TRANSMISSION OF A SYMBOL FROM A PLURALITY OF ANTENNAS

Abstract

Methods and apparatus are provided for transmitting a symbol from a plurality of antennas. In one example, a method comprises simultaneously transmitting, from each antenna, the symbol multiplied by a respective element of a selected column of an array. The number of rows of the array is at least the number of antennas, the number of columns of the array is at least 6, and the array comprises or is a subarray of a Hadamard-type Butson array that includes only a minimum number of non-real elements.

Description

TRANSMISSION OF A SYMBOL FROM A PLURALITY OF ANTENNAS Technical field The examples of the present invention relate to the transmission of a symbol, for example, a long training field (LTF), from a plurality of antennas. Background of the invention Advanced antenna systems can be used to significantly improve the performance of wireless communication systems in both the uplink (UL) and downlink (DL) directions. For example, advanced antennas can enable the use of the channel's spatial domain to improve the reliability and / or performance of transmissions, for example, by transmitting using multiple spatial streams (also called spacetime streams). The 802.11-16 standard, for example, specifies a set of matrices, often called P-matrices, where the rows (and columns) define a set of orthogonal vectors used as orthogonal cover codes for channel and pilot estimation when more than one spacetime stream is used (e.g., a multiple-input multiple-output, MIMO, operation). The rows or columns of these P-matrices can be applied to the long training field (LTF) and pilots embedded in the data symbols when they are transmitted. The P-matrices can be, for example, Hadamard matrices. A square matrix M of dimensions η × n is said to be a Hadamard matrix of the Butson type H(q, n) if: 1. Its inputs are all powers of the q-th root of unity, and 2. M · MH= ni. Here, the superscript (.)H denotes transposition of a Hermitian matrix and I is the identity matrix. For example, the discrete Fourier transform (DFT) matrix of order n is of Butson type H(n, n), and Hadamard matrices of Butson type H(2^ n) are real and binary (i.e., they have entries +1, -1). Hadamard matrices of the Butson type H(^, n) are orthogonal matrices (i.e., their rows are orthogonal vectors and / or their columns are orthogonal vectors) whose entries consist of +1, -1, j, -j. If a matrix is ​​of the Butson type H(2, n), then n is 1, 2, or an integer multiple of 4, while if a matrix is ​​of the Butson type H(4, n), then n is 1 or an even number that is not an integer multiple of 4. It follows that there are no Hadamard matrices of the Butson type 71(2,9), H(2,10), H(2,13), H(2,14), H(4,9), H(4,13). It can be verified that the Hadamard property H(4, n) of a matrix is ​​preserved by carrying out the following operations. 1) Negation of a row or column. 2) Multiplication of a row or column by j. 3) Permutation (i.e., exchange) of two rows or columns. Furthermore, any Butson-type Hadamard matrix H(4, n) can be transformed into a matrix whose first row and first column consist exclusively of +1 by these operations. Any matrix in this special form is said to be normalized. If a Butson-type Hadamard matrix A H(4, n) can be transformed into a Butson-type Hadamard matrix B H(4, n) by applying the three operations given above, then the two matrices A and B are said to be equivalent. Otherwise, the matrices are said to be non-equivalent. Any Butson-type Hadamard matrix H(A, n) is equivalent to a normalized Butson-type Hadamard matrix H(4, n). There are exactly 10 non-equivalent Butson-type matrices H(4,10) and exactly 752 non-equivalent Butson-type matrices H(4,14). If M is a Butson-type Hadamard matrix H(4, n), then MI is also a Butson-type Hadamard matrix. Here, the superscript (.) denotes matrix transposition. EHT (Extremely High Throughput) has been proposed as an improvement to the IEEE 802.11 standard. Specifically, EHT will provide support for up to 16 spacetime streams. Currently, the IEEE 802.11-16 standard and its amendment 802.11ax support up to 8 spacetime streams. Therefore, for example, there may be a need for arrays (e.g., P-arrays) of orders 9 < n < 16 to provide orthogonal cover codes for long training fields (LTFs) for up to 16 spacetime streams. Constructing P-matrixes for 8 or fewer spacetime flows is straightforward and can be done by inspection or by a computer-exhaustive search. However, as the dimension of the P-matrix increases, computer-exhaustive search becomes impractical. Brief description of the invention One aspect of the present invention provides a method for transmitting a symbol from a plurality of antennas. The method comprises simultaneously transmitting, from each antenna, the symbol multiplied by a respective element from a selected column of an array. The number of rows in the array is at least the number of antennas, the number of columns in the array is at least 6, and the array comprises or is a subarray of a Hadamard-type Butson array that includes only a minimal number of non-real elements. Another aspect of the present invention provides a method for transmitting a symbol from a plurality of antennas. The method comprises simultaneously transmitting, from each antenna, the symbol multiplied by a respective element from a selected row of an array. The number of columns of the array is at least the number of antennas, and the number of rows of the array is at least 6, and the array comprises or is a subarray of a Hadamard-type Butson array that includes only a minimal number of non-real elements. An additional aspect of the present invention provides an apparatus for transmitting a symbol from a plurality of antennas. The apparatus comprises a processor and a memory. The memory contains instructions executable by the processor so that the apparatus is operable to transmit simultaneously, from each antenna, the symbol multiplied by a respective element of a selected column of a matrix. The number of rows of