectively mimic the effects of frequency offset modulation, thereby enabling the receiver to employ a high sampling rate ADC to allow separation of different transmitters&#39; transmit signals in the received range spectrum. 
     As an optional step  1906 , time division modulation may be applied to the plurality of different frequency offset reference chirp signals for use with the plurality of transmit channel circuits. As indicated with the dashed lines, the time division modulation step may be omitted or skipped in the disclosed sequence  1900 . However, selected embodiments of the time division modulation step may employ an alternating transmission scheme whereby multiple transmit time slots are defined such that a first set of alternating transmit channels (e.g., even-numbered transmitters) are active in a first time slot and are suppressed in a second time slot, while a second set of alternating transmit channels (e.g., odd-numbered transmitters) are active in a second time slot and are suppressed in a first time slot. In this configuration, for each transmitter, its adjacent range spectrum segment is vacant, thereby enabling strong beyond-the-range targets to be corrected detected without imposing target interference. 
     At step  1908 , the frequency offset or phase-shifted reference chirp signals are conditioned and amplified for transmission over the corresponding transmit channel circuits. In selected embodiments, this processing is performed by the transmit channel circuits which each include an RF conditioning module (which filters the output of the corresponding FOM mixer or phase shifter) and power amplifier (which amplifies the RF conditioning module output for transmission over a corresponding transmit antenna). In embodiments where time-domain modulation is used in combination with the frequency/phase offset modulation, the non-adjacent transmit channel circuits may be controlled to sequentially condition and amplify transmit radar waveforms from non-adjacent transmit antennas. 
     At step  1910 , the reflected frequency/phase offset reference chirp signals from the different transmit channels are received and amplified at the receiver. In selected embodiments, one or more receive antennas at the receiver module receive target returns from the transmitted frequency/phase offset reference chirp signal waveforms as (radio frequency) antenna signals for subsequent amplification, such as by using a low noise amplifier to generate an amplified RF signal from the target returns. 
     At step  1912 , the amplified transmit channel signals are mixed with the reference chirp signal at the receiver to generate an intermediate frequency (IF) signal. In selected embodiments, the mixing step may be implemented by applying the reference chirp signal to a receiver module mixer which is also connected to receive the amplified transmit channel signals for mixing with the reference chirp signal, thereby generating an intermediate frequency signal. 
     At step  1914 , the intermediate frequency signal is conditioned for digital conversion. In selected embodiments, the conditioning process includes feeding the intermediate frequency signal to a high-pass filter, amplifying the filtered signal with a variable gain amplifier before being fed to a low-pass filter, thereby generating a re-filtered signal. 
     At step  1916 , the re-filtered conditioned IF signal is fed to a high-speed analog/digital converter (ADC) which has a digital signal output that is suitable for digital processing. Because the maximum unambiguous range extent for each frequency offset reference chirp signal is inversely related to the fast-time sampling interval, the ADC has a high sampling rate. For example, if a conventional TD-MIMO FCM radar uses a  40  mega-samples-per-second (Msps) ADC in the receiver module, the ADC sampling rate is increased to N×40 Msps to enable the N-transmitters MIMO operation using the disclosed FOM approach. Note also that depending on the radar system requirements and also upon the actual performance of the low-pass filter that directly precedes the ADC, the sample rate of the ADC may need to be increased beyond N×40 Msps. 
     At step  1918 , the digital processing is applied to separate the reflected transmit channel signals in the fast-time FFT or range domain, along with other radar signal processing steps. While any suitable radar signal processing steps may be used, each radar may be configured to perform fast-time FFT and slow-time FFT processing on the received radar signal to derive range and Doppler information. In the fast-time FFT processing, the frequency offset modulation of the reference chirp signals sent over the N transmission channels enables the spectrum to be divided into N consecutive segments with each being associated with a corresponding transmitter. Because the transmitters are separated or divided in the range domain and the waveform is based on LFM, the approach can also be referred to as the LFM range-division (RD) MIMO approach. Based on the range-spectrum division arrangement, the fast-time samples associated with distinct transmitters are then recovered (and whose sum and delta components are coherently summed for the case of I-channel only FOM,) and the subsequent MIMO virtual array processing can be carried out. 
     At step  1920 , the virtual MIMO array is constructed from the reflected transmit channel signals which originated from distinct transmit channels. In selected embodiments, the frequency/phase offset reference chirp signal target return data samples received from the distinct transmit channels are processed using mono-static and/or bi-static radar principles to construct and accumulate MIMO virtual array outputs. 
