Co-prime optical transceiver array

Abstract

A co-prime transceiver attains higher fill factor, improved side-lobe rejection, and higher lateral resolution per given number of pixels. The co-prime transceiver includes in part, a transmitter array having a multitude of transmitting elements and a receiver array having a multitude of receiving elements. The distance between each pair of adjacent transmitting elements is a first integer multiple of the whole or fraction of the wavelength of the optical. The distance between each pair of adjacent receiving elements is a second integer multiple of the whole or fraction of the wavelength of the optical signal. The first and second integers are co-prime numbers with respect to one another. The transceiver is fully realizable in a standard planar photonics platform in which the spacing between the elements provides sufficient room for optical routing to inner elements.

Claims

1. A co-prime optical transceiver comprising: a transmitter array comprising a plurality of transmitting elements wherein a distance between each pair of adjacent transmitting elements is defined by a first integer multiple of a length characterized by a wavelength of an optical signal; and a receiver array comprising a plurality of receiving elements wherein a distance between each pair of adjacent receiving elements is a second integer multiple of a length defined by the length, wherein said first and second integers are co-prime numbers with respect to one another; a plurality of detectors adapted to detect a signal received by the receiver array to generate a plurality of detected signals; and a plurality of phase modulators adapted to control phases of signals transmitted by the transmitted array in accordance with the plurality of the detected signals, wherein each of said transmitter and receiver arrays are two-dimensional arrays disposed symmetrically along a Cartesian coordinate system.

2. The transceiver array of claim 1 wherein said length is a fraction of the wavelength the optical signal.

3. A method of transmitting and receiving an optical signal, the method comprising: transmitting the optical signal via a transmitter array comprising a plurality of transmitting elements wherein a distance between each pair of adjacent transmitting elements is defined by a first integer multiple of a length characterized by a wavelength of an optical signal; receiving the optical signal via a receiver array comprising a plurality of receiving elements wherein a distance between each pair of adjacent receiving elements is a second integer multiple of a length defined by the length, wherein said first and second integers are co-prime numbers with respect to one another; detecting a signal received by the receiver array to generate a plurality of detected signals; and controlling phases of signals transmitted by the transmitted array in accordance with the detected signals, wherein each of said transmitter and receiver arrays are two-dimensional arrays disposed symmetrically along a Cartesian coordinate system.

4. The transceiver array of claim 3 wherein said length is a fraction of the wavelength of the optical signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a simplified top-level schematic view of an exemplary one-dimensional co-prime transceiver array, in accordance with one embodiment of the present invention.

(2) FIG. 2A shows computer simulation response of transmitter array of the transceiver of FIG. 1, in accordance with one embodiment of the present invention.

(3) FIG. 2B shows computer simulation response of the receiver array of the transceiver of FIG. 1, in accordance with one embodiment of the present invention.

(4) FIG. 2C shows computer simulation response of the transceiver of FIG. 1, in accordance with one embodiment of the present invention.

(5) FIG. 3 shows computer simulation response of the transceiver of FIG. 1 along different angular directions, in accordance with one embodiment of the present invention.

(6) FIG. 4 is a simplified top-level schematic view of an exemplary two-dimensional co-prime transceiver array, in accordance with one embodiment of the present invention.

(7) FIG. 5 is a simplified schematic block diagram of a one-dimensional transceiver array, in accordance with one exemplary embodiment of the present invention.

(8) FIG. 6 is a homodyne two-dimensional phased array, in accordance with one exemplary embodiment of the present invention.

(9) FIG. 7 is a heterodyne two-dimensional phased array, in accordance with one exemplary embodiment of the present invention.

(10) FIG. 8 is a simplified top-level schematic view of an exemplary two-dimensional co-prime transceiver array, in accordance with one embodiment of the present invention.

(11) FIG. 9A shows computer simulation of the transmission pattern of the transmitting array of the transceiver of FIG. 8 in a Cartesian coordinate system.

(12) FIG. 9B shows computer simulation of the response characteristics of the receiver array of the transceiver of FIG. 8 in a Cartesian coordinate system.

(13) FIG. 9C shows computer simulations of the characteristics of the phased array of FIG. 8 in a Cartesian coordinate system.