the matrix is ​​at least the number of antennas, the number of columns of the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butler matrix that includes only a minimal number of non-real elements. Another aspect of the present invention provides an apparatus for transmitting a symbol from a plurality of antennas. The apparatus comprises a processor and a memory. The memory contains instructions executable by the processor such that the apparatus is operable to transmit simultaneously, from each antenna, the symbol multiplied by a respective element of a selected row of an array. The number of columns of the array is at least the number of antennas, and the number of rows of the array is at least 6, and the array comprises or is a subarray of a Hadamard-type Butson array that includes only a minimal number of non-real elements. An additional aspect of the present invention provides an apparatus for transmitting a symbol from a plurality of antennas. The apparatus is configured to transmit simultaneously, from each antenna, the symbol multiplied by a respective element from a selected column of a matrix. The number of rows in the matrix is ​​at least the number of antennas, the number of columns in the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butson matrix that includes only a minimal number of non-real elements. An additional aspect of the present invention provides an apparatus for transmitting a symbol from a plurality of antennas. The apparatus is configured to transmit simultaneously, from each antenna, the symbol multiplied by a respective element from a selected row of an array. The number of columns in the array is at least the number of antennas, and the number of rows in the array is at least 6, and the array comprises or is a subarray of a Hadamard-type Butson array that includes only a minimal number of non-real elements. Brief description of the drawings For a better understanding of the examples of the present invention, and to show more clearly how the examples can be carried out, reference will now be made, by way of example only, to the following drawings in which: Figure 1 is an example of a Hadamard-type Butson matrix H(4,6) that has a minimum number of non-real entries. Figure 2 is an example of a Hadamard-type Butson matrix H(4,10) that has a minimum number of non-real entries. Figure 3 is an example of a Hadamard matrix of the Butson type 14) that has a minimum number of non-real entries. Figure 4 is a flowchart of an example of a method for transmitting a symbol from a plurality of antennas. Figure 5 is a flowchart of an example of a method for transmitting a symbol from a plurality of antennas. Figure 6 shows an example of an apparatus for transmitting a symbol from a plurality of antennas. Figure 7 shows an example of an apparatus for transmitting a symbol from a plurality of antennas. ΙνΙΛ / α / ΖνΖΊ / υΊ Uf 03 Detailed description of the invention The following specific details, such as particular modalities or examples, are provided for explanatory and non-limiting purposes. Those skilled in the art will appreciate that other examples besides these specific details may be used. In some cases, detailed descriptions of well-known methods, nodes, interfaces, circuits, and devices are omitted to avoid obscuring the description with unnecessary detail. Those skilled in the art will appreciate that the functions described can be implemented on one or more nodes using hardware circuitry (e.g., analog and / or discrete logic gates interconnected to perform a specialized function, ASICs, PLAs, etc.) and / or using software programs and data in conjunction with one or more digital microprocessors or general-purpose computers. Nodes communicating via the air interface also have suitable radio communication circuitry.Furthermore, where appropriate, the technology may be considered to be fully incorporated within any form of computer-readable memory, such as solid-state memory, magnetic disk, or optical disk containing an appropriate set of computer instructions that would cause the processing circuits to carry out the techniques described in this document. The hardware implementation may include or encompass, without limitation, digital signal processor (DSP) hardware, a reduced instruction set processor, hardware circuitry (e.g., digital or analog) including, but not limited to, application-specific integrated circuits (ASICs) and / or field-programmable gate arrays (FPGA(s)), and (where appropriate) state machines capable of performing such functions. The exemplary embodiments of the present invention provide arrays in which the rows (or alternatively the columns) are used as orthogonal cover codes, for example, for long training fields (LTFs) or pilot symbols. For example, the arrays and associated orthogonal cover codes can support (up to) 10 and (up to) 14 spacetime flows. The proposed orthogonal cover code examples are defined in terms of (4,6), (4,10), and (4,14) type Hadamard arrays of the Butson type, and the elements of these arrays consist exclusively of ±{1, j}. That is, each element is +1, 1, +j₀ - j. Furthermore, for example, for a (n) type Hadamard array of the Butson type, the array can contain only n non-real elements (for example, purely imaginary, j₀ - j), respectively, which in some examples may be the minimum possible number of non-real elements.Since, for example, multiplication by j (for example, before a symbol is transmitted) may involve only the exchange of parts. ΙνΙΛ / α / ZνΖΊ / υΊ Uf 03 imaginary and real, the application of the matrices described in this document to LTF or pilot symbols may, in some examples, have a lower computational complexity compared to the use of Hadamard-type Butson matrices with more non-real elements. Here we propose the use of Butson-type Hadamard matrices with a minimum number of non-real elements, where each element of the matrix is ​​one of the four values ​​±{1, j}. In some examples, it may be desirable to minimize the number of non-real (e.g., purely imaginary) entries