For two-dimensional IIR digital filters described by the Fornasini-Marchesini second model, the problem of jointly optimizing high-order error feedback and realization to minimize the effects of roundoff noise at the filter output subject to l2-scaling constraints is investigated. The problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem is then solved iteratively by applying an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. Finally, a numerical example is presented to illustrate the validity and effectiveness of the proposed technique.

In this paper, a low-complexity symbol-spaced turbo frequency domain equalization (FDE) algorithm based on Laurent decomposition is proposed for precoded binary continuous phase modulation (CPM) with modulation index h=1/2. At the transmitter, a precoder is utilized to eliminate the inherent memory of the CPM signal. At the receiver, a matched filter based on Laurent decomposition is utilized to make the detection symbol-spaced. As a result, the symbol-spaced iteration can be taken between the equalizer and the decoder directly without a CPM demodulator, and we derive a symbol-spaced soft interference cancellation frequency domain equalization (SSIC-FDE) algorithm for binary CPM with h=1/2. A new data block structure for FDE of partial response CPM is also presented. The computational complexity analysis and simulations show that this approach provides a complexity reduction and an impressive performance improvement over previously proposed turbo FDE algorithm for binary CPM with h=1/2 in multi-path fading channels.

This paper improves the family size of quadrature amplitude modulation (QAM) complementary sequences with binary inputs. By employing new mathematical description: B-type-2 of 4q-QAM constellation (integer q ≥ 2), a new construction yielding 4q-QAM complementary sequences (CSs) with length 2m (integer m ≥ 2) is developed. The resultant sequences include the known QAM CSs with binary inputs as special cases, and the family sizes of new sequences are approximately 22·2q-4q-1(22·2q-3-1) times as many as the known. Also, both new sequences and the known have the same the peak envelope power (PEP) upper bounds, when they are used in an orthogonal frequency-division multiplexing communication system.

The shift-and-add property (SAP) of a p-ary m-sequence {ak} with period N=pn-1 means that this sequence satisfies the equation {ak+η}+{ak+τ}={ak+λ} for some integers η, τ and λ. For an arbitrarily-given p-ary m-sequence {ak}, we develop an algebraic approach to determine the integer λ for the arbitrarily-given integers η and τ. And all trinomials can be given. Our calculation only depends on the reciprocal polynomial of the primitive polynomial which produces the given m-sequence {ak}, and the cyclotomic cosets mod pn-1.

In an approximately synchronized (AS) code-division multiple-access (CDMA) communication system, zero correlation zone (ZCZ) sequences can be used as its spreading sequences so that the system suppresses multiple access interference (MAI) and multi-path interference (MPI) fully and synchronously. In this letter, the mutually orthogonal (MO) ZCZ polyphase sequence sets proposed by one of the authors are improved, and the resultant ZCZ sequences in each set arrive at the theoretical bound regarding ZCZ sequences under some conditions. Therefore, the improved MO ZCZ sequence sets are optimal.

The minimization problem of an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints is formulated for a class of two-dimensional (2-D) state-space digital filters. First, the problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algorithm with closed-form formula for gradient evaluation. The coordinate transformation matrix obtained is then used to synthesize the optimal 2-D state-space filter structure that minimizes the L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints. Finally, a numerical example is presented to illustrate the utility of the proposed technique.

Block-state realization of state-space digital filters offers reduced implementation complexity relative to canonical state-space filters while filter's internal structure remains accessible. In this paper, we present a quantitative analysis on l2 coefficient sensitivity of block-state digital filters. Based on this, we develop two techniques for minimizing average l2-sensitivity subject to l2-scaling constraints. One of the techniques is based on a Lagrange function and some matrix-theoretic techniques. The other solution method converts the problem at hand into an unconstrained optimization problem which is solved by using an efficient quasi-Newton algorithm where the key gradient evaluation is done in closed-form formulas for fast and accurate execution of quasi-Newton iterations. A case study is presented to demonstrate the validity and effectiveness of the proposed techniques.

Based on the concept of polynomial operators, this paper explores generalized direct-form II structure and its state-space realization for two-dimensional separable-denominator digital filters of order (m, n) where a structure with 3(m+n)+mn+1 fixed parameters plus m+n free parameters is introduced and analyzed. An l2-scaling method utilizing different coupling coefficients at different branch nodes to avoid overflow is presented. Expressions of evaluating the roundoff noise for the filter structure as well as its state-space realization are derived and investigated. The availability of the m+n free parameters is shown to be beneficial as the roundoff noise measures can be minimized with respect to these free parameters by means of an exhaustive search over a set with finite number of candidate elements. The important role these parameters can play in the endeavors of roundoff noise reduction is demonstrated by numerical experiments.

Combinatorial interaction testing has been well studied in recent years, and has been widely applied in practice. It generally aims at generating an effective test suite (an interaction test suite) in order to identify faults that are caused by parameter interactions. Due to some constraints in practical applications (e.g. limited testing resources), for example in combinatorial interaction regression testing, prioritized interaction test suites (called interaction test sequences) are often employed. Consequently, many strategies have been proposed to guide the interaction test suite prioritization. It is, therefore, important to be able to evaluate the different interaction test sequences that have been created by different strategies. A well-known metric is the Average Percentage of Combinatorial Coverage (shortly APCCλ), which assesses the rate of interaction coverage of a strength λ (level of interaction among parameters) covered by a given interaction test sequence S. However, APCCλ has two drawbacks: firstly, it has two requirements (that all test cases in S be executed, and that all possible λ-wise parameter value combinations be covered by S); and secondly, it can only use a single strength λ (rather than multiple strengths) to evaluate the interaction test sequence - which means that it is not a comprehensive evaluation. To overcome the first drawback, we propose an enhanced metric Normalized APCCλ (NAPCC) to replace the APCCλ Additionally, to overcome the second drawback, we propose three new metrics: the Average Percentage of Strengths Satisfied (APSS); the Average Percentage of Weighted Multiple Interaction Coverage (APWMIC); and the Normalized APWMIC (NAPWMIC). These metrics comprehensively assess a given interaction test sequence by considering different interaction coverage at different strengths. Empirical studies show that the proposed metrics can be used to distinguish different interaction test sequences, and hence can be used to compare different test prioritization strategies.