DETAILED DESCRIPTION OF THE INVENTION

(14) Embodiments of the present invention include a co-prime optical phased array transceiver. The spacing of the receiver and/or transmitter array elements is used to provide flexibility and enhance optical routing, thereby improving performance. The spacing also increases the receiver and/or transmitter aperture size compared to a uniformly arranged and distributed array of receiving and/or transmitting elements. However, the spacing of the elements in the transmitter and the receiver results in grating lobes in the response of both the transmitter and the receiver and reducing the usable field-of-view of the transmitter and the receiver to the spacing between two adjacent grating lobes. In accordance with embodiments of the present invention, the transmitter and receiver array element spacing are designed such that the combined system achieves an improved performance and a large field-of-view compared to individual performance of the transmitter and receiver array. Consequently, in accordance with the embodiments of the present invention, the beam-width, the magnitude of side lobes, grating lobes, and other characteristics of the beam can be controlled and modified to further enhance performance of the phased array transceiver.

(15) An optical phased array receiver captures the incident light by its aperture—formed using an array of receiving elements—and processes it to determine, among other things, the direction of the incident light, or to look at the light coming from specific points or directions and suppress light from other points and directions.

(16) Assume an optical co-prime transceiver with a receiver having N.sub.rx≥2 receiving elements and a transmitter having N.sub.tx≥2 transmitting elements, in accordance with one embodiment of the present invention. The spacing d.sub.rx between each pair of adjacent receiving elements is defined by d.sub.rx=n.sub.rxd.sub.x, where d.sub.x is a unit spacing determined by the minimum optical routing spacing. The spacing d.sub.tx between each pair of adjacent transmitting elements is defined by d.sub.tx=n.sub.txd.sub.x spacing. Because in a co-prime transceiver, in accordance with embodiments of the present invention, n.sub.rx and n.sub.tx are co-prime numbers with respect to each other, the co-prime transceiver has a performance that is equivalent to that of a conventional transceiver having N.sub.rxN.sub.tx receiving-transmitting elements with uniform d.sub.x spacing. Side-lobe rejection is known to improve with increasing number of receiving-transmitting elements.

(17) A conventional uniform transmitter or receiver array with N transmitting or receiving elements and transmitting/receiving element spacing of d.sub.x reconstructs the

(18) $\left[-\frac{\pi }{2},\frac{\pi }{2}\right]$
field of view image up to spatial frequency resolution bandwidth given by the largest spacing of x.sub.N=Nd.sub.x if d.sub.x=λ/2, where λ is the wavelength of the optical signal. However, the unit spacing of λ/2 is difficult to achieve due to planar routing constraints. Increasing the inter-element spacing beyond λ/2 to attain improve resolution results in reduction of the field-of-view. A co-prime transceiver achieves improved resolution without sacrificing the field-of-view with a reduced number of elements.

(19) An optical co-prime transceiver having M transmitting elements and N receiving elements achieves a performance that is equivalent to that of conventional transceiver having MN transmitting-receiving elements. Such a co-prime transceiver not only requires fewer number of transmitting-receiving elements, it achieves side-lobes that are considerably lower. By increasing the number of elements in the transmitter and receiver, a narrower beam and thus lower side-lobes are obtained. In one example, a co-prime transceiver with 2(N+M) transmitting-receiving elements can have side-lobes that are much lower compared to a conventional uniform transceiver. Increasing the number of transmitter and receiver elements while keeping the distance of the transmitter and receiver elements constant results in improved performance for the co-prime array as it does for a uniform array.

(20) In accordance with one embodiment of the present invention, the distance between each pair of adjacent transmitting elements of a co-prime phased array transceiver is defined by a first integer multiple T of a distance d.sub.x (i.e., Td.sub.x), and the distance between each pair of adjacent receiving elements of the co-prime phased array transceiver is defined by a second integer multiple R of the distance d.sub.x (i.e., Rd.sub.x), wherein T and R are co-prime numbers with respect to one another. The number of transmitting elements of the co-prime transceiver is P and the number of receiving elements of the co-prime transceiver is Q, where P and Q are integers greater than or equal to two, and d.sub.x may be equal to either λ,

(21) $\frac{\lambda }{2},\frac{\lambda }{4}$
or any other real factor of λ—the wavelength of the optical signal being used. A co-prime phased array transceiver, in accordance with embodiments of the present invention, therefore has more relaxed routing constraints. The higher the number of transmitter and receiver elements, the larger the spacing between the receiver elements and the spacing between the transmitter elements can be to permit signal routing to the elements in two-dimensions.