in the matrix, since real multiplications with real entries (elements) in the matrix can be less computationally complex than multiplications with non-real elements, even with elements of j and -j. The following proposition gives a lower bound on the minimum number of non-real (e.g., purely imaginary) entries in a Butson-type matrix H(4, n). Suppose that n > 2 is an even integer not divisible by 4 (i.e., n = 6, 10, 14, ...). Then any Hadamard matrix M of type Butson H(4, n) has at least n purely imaginary entries. To show this, consider an arbitrary Hadamard matrix M of type Butson (n) having p nonreal (e.g., purely imaginary) entries. Suppose here that p < n, and derive a contradiction. Since, for the purposes of this contradictory example, p < n, then there is at least one row containing only real-valued entries. Let a denote a row of M consisting of real elements and m denote any other row not in M. Now, since a - mH = 0, it follows that the number of nonreal (e.g., purely imaginary) entries in M ​​is even. Therefore, p is even, p < n - 2, and M has at most p / 2 rows containing purely imaginary elements. It follows that the number of rows with real values ​​in M ​​is at least: That is, M has 4 or more rows with real values. Consider three different rows of real values ​​from M, say a, b, c. By multiplying some columns of M by -1, we can assume that all entries in a are +1. Since a - bT = 0, it follows that n / 2 entries in b are +1, while the remaining n / 2 are -1. By permuting columns if necessary, we can assume that the first n / 2 entries in b are positive. Since a - cT = 0, it follows that the sum of the first n / 2 entries in c plus the sum of the last n / 2 entries in c equals zero. Furthermore, since a - cT = 0, it follows that the sum of the first n / 2 entries in c minus the sum of the last n / 2 entries in c equals zero. Therefore, the sum of the first n / 2 entries in c is zero. This implies that n / 2 is even, which in turn implies that n is divisible by 4, contradicting the hypothesis that n is not divisible by 4.This concludes that a Hadamard matrix M of the Butson type H(4, n) must have at least n purely imaginary entries. The methods described herein propose the use of Butson-type Hadamard matrices with the minimum number of non-real (i.e., purely imaginary) entries, for example, n entries for a Butson-type Hadamard matrix H(4, n). For instance, in the case of up to 5 or 6 spacetime streams, it is proposed to use a Butson-type Hadamard matrix H(4,6) or a submatrix of that matrix (particularly for up to 5 spacetime streams). Figure 1 shows an example of a matrix 100 that is a Butson-type Hadamard matrix H(4, 6) with the minimum number (6) of non-real (purely imaginary in this case) entries and 30 real entries. In the case of up to 9 or 10 spacetime flows, for example, it is proposed to use a Hadamard-type Butson matrix H(4,10) or a submatrix of that matrix (particularly for up to 9 spacetime flows). Figure 2 shows an example of a 200 matrix that is a Hadamard-type Butson matrix H(4,10) that has the minimum number (10) of non-real (purely imaginary in this case) entries and 90 real entries. In the case of up to 13 or 14 spacetime flows, for example, it is proposed to use a Hadamard-type Butson matrix H(4,14) or a submatrix of that matrix (particularly for up to 13 spacetime flows). Figure 3 shows an example of a 300 matrix that is a Hadamard-type Butson matrix H(4, 14) that has the minimum number (14) of non-real (purely imaginary in this case) entries and 182 real entries. Figure 4 is a flowchart of an example of a 400 method for transmitting a symbol from a plurality of antennas. In some examples, the symbol may comprise or include a long training field (LTF) symbol or one or more pilot symbols, and / or may comprise an OFDM symbol. The method comprises, in step 402, simultaneously transmitting, from each antenna, the symbol multiplied by a respective element from a selected column of an array. The number of rows in the array is at least the number of antennas, the number of columns in the array is at least 6, and the array comprises or is a subarray of a Butson-type Hadamard array that includes only a minimal number of non-real elements. In some examples, the number of non-real elements in the array is equal to the number of rows and / or the number of columns in the array. Thus, for example, the symbol can be transmitted and multiplied by an element from the selected column of the matrix, the element corresponding to the antenna from which the symbol is transmitted. The element can be different for each antenna, although in some examples the value of some of the elements may be the same (for example, selected between +1 and ±j). In some examples, the number of spacetime streams to be transmitted or being transmitted is less than the order (size, number of rows / columns) of the Hadamard matrix. For example, the matrix might be a 14x14 matrix, while 13 spacetime streams might be transmitted (for example, using a 13x14 submatrix of the Butson-type Hadamard matrix). In some examples, the matrix used to provide orthogonal coverage codes for 15 spacetime streams might be a 15x16 matrix. In some examples, the number of spacetime streams is equal to the number of antennas. In some examples, more than one symbol is transmitted, for example, at least the number of spacetime streams. In some examples, the number of times the symbol is repeated over time (including the first transmission) is equal to the number of columns in the matrix (for example, 14 columns for a 14x14 Hadamard matrix of the Butson type). In some examples, the 400 method may involve transmitting at least one additional symbol, which, for each additional symbol, involves simultaneously transmitting the additional symbol from each antenna. ΙνΙΛ / α / ZνΖΊ / υΊ Uf 03 multiplied by a respective element of a matrix column that is associated with the additional symbol. That is, for example, as part of a training sequence, in a first time period, the symbol is transmitted and