Binary Signature Sets Research Articles

Constructions of Binary Signature Sets With Optimal Odd Total Squared Correlation and Their Application to Device Activity Detection

Massive machine type communication (mMTC) is one of the core components of 6G communication systems to fulfil the demand of massive connectivity of billions of Internet-of-Things (IoT) devices. Due to its various advantages, grant-free random access schemes are considered as a promising technique to implement mMTC. The key to grant-free random access is active device detection at the base station. In this paper, firstly we introduce the odd total squared correlation (OTSC) of binary signature sets, then derive a corresponding lower bound. Systematic constructions of optimal signature sets based on the known odd periodic complementary sets (OPCS), almost binary sequences, large Kasami subsets and ideal sequences are presented, which are all optimal with respect to the derived OTSC lower bound. Next, it is demonstrated that the optimal OTSC signature sets can be effectively used in massive device activity detection. Using efficient approximate message passing with minimum mean squared error (AMP-MMSE) algorithm, it is shown that the sensing matrices arising from OTSC-optimal signature sets and periodic total squared correlation (PTSC)-optimal signature sets performs better than the popular Gaussian random matrix.

Optimal Upward Scaling of Minimum-TSC Binary Signature Sets

We consider upward scaling an overloaded min-TSC binary signature set and propose an optimal solution based on improved sphere decoding algorithm. Instead of previous suboptimal approach, we are guaranteed to find the optimal maximum-likelihood (ML) searching result with low complexity.

New Bounds and Optimal Binary Signature Sets - Part II: Aperiodic Total Squared Correlation

We derive new bounds on the aperiodic total squared correlation (ATSC) of binary antipodal signature sets for any number of signatures K and any signature length L. We then present optimal designs that achieve the new bounds for several (K,L) cases. As interesting -arguably- side results, we show that individual maximal merit factor sequences (for example Barker sequences) are single-user ATSC-optimal, while neither the familiar Gold nor the Kasami set designs are ATSC-optimal in general. The ATSC-optimal signature set designs provided in this work are in this sense better suited for asynchronous and/or multipath code-division multiplexing applications.

New Bounds and Optimal Binary Signature Sets—Part I: Periodic Total Squared Correlation

We derive new bounds on the periodic (cyclic) total squared correlation (PTSC) of binary antipodal signature sets for any number of signatures K and any signature length L. Optimal designs that achieve the new bounds are then developed for several (K,L) cases. As an example, it is seen that complete (K = L + 2) Gold sets are PTSC optimal, but not, necessarily, Gold subsets of K <; L + 2 signatures. In contrast, arguably against common expectation, the widely used Kasami sets are not PTSC optimal in general. The optimal sets provided herein are in this sense better suited for asynchronous and/or multipath code-division multiplexing applications.

Upward scaling of minimum-TSC binary signature sets

We develop a binary signature design procedure to scale upwards overloaded minimum total-squared-correlation (TSC) binary signature sets. The quality of the design is measured against the recently published binary TSC bounds.

Binary signature sets for increased user capacity on the downlink of cdma systems

We compare the maximum achievable common signal to interference and noise ratio (SINR) target level K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> in the downlink of various code division multiple access (CDMA) systems with binary sequence sets. We derive an upper bound to K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> for binary systems with symbol-aligned users, and we compare this upper bound to the value of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> for quasi-orthogonal sequences (QOS), Grassmannian signatures and binary Pados-Karystinos signatures. Secondly, we turn our attention to systems where the (binary) signatures of the users are displaced with respect to each other. In this context, we show that the value of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> of improved random O(rthogonal)CDMA/OCDMA (O/O) can further be increased as compared to the original improved. O/O system (with square-root cosine rolloff pulses) by an appropriate choice of the chip pulse. In addition to this, improved O/O systems with fixed signature set can achieve values of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> that are as high as those in the improved random O/O system, while not having the drawback of a spread on K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> . Applying a steepest descent search to such a fixed improved O/O system, can result in a system with a binary signature set that has even higher values for K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> well beyond the upper bound on K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> for systems with aligned chip pulses

The Maximum Squared Correlation, Sum Capacity, and Total Asymptotic Efficiency of Minimum Total-Squared-Correlation Binary Signature Sets

The total squared correlation (TSC), maximum squared correlation (MSC), sum capacity (C/sub sum/), and total asymptotic efficiency (TAE) of underloaded signature sets, as well as the TSC and C/sub sum/ of overloaded signature sets are metrics that are optimized simultaneously over the real/complex field. In this present work, closed-form expressions are derived for the MSC, C/sub sum/, and TAE of minimum-TSC binary signature sets. The expressions disprove the general equivalence of these performance metrics over the binary field and establish conditions on the number of signatures and signature length under which simultaneous optimization can or cannot be possible. The sum-capacity loss of the recently designed minimum-TSC binary sets is found to be rather negligible in comparison with minimum-TSC real/complex-valued (Welch-bound-equality) sets.

New bounds on the total squared correlation and optimum design of ds-cdma binary signature sets

The Welch lower bound (see Welch, R.L., IEEE Trans. Inform. Theory, vol.IT-20, p.397-9, 1974) on the total squared correlation (TSC) of signature sets is known to be tight for real-valued signatures and loose for binary signatures whose number is not a multiple of four. We derive new bounds on the TSC of binary signature sets for any number of signatures K and any signature length L. Then, for almost all K, L in {1,2,...,256}, we design optimum binary signature sets that achieve the new bounds. The design procedure is based on simple transformations of Hadamard matrices.

Meeting the Welch and Karystinos-Pados Bounds on DS-CDMA Binary Signature Sets

The Welch lower bound on the total-squared-correlation (TSC) of binary signature sets is loose for binary signature sets whose length L is not a multiple of 4. Recently Karystinos and Pados l6,7r developed new bounds that are better than the Welch bound in those cases, and showed how to achieve the bounds with modified Hadamard matrices except in a couple of cases. In this paper, we study the open cases.