(22) A one-dimensional co-prime transceiver with P transmitting elements and Q receiving elements has a performance characteristics that is substantially equivalent to that of a conventional uniform transceiver having PQ transmitting-receiving elements. Similarly, a two-dimensional co-prime transceiver with 2P transmitting elements and 2Q receiving elements has a performance characteristics that is substantially equivalent to that of a conventional uniform transceiver having 16(PQ).sup.2 transmitting-receiving elements.

(23) FIG. 1 is a simplified top-level schematic view of an exemplary one-dimensional co-prime transceiver array 10 shown as having 8 transmitting elements 12 and 6 receiving elements 14. Transmitting elements 12 are shown as forming a transmitting array 15, and receiving elements 14 are shown as forming a receiving array 18. The distance d.sub.t between each pair of adjacent transmitting elements is assumed to be equal to 3d.sub.x and the distance d.sub.r between each pair of adjacent receiving elements is assumed to be equal to 4d.sub.x, where d.sub.x is assumed to be equal to half the wavelength of the light, namely

(24) $\frac{\lambda }{2}.$

(25) Plot 25 of FIG. 2A shows computer simulation response of transmitter array 15 of FIG. 1 and plot 30 of FIG. 2B shows computer simulation response of receiver array 18 of FIG. 1. Plot 35 of FIG. 2C shows computer simulation response of transceiver array 10 of FIG. 1. The transmitter array is shown as illuminating 5 directions in FIG. 2A and the receiver array is shown as collecting light from 3 directions. However, at any given time only one of the transmitter and receiver beams align and the transceiver behaves as if there is only one transmitter and one receiver illuminating and receiving from the same direction.

(26) Despite the fact that the transmitter array and receiver array each have several side-lobes, their combined response rejects all the side-lobes. Sliding the response of the transmitter array across the response of the receiver array shows that at any arbitrary angle, their combined response has a minimum side-lobe. As seen from FIG. 2B, transceiver array 10 has a peak response at 0° angle and has substantially the same response characteristics as a conventional uniform transceiver with 8×6=48 (the product of the number of transmitting elements and the number of receiving elements of the co-prime transceiver in accordance with embodiments of the present invention) receiver elements, and a single transmitting element, or 48 transmitters and a single receiver.

(27) Sweeping the transceiver phased-array to acquire signal from all directions results in the response shown in FIG. 3. As seen from FIG. 3, the co-prime receiver array maintains a desirable side-lobe rejection ratio when acquiring signal from any given direction.

(28) FIG. 4 is a simplified top-level schematic view of an exemplary two-dimensional co-prime transceiver phased array 100, in accordance with another exemplary embodiment of the present invention. Co-prime transceiver array 100 is shown as having a receiver array 150 and a transmitter array 200. Receiver array 150 is shown as having 36 receiving elements 14 and transmitter array 200 is shown as having 64 transmitting elements 12. The distance d.sub.r between each pair of adjacent receiving elements 14 is assumed to be 4d.sub.x, and the distance d.sub.t between each pair of adjacent transmitting elements 12 is assumed to be 3d.sub.x, where d.sub.x is assumed to be equal to the wavelength of the light used by the transceiver phased array 100. Receiver array 150 is shown as having 36 receiving elements and transmitter array 200 is shown as having 64 element. Accordingly, in co-prime transceiver phased array 100, parameter P is equal to 64 and parameter Q is equal to 36.

(29) FIG. 5 is a simplified schematic block diagram of a one-dimensional transceiver array having N transmitters N.sub.t and receivers N.sub.r. The optical signal generated by coherent electromagnetic source 802 is split into N signals by splitter 804, each of which is phase modulated by a different one of phase modulators (PM) 806 and transmitted by a different one of the transmitters, collectively identified using reference number 800. The signals received by receiving elements 820 are modulated in phase by PMs 826 and detected by detectors 828. The output signals of the detectors is received by control and processing unit 824 which, in turn, controls the phases of PMs 806 and 826.

(30) A co-prime transmitter and receiver pair will each have several side-lobes. However, their combined radiation pattern will only have one main lobe. Each transmitter and receiver need to be set such that the relative phase between the elements is linearly increasing. Assume that the relative phase steps of the transmitters is ϕ.sub.t and relative phase step of receivers is ϕ.sub.r. As a result, the transmitter and receiver phased array will have the center-lobe pointing in a specific direction which are uncorrelated with respect to each other. However, their combined radiation pattern will have one main lobe. If ϕ.sub.t and ϕ.sub.r are swept from zero to 2π, the combined main-lobe will be swept across the field of view as well. The combined main-lobe has the maximum amplitude when any two of the transmitter and receiver main lobe are aligned in substantially the same direction.