elements of a first matrix column are used; and during a subsequent time period, the symbol is transmitted again and elements of a different matrix column are used. In some examples, the symbol may be transmitted again one or more times in subsequent additional time periods of the training sequence using a different matrix column each time. Thus, for example, the selected column and each column associated with each additional symbol comprise different matrix columns. Figure 5 shows an alternative example of a 500 method for transmitting a symbol from a plurality of antennas. The 500 method differs from the 400 method in that the symbol is multiplied by a respective element of a selected column, rather than a row, of the matrix. Thus, the 500 method comprises, in step 502, simultaneously transmitting, from each antenna, the symbol multiplied by a respective element of a selected row of a matrix. The number of columns in the matrix is ​​at least the number of antennas, and the number of rows in the matrix is ​​at least 6. The matrix comprises, or is a submatrix of, a Butson-type Hadamard matrix that includes only a minimal number of non-real elements. Any alternative described with respect to the 400 method in Figure 4 can also be applied to the 500 method in Figure 5, except that a row is referred to instead of a column, and a column instead of a row, where appropriate. It should be noted that actual implementations of the 400 or 500 method may or may not specifically use a row or column of a matrix. Instead, for example, calculations or operations can be performed that effectively cause the symbol to be transmitted as if it had been multiplied by a value from a matrix that comprises or is a submatrix of an actual maximum-excess Hadamard matrix, even if other operations, vectors, and / or matrices are used instead. In some examples, the number of antennas is at least the number of spacetime streams, for example, at least 6. The array may comprise a 6x6, 10x10, or 14x14 array. For example, the array comprises an array M or a subarray of M, where M comprises or is equivalent to one of the 100-300 arrays shown in Figures 1-3, respectively. For example, modalities that use up to 10 space streams and / or transmit a symbol in up to 10 different time periods may use the 200 array or an equivalent. In some examples, where the number of spacetime flows is up to m = 9, it is proposed to use a submatrix of a Butson-type Hadamard matrix H(4,10) with the minimum number of non-real elements to provide orthogonal vectors to apply to a symbol (e.g., at different time periods). The matrix to be used can be, for example, of dimension m × 10 and, therefore, can be a submatrix of a Butson-type Hadamard matrix H(4,10). When, for example, the number of spacetime flows is up to m = 5, a submatrix of dimension m × 6 of a Butson-type Hadamard matrix H(4,6) with the minimum number of non-real elements can be used. When, for example, the number of space-time flows is up to m = 13, one can use an m × 14 dimension submatrix of a Hadamard-type Butson matrix H(4,14) with the minimum number of non-real elements. Figure 6 shows an example of a 600 apparatus for transmitting a symbol from a plurality of antennas. In some examples, the 600 apparatus can be configured to carry out the 400 method described above with reference to Figure 4, or any of the other examples described in this document. The apparatus 600 comprises a processor 602 and a memory 604 communicating with the processor 602. The memory 604 contains instructions executable by the processor 602. In one embodiment, the memory 604 contains instructions executable by the processor 602 such that the apparatus 600 is operable to simultaneously transmit, from each antenna, the symbol multiplied by a respective element of a selected column of a matrix. The number of rows of the matrix is ​​at least the number of antennas, the number of columns of the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butler matrix that includes only a minimal number of non-real elements. Figure 700 shows an example of a 700 apparatus for transmitting a symbol from a plurality of antennas. In some examples, the 700 apparatus can be configured to carry out the 500 method described above with reference to Figure 5, or any of the other examples described in this document. The apparatus 700 comprises a processor 702 and a memory 704 communicating with the processor 702. The memory 704 contains instructions executable by the processor 702. In one embodiment, the memory 704 contains instructions executable by the processor 702 such that the apparatus 700 is operable to simultaneously transmit, from each antenna, the symbol multiplied by a respective element of a selected row of a matrix. The number of columns of the matrix is ​​at least the number of antennas, and the number of rows of the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butler matrix that includes only a minimal number of non-real elements. It should be noted that the examples mentioned above illustrate rather than limit the invention, and that those skilled in the art will be able to devise many alternative examples without departing from the scope of the accompanying statements. The word "comprising" does not exclude the presence of elements or steps other than those listed in a claim, "a" does not exclude a plurality, and a single processor or other unit may perform the functions of several units listed in the statements below. When the terms "first," "second," etc., are used, they should be understood simply as labels for the convenient identification of a particular feature. In particular, they should not be interpreted as describing the first or second feature of a plurality of such features (i.e., the first or second of such features occurring in time or space) unless explicitly stated otherwise.The steps of the methods described herein may be carried out in any order unless expressly stated otherwise. Any references in the statements shall not be construed as limiting their scope.