     At step  1922 , the MIMO virtual array outputs are processed by range, Doppler, and angle estimation processes and the target map is generated to identify the range, Doppler, and angle values for each detected target. The range, Doppler, and angle estimators are typically based on Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) processors. More advanced spectral estimators including but not limited to Multiple-signal Classifier (MUSIC) and Estimator of Signal Parameters via Rotational Invariance Technique (ESPRIT) processors, may also be used for angle processing. In selected embodiments, the radar controller processor may be configured to produce map data identifying paired range (r), Doppler ({dot over (r)}) and angle (θ) values for each detected/target object. 
     As disclosed herein, selected embodiments of the disclosed frequency offset modulation range division MIMO radar system may provide several enhancements when compared with conventional radar systems. In addition to enabling the construction of very large 
     MIMO arrays for automotive Frequency Modulation Continuous Wave (FMCW) radars that transmit Linear Frequency Modulation (LFM) waveforms, the disclosed radar system can use RF front-end and signal processing blocks of existing radar designs without significant modifications, thereby minimizing the cost of developing the new solution. In addition, the combination of FOM RD and TD MIMO approaches enables strong beyond-the-range targets to be corrected detected without imposing target interference. In addition, the present disclosure enables the number of virtual antenna elements to be constructed via a MIMO approach to equal the product of the number of physical transmit and receiver antenna elements, thereby forming a larger aperture than can be formed from the total number of physical elements and improving the angular resolution. 
     By now it should be appreciated that there has been provided a radar architecture, circuit, method, and system in which a reference signal generator is configured to produce a transmit reference signal a sequence of waveforms (e.g., a chirp signal). In addition, a waveform generator is provided which includes (1) a frequency offset signal generator for generating a plurality of different frequency offset tones separated from one another by an offset frequency Δf, and (2) a plurality of single channel modulation mixers configured to produce generate a plurality of transmit signals, each having a different frequency offset from the transmit reference signal, where each single channel modulation mixer is connected to mix the transmit reference signal with one of the plurality of different frequency offset tones, thereby generating a frequency offset transmit signal as one of the plurality of transmit signals. In selected embodiments, each single channel modulation mixer is an I-branch only frequency offset mixer, or a Q-channel frequency offset mixer. In selected embodiments, each frequency offset transmit signal generated by the single channel modulation mixer may include an upshifted sum component and a downshifted delta component. In selected embodiments, the waveform generator generates the plurality of transmit signals which include a first transmit signal for a first transmit antenna which has no frequency offset from the transmit reference signal, and a plurality of frequency offset transmit signals for a corresponding plurality of transmit antennas, each being separated from the first transmit signal by an integer multiple of the offset frequency Δf that is twice as large as each individual transmitter&#39;s instrumented range-spectrum bandwidth. In an example of such embodiments, the first transmit signal may be transmitted at a center frequency of a periodic frequency spectrum, and the plurality of frequency offset transmit signals may be transmitted, respectively, at 40 MHz intervals from the center frequency. In other embodiments, the waveform generator generates the plurality of transmit signals which include a first transmit signal for a first transmit antenna which has a first frequency offset from the transmit reference signal, and a plurality of frequency offset transmit signals for a corresponding plurality of transmit antennas, each being separated from the first transmit signal by an integer multiple of the offset frequency Δf that is twice as large as each individual transmitter&#39;s instrumented range-spectrum bandwidth. In an example of such embodiments, the first transmit signal may be transmitted at a first channel offset frequency that is 20 MHz from a center frequency of a periodic frequency spectrum, and the plurality of frequency offset transmit signals may be transmitted, respectively, at 40 MHz intervals from the first channel offset frequency. The radar system also includes a signal encoder to encode the plurality of transmit signals using a signal conditioning and power amplification to produce and transmit N radio frequency encoded transmit signals over N transmit antennas. The radar system also includes a receiver module connected between one more receive antennas and a radar control processing unit to generate a digital signal from a received target return signal reflected from the N radio frequency encoded transmit signals by a target, where the radar control processing unit is configured to process the digital signal with fast time processing steps to generate a range spectrum comprising N segments which correspond, respectively, to the N radio frequency encoded transmit signals transmitted over the N transmit antennas. In selected embodiments, the receiver module includes at least a first receive antenna is provided to receive a target return signal reflected from the N radio frequency encoded transmit signals by a target. The receiver module may also include a downconverter that is configured to mix the target return signal with the transmit reference signal, thereby producing an intermediate frequency signal. In addition, a high-speed analog-to-digital converter is connected to convert the intermediate frequency signal to a digital signal. In selected FOM embodiments, the high-speed analog-to-digital converter has a sampling rate f s  of at least 2N times the offset frequency Δf. The radar system also includes a radar control processing unit that is configured to process the digital signal with fast time processing steps to generate a range spectrum comprising N segments which correspond, respectively, to the N radio frequency encoded transmit signals transmitted over the N transmit antennas. In selected embodiments, the radar control processing unit is also configured to construct a MIMO virtual array by extracting information corresponding to the N radio frequency encoded transmit signals from the N consecutive segments in the range spectrum. 
