The invention considered by this US decision relates to signal transmission rather than software, as such.  It does, however, require the application of a mathematical concept just as many software patents do, and so is highly relevant to software patents.
Claims of US patent 5,659,891 in the name of Mobile Telecommunications Technologies, LLC were found to be patent eligible subject matter under 35 USC 101 because the invention uses any potentially abstract idea in a process designed to solve a technological problem in conventional industry practice.
  •  An invention is not patent ineligible merely because it requires the use of a mathematical equation.
  • A claim is not abstract merely because some requirements can be rewritten in the language of mathematics.
  • A patent may be valid if it employs a mathematical formula in a process designed to solve a technological problem in conventional industry practice.

Broad description of the invention
The ‘891 patent claims methods and systems that  use multicarrier modulation using co-located transmitters to achieve higher transmission capacity for mobile paging and two-way digital communication.
Characteristic Claim
1. A method of operating a plurality of paging carriers in a single mask-defined, bandlimited channel comprising the step of transmitting said carriers from the same location with said carriers having center frequencies within said channel such that the frequency difference between the center frequency of the outer most of said carriers and the band edge of the mask defining said channel is more than half the frequency difference between the center frequencies of each adjacent carrier.
Mobile Telecommunication Technologies, LLC is the patentee of US 5,659,891. The defendant Leap Wireless Intenational, Inc contended that the patent is directed to an abstract idea and hence invalid.
The Supreme Court has held that there are three specific exceptions to patent eligibility under s101: laws of nature, natural phenomena, and abstract ideas.  A two part test for distinguishing patents that claim laws of nature, natural phenomena and abstract ideas from those that claim patent eligible applications of the concepts was first stated in Mayo Collaborative Servs. v. Prometheus Labs., Inc, 132 S. Ct. 1289. 1296097 (2012), and developed in Alice Corp. Pty Ltd v. CLS Bank Itn’l, 132 S. Ct. 2347, 2355 (2014).  In a first step, it is determined if the claims are directed to a law of nature, natural phenomenon or abstract idea.  If not, the claims pass muster under s101 (Ultramercial v Hulu). In making this determination, the court looks at what the claims cover (Ultramercial v Hulu). It is often useful to determine the breadth of the claims in order to determine whether the claims extend to cover a ‘fundamental … practice long prevalent in our system …”.
The court applies a second step only if it finds in the first step that the claims are directed to a law of nature, natural phenomena or abstract idea (Alice). The second step requires the court to determine whether the elements of the claim individually, or as an ordered combination, “transform the nature of the claim” into a patent-eligible application. The second step may be described as a search for an inventive concept. Steps that are in context not obvious, not already in use, or purely conventional may result in patent-eligibility (Diamond v. Diehr). However, insignificant post-solution activity will not result in patent-eligibility (Parker v Flook). A claim may become patent-eligible when the “claimed process includes not only a law of nature but also several unconventional steps … that confine the claims to a particular, useful application of the principle (Mayo).
In considering step 1, Leap alledged that claim 1 covers the “abstract idea of selecting the transmission frequencies for multi-carrier transmission via a mathematical formula”.  The court found that under step 1, the patent was not directed to an abstract idea.  Claim 1 teaches a way of transmitting “paging carriers” in a “bandlimited channel” where the “paging carriers” are transmitted from the “same location” and are modulated with reference to two different frequencies: one frequency at the edge “band edge of the mask” and the other frequency at the center of “each adjacent carrier”. Transmitting “paging carriers” from “the same location” and modulating their transmission frequencies is not an abstract idea in the vein of “a fundamental economic practice”, as for the alleged invention considered in Alice. 
The court rejected the allegation that the claims are directed to an abstract idea because portions can be expressed mathematically. No authority was cited in support of this allegation.  The supreme court has repeatedly emphasised that the bar on patenting abstract ideas “embodies the longstanding rule that an idea of itself is not patentable” (Alice).  Leap did not show that claim 1 is an attempt to patent a mathematical formula. The fact that some requirements of a claim can be rewritten in the language of mathematics does not inherently mean that the claim is directed to an abstract idea because “at some level, all inventions embody, use, reflect, rest upon, or apply laws of nature, natural phenomena, or abstract idea” (Alice).

While the court found that claim 1 was not directed to an abstract idea under step 1, it nevertheless considered step 2 and determined that the additional elements of claim 1 would transform it into a patent-eligible application. While the patent might employ a mathematical formula, it uses that formula in a process designed to solve a technological problem in conventional industry practice. (Alice, quoting Diehr).

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