Claims

1. A method for transmitting a symbol from a plurality of antennas, wherein the method comprises: transmitting simultaneously, from each antenna, the symbol multiplied by a respective element of a selected column of a matrix; wherein the number of rows of the matrix is ​​at least the number of antennas, the number of columns of the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butler matrix that includes only a minimum number of non-real elements.

2. The method according to claim 1, further comprising: transmitting at least one additional symbol comprises, for each additional symbol, simultaneously transmitting, from each antenna, the additional symbol multiplied by a respective element of a column of the matrix that is associated with the additional symbol.

3. The method according to claim 2, wherein the selected column and each column associated with each additional symbol comprise different columns of the matrix.

4. A method for transmitting a symbol from a plurality of antennas, wherein the method comprises: transmitting simultaneously, from each antenna, the symbol multiplied by a respective element of a selected row of a matrix; wherein the number of columns of the matrix is ​​at least the number of antennas, and the number of rows of the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butler matrix that includes only a minimum number of non-real elements.

5. The method according to claim 4, further comprising: transmitting at least one additional symbol comprises, for each additional symbol, simultaneously transmitting, from each antenna, the additional symbol multiplied by a respective element of a row of the matrix that is associated with the additional symbol.

6. The method according to claim 5, wherein the selected row and each row associated with each additional symbol comprise different rows of the array.

7. The method in accordance with any of claims 2, 3, 5 and 6, wherein the symbol and the at least one additional symbol comprise at least 6 OFDM symbols.

8. The method in accordance with any of the preceding claims, wherein the number of antennas is at least 5.

9. The method in accordance with any of the preceding claims, wherein the matrix comprises a 6x6, 10x10 or 14x14 matrix.

10. The method according to any of the preceding claims, wherein the array comprises an array M or a subarray of M, wherein M comprises or is equivalent to:

11. The method according to any of claims 1 to 9, wherein the array comprises an array M or a subarray of M, wherein M comprises or is equivalent to 10:

12. The method according to any of claims 1 to 9, wherein the array comprises an array M or a subarray of M, wherein M comprises or is equivalent to 13. The method in accordance with any of the preceding claims, wherein the symbol comprises an OFDM symbol.