     In another form, there is provided a radar system architecture and method for operating same. In the disclosed methodology, a transmit reference signal is generated at a transmitter module, such as by generating a chirp signal. In addition, the transmitter module supplies the transmit reference signal to a plurality of single channel modulation mixers configured to generate a plurality of transmit signals, each having a different frequency offset from the transmit reference signal, where each single channel modulation mixer is connected to mix the transmit reference signal with one of a plurality of different frequency offset tones separated from one another by an offset frequency Δf, thereby generating a frequency offset transmit signal as one of the plurality of transmit signals. In selected embodiments, each frequency offset transmit signal generated by the single channel modulation mixer comprises an upshifted sum component and a downshifted delta component. In selected embodiments, the transmit reference signal is supplied to the plurality of single channel modulation mixers by (1) supplying the transmit reference signal as a first transmit signal directly to a first transmit channel circuit for signal conditioning and power amplification at the transmitter module without any frequency offset, and (2) supplying the transmit reference signal to the plurality of single channel modulation mixers which generate, respectively, a plurality of frequency offset transmit signals which are supplied to a corresponding plurality of transmit channel circuits for signal conditioning and power amplification at the transmitter module, each of the plurality of frequency offset transmit signals being separated from the first transmit signal by an integer multiple of the offset frequency Δf that is twice as large as each individual transmitter&#39;s instrumented range-spectrum bandwidth. In an example of such embodiments, the first transmit signal may be encoded for signal conditioning and power amplification at the transmitter module for transmission at a center frequency of a periodic frequency spectrum, and the plurality of frequency offset transmit signals may be encoded for signal conditioning and power amplification at the transmitter module for transmission, respectively, at 40 MHz intervals from the center frequency. In other embodiments, the transmit reference signal is supplied to the plurality of single channel modulation mixers by supplying the transmit reference signal to the plurality of single channel modulation mixers which generate, respectively, a plurality of frequency offset transmit signals which are supplied to a corresponding plurality of transmit channel circuits for signal conditioning and power amplification at the transmitter module, the plurality of frequency offset transmit signals comprising a first transmit signal having a first frequency offset from the transmit reference signal and one or more frequency offset transmit signals being separated from the first transmit signal by an integer multiple of the offset frequency Δf that is twice as large as each individual transmitter&#39;s instrumented range-spectrum bandwidth. In an example of such embodiments, the first transmit signal is transmitted at a first channel offset frequency that is 20 MHz from a center frequency of a periodic frequency spectrum, and where the one or more frequency offset transmit signals are transmitted, respectively, at 40 MHz intervals from the first channel offset frequency. In addition, the transmitter module encodes the plurality of transmit signals using a signal conditioning and power amplification to produce N radio frequency encoded transmit signals. In addition, the transmitter module transmits the N radio frequency encoded transmit signals over N transmit antennas. At a receiver module, a received target return signal reflected from the N radio frequency encoded transmit signals by a target is processed to generate a digital signal which is processed with fast time processing steps to generate a range spectrum comprising N segments which correspond, respectively, to the N radio frequency encoded transmit signals transmitted over the N transmit antennas. In selected embodiments of processing the received target return signal, a first receive antenna receives a target return signal reflected from the N radio frequency encoded transmit signals by a target. In addition, the receiver module mixes the target return signal with the transmit reference signal to produce an intermediate frequency signal. In addition, the receiver module converts the intermediate frequency signal to a digital signal with a high-speed analog-to-digital converter so that the digital signal may be processed with fast time processing steps to generate a range spectrum comprising N segments which correspond, respectively, to the N radio frequency encoded transmit signals transmitted over the N transmit antennas. In selected embodiments, the high-speed analog-to-digital converter has a sampling rate f s  of at least 2N times the offset frequency Δf. The disclosed methodology may also construct a MIMO virtual array by extracting information corresponding to the N radio frequency encoded transmit signals from the N consecutive segments in the range spectrum. 
