Conference Paper

Pilot design for a cellular wireless system based on Costas arrays.

DOI: 10.1109/PIMRC.2010.5671673 Conference: Proceedings of the IEEE 21st International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC 2010, 26-29 September 2010, Istanbul, Turkey
Source: DBLP

ABSTRACT In this paper, we present a pilot design for an OFDM cellular system based on Costas arrays. The design provides pilot symbols for both common and dedicated pilots for MIMO transmission. The pilot symbols are designed so that pilots from different cells intersect minimally. The design results in a large number of available distinct pilot symbol patterns with minimally overlapping resource elements that may be assigned to different cells which simplifies cell planning. The design is described in the context of IEEE 802.16m, but is applicable to any OFDM system. Performance of the pilot design in noise and interference limited environments is presented and is shown to be on par with currently used pilot designs while providing a larger number of patterns.

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    ABSTRACT: A Costas array is an n × n array of dots and blanks with exactly one dot in each row and column, and with distinct vector differences between all pairs of dots. As a frequency-hop pattern for radar or sonar, a Costas array has an optimum ambiguity function, since any translation of the array parallel to the coordinate axes produces at most one out-of-phase coincidence. We conjecture that n × n Costas arrays exist for every positive integer n. Using various constructions due to L. Welch, A. Lempel, and the authors, Costas arrays are shown to exist when n = p - 1, n = q - 2, n = q - 3, and sometimes when n = q - 4 and n = q - 5, where p is a prime number, and q is any power of a prime number. All known Costas array constructions are listed for 271 values of n up to 360. The first eight gaps in this table occur at n = 32, 33, 43, 48, 49, 53, 54, 63. (The examples for n = 19 and n = 31 were obtained by augmenting Welch's construction.) Let C(n) denote the total number of n × n Costas arrays. Costas calculated C(n) for n ≤ 12. Recently, John Robbins found C(13) = 12828. We exhibit all the arrays for n ≤ 8. From Welch's construction, C(n) ≥ 2n for infinitely many n. Some Costas arrays can be sheared into "honeycomb arrays." All known honeycomb arrays are exhibited, corresponding to n = 1, 3, 7, 9, 15, 21, 27, 45. Ten unsolved problems are listed.
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