(31) Therefore, by setting a linear phase delay step between the elements of each of the transmitters and the receivers, and slowly varying the phase delay step of either the transmitters or the receivers, a co-prime phased array that has a single main lobe and can sweep the entire field of view is achieved.

(32) In the one-dimensional array shown in FIG. 5, the control and processing unit 802 adjusts the relative phase between the elements using the phase modulators such that the receiver elements have linear relative phase difference of (0, ϕ.sub.r, 2ϕ.sub.r, 3ϕ.sub.r, . . . , (N.sub.r−1)ϕ.sub.r) and the transmitter elements have linear relative phase difference of (0, ϕ.sub.t, 2ϕ.sub.t, 3ϕ.sub.t, . . . , (N.sub.t−1)ϕ.sub.t). It is understood that ϕ.sub.r, ϕ.sub.t can have any value in the range of [0,2π].

(33) FIG. 6 is a simplified schematic block diagram of a two-dimensional transceiver array having an array of N.sub.t×N.sub.t transmitters and an array of N.sub.r×N.sub.r receivers. The two-dimensional transceiver shown in FIG. 6 has a homodyne architecture but is otherwise similar to the one-dimensional transceiver shown in FIG. 5.

(34) FIG. 7 is a simplified schematic block diagram of a heterodyne two-dimensional transceiver array having an array of N.sub.t×N.sub.t transmitters and an array of N.sub.r×N.sub.r receivers. The two-dimensional transceiver architecture shown in FIG. 7 is also shown as including an additional splitter 832 and a multitude of mixers 830. The signal detection scheme described above is also applicable to both homodyne as well as heterodyne array architectures.

(35) In accordance with another embodiment of the present invention, the array elements are symmetrical in a polar coordinate system. FIG. 8 is a simplified top-level schematic view of an exemplary two-dimensional co-prime transceiver phased array 300, in accordance with another exemplary embodiment of the present invention. Co-prime transceiver array 300 is shown as having a receiver array 325 and a transmitter array 350. Receiver array 325 is shown as having 60 receiving elements 12, and transmitter array 350 is shown as having 30 transmitting elements 14.

(36) Operation wavelength of the exemplary transceiver 300 is 1550 nm. Transmitter array 350 is further shown as having 4 rings of radiators. The rings from the most inner ring to the most outer rings have 3, 6, 9, 12 radiating elements placed on concentric circles with 6 um, 12 um, 18 um, 24 um radii respectively. The receiver array 325 is shown as having 5 concentric rings of receiving elements. The rings from the most inner ring to the most outer rings have 4, 8, 12, 16, and 20 elements placed on concentric circles with radii of 13 um, 26 um, 39 um, 52 um, and 65 um respectively.

(37) In the embodiment shown in FIG. 8, the transmitter and receiver array beams overlap at a single point in space. The relative spacing between the transmitting elements and the receiving determine the far-field radiation pattern associated with the phased array 300. The relative spacing between the transmitting and receiving elements may be assigned arbitrary or based on a uniform element placement so long as the transmitter and receiver radiation patterns overlap at substantially a single point in space.

(38) FIG. 9A shows the transmission pattern of array 300 of transceiver 300 assuming isotropic transmitting elements are used. As is seen from FIG. 9A, the transmission patterns has two grating lobes 405, 410. FIG. 9B shows the far-field response pattern of the receiver array 325 of transceiver 300. Several strong side-lobes with amplitudes 5 dB lower than peak-power are present in FIG. 9B.

(39) FIG. 9C shows the radiation pattern of transceiver 300 which is the product of the patterns shown in FIGS. 14A and 14B. As is seen from FIG. 9C, the radiation pattern of transceiver 300 suppresses the strong grating lobes of the transmitter and attenuates the strong side-lobes of the receiver resulting in a system radiating pattern that outperforms the patterns of both the transmitter and the receiver taken individually. As is seen, the transmitter and receiver beam-pattern overlap only in the broadside direction along the zero angle.

(40) The above embodiments of the present invention are illustrative and not limitative. The embodiments of the present invention are not limited by the aperture size or the number of elements in the array of transmitters or receivers. The above embodiments of the present invention are not limited by the wavelength of the light. The above embodiments of the present invention are not limited by the number of semiconductor substrates that may be used to form a transmitter, receiver or transceiver array. Other modifications and variations will be apparent to those skilled in the art and are intended to fall within the scope of the appended claims.