     In yet another form, there is provided a computer program product stored in non-transitory machine-readable storage medium comprising instructions for execution by one or more processors in a radar system having N transmit antennas and a receive antenna for detecting an object. As disclosed, the computer program product includes instructions for configuring a reference signal generator to produce a transmit reference signal. In addition, the computer program product includes instructions for configuring a waveform generator to supply the transmit reference signal to a plurality of single channel modulation mixers for generating a plurality of transmit signals, each having a different frequency offset from the transmit reference signal, where each single channel modulation mixer is connected to mix the transmit reference signal with one of a plurality of different frequency offset tones separated from one another by an offset frequency Δf, thereby generating a frequency offset transmit signal as one of the plurality of transmit signals which are encoded using signal conditioning and power amplification to produce and transmit N radio frequency encoded transmit signals over N transmit antennas. In selected embodiments, each frequency offset transmit signal generated by the single channel modulation mixer may include an upshifted sum component and a downshifted delta component. In addition, the computer program product includes instructions for configuring a downconverter to produce an intermediate frequency signal by mixing the transmit reference signal with a target return signal which is received at the receive antenna as a result of the N radio frequency encoded transmit signals reflecting off the object. In addition, the computer program product includes instructions for configuring a high-speed analog-to-digital converter to convert the intermediate frequency signal to a digital signal. In selected embodiments, the high-speed analog-to-digital converter has a sampling rate f s  of at least 2N times the offset frequency Δf. In addition, the computer program product includes instructions for configuring a radar control processing unit to process the digital signal with fast time processing steps to generate a range spectrum comprising N segments which correspond, respectively, to the N radio frequency encoded transmit signals transmitted over the N transmit antennas. The computer program product may also instructions that, when executed by the by one or more processors, causes the radar system to construct a MIMO virtual array by extracting information corresponding to the N radio frequency encoded transmit signals from the N consecutive segments in the range spectrum. 
     In still yet another form, there is an automotive radar system on a chip (SOC) for detecting an object and method for operating same. The disclosed automotive radar SOC includes N transmit antennas and one or more receive antennas. The disclosed automotive radar 
     SOC also includes a reference signal generator for generating a transmit reference signal. In addition, the disclosed automotive radar SOC includes a waveform generator for generating a plurality of different frequency offset tones separated from one another by an offset frequency Δf. The disclosed automotive radar SOC also includes a transmit module which includes a plurality of I-channel only modulation mixers connected to generate a plurality of transmit signals from the transmit reference signal, each having a different frequency offset from the transmit reference signal. As disclosed, each I-channel only modulation mixer is connected to mix the transmit reference signal with one of a plurality of different frequency offset tones separated from one another by an offset frequency Δf, thereby generating a frequency offset transmit signal as one of the plurality of transmit signals. In the transmit module, there is also signal conditioning and power amplification circuitry to produce and transmit N radio frequency encoded transmit signals over the N transmit antennas. The disclosed automotive radar SOC also includes a receiver module connected between the one more receive antennas and a radar control processing unit to generate a digital signal from a received target return signal reflected from the N radio frequency encoded transmit signals by a target, where the radar control processing unit is configured to process the digital signal with fast time processing steps to generate a range spectrum comprising N segments which correspond, respectively, to the N radio frequency encoded transmit signals transmitted over the N transmit antennas. 
     Although the described exemplary embodiments disclosed herein focus on example automotive radar circuits, systems, and methods for using same, the present invention is not necessarily limited to the example embodiments illustrate herein. For example, various embodiments of a co-located or distributed aperture radar may be applied in non-automotive applications, and may use additional or fewer circuit components than those specifically set forth. Thus, the particular embodiments disclosed above are illustrative only and should not be taken as limitations upon the present invention, as the invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Accordingly, the foregoing description is not intended to limit the invention to the particular form set forth, but on the contrary, is intended to cover such alternatives, modifications and equivalents as may be included within the spirit and scope of the invention as defined by the appended claims so that those skilled in the art should understand that they can make various changes, substitutions and alterations without departing from the spirit and scope of the invention in its broadest form. 
     Benefits, other advantages, and solutions to problems have been described above with regard to specific embodiments. However, the benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature or element of any or all the claims. As used herein, the terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.