### Abstract

Multiple-input multiple-output (MIMO) radar systems allow each antenna element to transmit a different waveform. This waveform diversity can be exploited to enhance the beampattern design, in particular, effective management of radar radiation power in directions of interest. We address the problem of designing a beampattern for MIMO radar, which in turn is determined by the transmit waveform. While unconstrained design is straightforward, a key open challenge is enforcing the constant modulus constraint on the radar waveform. It is well known that the problem of minimizing deviation of the designed beampattern from an idealized one subject to the constant modulus constraint constitutes a hard nonconvex problem. Existing methods that address constant modulus invariably lead to a stiff tradeoff between analytical tractability (achieved by relaxations and approximations) and realistic design that exactly achieves constant modulus but is computationally burdensome. A new approach is proposed in our paper, which involves solving a sequence of convex equality constrained quadratic programs, each of which has a closed form solution and such that constant modulus is achieved at convergence. We further prove that the converged solution satisfies the Karush-Kuhn-Tucker optimality conditions of the aforementioned hard nonconvex problem. We evaluate the proposed successive closed forms (SCF) algorithm against the state-of-the art MIMO beampattern design techniques in both narrowband and wideband setups and show that the SCF breaks the tradeoff between desirable performance and the associated computation cost.

Original language | English (US) |
---|---|

Article number | 7840054 |

Pages (from-to) | 2588-2599 |

Number of pages | 12 |

Journal | IEEE Transactions on Signal Processing |

Volume | 65 |

Issue number | 10 |

DOIs | |

State | Published - May 15 2017 |

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### All Science Journal Classification (ASJC) codes

- Signal Processing
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Signal Processing*,

*65*(10), 2588-2599. [7840054]. https://doi.org/10.1109/TSP.2017.2664040

}

*IEEE Transactions on Signal Processing*, vol. 65, no. 10, 7840054, pp. 2588-2599. https://doi.org/10.1109/TSP.2017.2664040

**Tractable Transmit MIMO Beampattern Design under a Constant Modulus Constraint.** / Aldayel, Omar; Monga, Vishal; Rangaswamy, Muralidhar.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Tractable Transmit MIMO Beampattern Design under a Constant Modulus Constraint

AU - Aldayel, Omar

AU - Monga, Vishal

AU - Rangaswamy, Muralidhar

PY - 2017/5/15

Y1 - 2017/5/15

N2 - Multiple-input multiple-output (MIMO) radar systems allow each antenna element to transmit a different waveform. This waveform diversity can be exploited to enhance the beampattern design, in particular, effective management of radar radiation power in directions of interest. We address the problem of designing a beampattern for MIMO radar, which in turn is determined by the transmit waveform. While unconstrained design is straightforward, a key open challenge is enforcing the constant modulus constraint on the radar waveform. It is well known that the problem of minimizing deviation of the designed beampattern from an idealized one subject to the constant modulus constraint constitutes a hard nonconvex problem. Existing methods that address constant modulus invariably lead to a stiff tradeoff between analytical tractability (achieved by relaxations and approximations) and realistic design that exactly achieves constant modulus but is computationally burdensome. A new approach is proposed in our paper, which involves solving a sequence of convex equality constrained quadratic programs, each of which has a closed form solution and such that constant modulus is achieved at convergence. We further prove that the converged solution satisfies the Karush-Kuhn-Tucker optimality conditions of the aforementioned hard nonconvex problem. We evaluate the proposed successive closed forms (SCF) algorithm against the state-of-the art MIMO beampattern design techniques in both narrowband and wideband setups and show that the SCF breaks the tradeoff between desirable performance and the associated computation cost.

AB - Multiple-input multiple-output (MIMO) radar systems allow each antenna element to transmit a different waveform. This waveform diversity can be exploited to enhance the beampattern design, in particular, effective management of radar radiation power in directions of interest. We address the problem of designing a beampattern for MIMO radar, which in turn is determined by the transmit waveform. While unconstrained design is straightforward, a key open challenge is enforcing the constant modulus constraint on the radar waveform. It is well known that the problem of minimizing deviation of the designed beampattern from an idealized one subject to the constant modulus constraint constitutes a hard nonconvex problem. Existing methods that address constant modulus invariably lead to a stiff tradeoff between analytical tractability (achieved by relaxations and approximations) and realistic design that exactly achieves constant modulus but is computationally burdensome. A new approach is proposed in our paper, which involves solving a sequence of convex equality constrained quadratic programs, each of which has a closed form solution and such that constant modulus is achieved at convergence. We further prove that the converged solution satisfies the Karush-Kuhn-Tucker optimality conditions of the aforementioned hard nonconvex problem. We evaluate the proposed successive closed forms (SCF) algorithm against the state-of-the art MIMO beampattern design techniques in both narrowband and wideband setups and show that the SCF breaks the tradeoff between desirable performance and the associated computation cost.

UR - http://www.scopus.com/inward/record.url?scp=85017718819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017718819&partnerID=8YFLogxK

U2 - 10.1109/TSP.2017.2664040

DO - 10.1109/TSP.2017.2664040

M3 - Article

AN - SCOPUS:85017718819

VL - 65

SP - 2588

EP - 2599

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 10

M1 - 7840054

ER -