14. The method in accordance with any of the preceding 5 claims, wherein the symbol comprises a long training field (LTF) symbol.

15. The method according to any of the preceding claims, wherein each element of the matrix is ​​selected from 1, -1, j and -j, where j = . 10 16. The method in accordance with any of the preceding claims, wherein the number of non-real elements of the matrix is ​​equal to the number of rows and / or the number of columns of the matrix.

17. A computer program comprising 15 instructions that, when executed on at least one processor, cause the at least one processor to carry out the method in accordance with any of claims 1 to 16.

18. A carrier containing the computer program according to claim 17, wherein the carrier comprises an electronic signal, an optical signal, a radio signal, or a computer-readable storage medium.

19. A computer program product comprising a non-transient, computer-readable medium having stored therein the computer program in accordance with claim 17.

20. An apparatus for transmitting a symbol from a plurality of antennas, wherein the apparatus comprises a processor and a memory, wherein the memory contains instructions executable by the processor so that the apparatus is operable to: transmit simultaneously, from each antenna, the symbol multiplied by a respective element of a selected column of a matrix; wherein the number of rows of the matrix is ​​at least the number of antennas, the number of columns of the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butler matrix that includes only a minimum number of non-real elements.

21. The apparatus according to claim 20, wherein the memory contains instructions executable by the processor such that the apparatus is operable to: transmit at least one additional symbol comprising, for each additional symbol, simultaneously transmitting, from each antenna, the additional symbol multiplied by a respective element of a column of the matrix that is associated with the additional symbol.

22. The apparatus according to claim 21, wherein the selected column and each column associated with each additional symbol comprise different columns of the matrix.

23. An apparatus for transmitting a symbol from a plurality of antennas, wherein the apparatus comprises a processor and a memory, wherein the memory contains instructions executable by the processor so that the apparatus is operable to: transmit simultaneously, from each antenna, the symbol multiplied by a respective element of a selected row of a matrix; wherein the number of columns of the matrix is ​​at least the number of antennas, and the number of rows of the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butler matrix that includes only a minimum number of non-real elements.

24. The apparatus according to claim 23, wherein the memory contains instructions executable by the processor so that the apparatus is operable to: transmit at least one additional symbol comprising, for each additional symbol, simultaneously transmitting, from each antenna, the additional symbol multiplied by a respective element of a row of the matrix that is associated with the additional symbol.

25. The apparatus according to claim 24, wherein the selected row and each row associated with each additional symbol comprise different rows of the array.

26. The apparatus according to any of claims 21, 22, 24 and 25, wherein the symbol and the at least one additional symbol comprise at least 6 OFDM symbols.

27. The apparatus according to any of claims 20 to 26, wherein the number of antennas is at least 5.

28. The apparatus according to any of claims 20 to 27, wherein the array comprises a 6x6, 10x10 or 14x14 array.

29. The apparatus according to any of claims 20 to 28, wherein the array comprises an array M or a subarray of M, wherein M comprises or is equivalent to:

30. The apparatus according to any of claims 20 to 28, wherein the array comprises array M or a subarray of M, wherein M comprises (equivalent to: the one is 5 31. The apparatus according to any of claims 20 to 28, wherein the array comprises array M or a subarray of M, wherein M comprises t equivalent to: the one is 32. The apparatus according to any of claims 20 to 31, wherein the symbol comprises an OFDM symbol.

33. The apparatus according to any of claims 20 to 32, wherein the symbol comprises a long training field (LTF) symbol.

34. The apparatus according to any of claims 20 to 33, wherein the number of non-real elements of the matrix is ​​equal to the number of rows and / or the number of columns of the matrix.

35. An apparatus for transmitting a symbol from a plurality of antennas, the apparatus being configured to: transmit simultaneously, from each antenna, the symbol multiplied by a respective element of a selected column of a matrix; wherein the number of rows of the matrix is ​​at least the number of antennas, the number of columns of the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butler matrix that includes only a minimum number of non-real elements.

36. An apparatus for transmitting a symbol from a plurality of antennas, the apparatus being configured to: transmit simultaneously, from each antenna, the symbol multiplied by a respective element of a selected row of a matrix; wherein the number of columns of the matrix is ​​at least the number of antennas, and the number of rows of the matrix is ​​at least 6, and the matrix comprises or is a submatrix of a Hadamard-type Butler matrix that includes only a minimum of 5 non-real elements. IVIA / a / ¿U21 / UlU / OO

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