Generalized frequency response function matrix for MIMO non-linear systems

Swain, Akshya; Billings, S.A.

doi:10.1080/00207170010030144

Cited by 80 publications

(38 citation statements)

References 21 publications

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“…Furthermore, since the MIMO Volterra kernels are identified using least squares estimation techniques [7], the identification complexity, given in terms of the number of arithmetic operations, grows as O (N × M ) [9], where N is the number of excited input tones and M is total number of third order basis functions (static and dynamic). Separation of the individual third order kernels reduces the size of the regression matrix by a factor of 6.…”

Section: B Sparse Even and Odd Gridmentioning

confidence: 99%

Multitone Design for third order MIMO Volterra Kernels

Khan

Zenteno

Händel

et al. 2017

2017 IEEE MTT-S International Microwave Symposium (IMS)

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Abstract-This paper proposes a technique for designing multitone signals that can separate the third order multiple input multiple output (MIMO) Volterra kernels. Multitone signals fed to a MIMO Volterra system yield a spectrum that is a permutation of the sums of the input signal tones. This a priori knowledge is used to design multitone signals such that the output from the MIMO Volterra kernels does not overlap in the frequency domain, hence making it possible to separate these kernels from the output of the MIMO Volterra system. The proposed technique is applied to a 2×2 RF MIMO transmitter to determine its dominant hardware impairments. For input crosstalk, the proposed method reveals the dominant self and cross kernels whereas for output crosstalk, the proposed method reveals that only the self kernels are dominant.

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Section: B Sparse Even and Odd Gridmentioning

confidence: 99%

Multitone Design for third order MIMO Volterra Kernels

Khan

Zenteno

Händel

et al. 2017

2017 IEEE MTT-S International Microwave Symposium (IMS)

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“…This theory has been extended to multiple input multiple output systems (MIMO) in [31][32][33]. However, it is convenient to describe the Volterra series in discrete complex baseband representation as in [6,34] since communication signals are denoted and manipulated in this domain.…”

Section: Volterra Analysismentioning

confidence: 99%

“…However, it is convenient to describe the Volterra series in discrete complex baseband representation as in [6,34] since communication signals are denoted and manipulated in this domain. The continuous time MIMO Volterra [31][32][33] and the complex base-band formalism [34] were combined in [23], in which a complex 2 × 2 Volterra system was formulated. Extending that results to an arbitrary number of carriers, we get:…”

Section: Volterra Analysismentioning

confidence: 99%

“…The large number of parameters in the latter is a well-known problem and has given rise to large research efforts in finding more parameter-efficient models [11]. There is a certain level of redundancy in the formulation due to the permutations of the terms that can lead to identical contribution, such as, x i x j x * z = x j x i x * z , referred as symmetry [33]. The general trends are, however, the same as presented in Figure 2 even if redundancy is considered.…”

Section: Volterra Analysismentioning

confidence: 99%

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Low complexity predistortion and equalization in nonlinear multicarrier satellite communications

Zenteno

Piazza

Shankar

et al. 2015

EURASIP J. Adv. Signal Process.

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Aiming to reduce the power/mass requirements in satellite transponders and to reduce mission costs, joint amplification of multiple carriers using a single high-power amplifier (HPA) is being considered. In this scenario, a careful investigation of the resulting power efficiency is essential as amplification is nonlinear, and multicarrier signals exhibit enlarged peak-to-average power ratio. Thus, operating the amplifier close to saturation vastly increases signal distortion resulting in a severe degradation of performance, especially for higher order modulations. This paper proposes a reduced-complexity digital predistortion (DPD) scheme at the transmitter and a corresponding equalizer (EQ) at the receiver to mitigate these nonlinear effects. Scenarios include both the forward as well as the return links. In particular, the paper exploits the MIMO Volterra representation and builds on a basis pursuit approach using a LASSO (least absolute shrinkage and selection operator) algorithm to achieve an efficient basis representation, avoiding large computational complexity, to describe the selection of predistorter/equalizer model. The work further compares and contrasts the two mitigation techniques taking various system aspects into consideration. The gains in performance and amplification efficiency demonstrated by the use of DPD/ EQ motivate their inclusion in next-generation satellite systems.

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“…Some of the early attempts were made by using the describing function method to obtain an approximate characterization of the steady-state response, e.g., in Fukuma et al (1984); Grensted (1955). For weakly nonlinear systems arising from electronic circuits, the steady-state responses are often investigated using the Volterra series theory (see, e.g., Chua & Tang (1982), Lang & Billings (2000), Sandberg (1984) and Swain & Billings (2001)). …”

Section: Introductionmentioning

confidence: 99%

Lyapunov characterization of forced oscillations

Teel

Lin

2005

Automatica

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This paper develops a Lyapunov approach to the analysis of input-output characteristics for systems under the excitation of a class of oscillatory inputs. Apart from sinusoidal signals, the class of oscillatory inputs include multi-tone signals and periodic signals which can be described as the output of an autonomous system. The Lyapunov approach is developed for linear systems, homogeneous systems (differential inclusions) and nonlinear systems (differential inclusions), respectively. In particular, it is established that the steady-state gain can be arbitrarily closely characterized with Lyapunov functions if the output response converges exponentially to the steady-state. Other output measures that will be characterized include the peak of the transient response and the convergence rate. Tools based on linear matrix inequalities (LMIs) are developed for the numerical analysis of linear differential inclusions (LDIs). This paper's results can be readily applied to the evaluation of frequency responses of general nonlinear and uncertain systems by restricting the inputs to sinusoidal signals. Guided by the numerical result for a second order LDI, an interesting phenomenon is observed that the peak of the frequency response can be strictly larger than the L 2 gain. • x 1 , x 2 : the inner product of x 1 and x 2 .• X : Matrix norm induced from the Euclidean norm.• u : ess.sup t 0 |u(t)| for an essentially bounded func- increasing. It is said to belong to class K ∞ if, in addition, it is unbounded.• A function : R 0 × R 0 → R 0 is said to belong to class KL if, for each t 0, (·, t) is nondecreasing and lim s→0 + (s, t) = 0, and for each s 0, (s, ·) is nonincreasing and lim t→∞ (s, t) = 0.

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Generalized frequency response function matrix for MIMO non-linear systems

Cited by 80 publications

References 21 publications

Multitone Design for third order MIMO Volterra Kernels

Multitone Design for third order MIMO Volterra Kernels

Low complexity predistortion and equalization in nonlinear multicarrier satellite communications

Lyapunov characterization of forced oscillations

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