WO2013135934A1 - Method for spherically decoding signals from maximum-likelihood multiple-input and multiple-output (mimo) communication systems - Google Patents

Abstract

In which use is made of a box minimization benchmark method which accelerates the spherical decoding and which comprises a preprocessing step and a searching step. The method provides a new feasibility test included in the searching step, in which signals sck_i are obtained which, when not in the box, result in the signal scr_i being obtained, which reduces and simplifies the number of minimizations, reducing the computing time and therefore the cost of the decoding in terms of time. In addition, the method uses these signals scr_i and/or sck_i to select an initial signal x⁰ which is used in the box minimization method, which also minimizes the cost of the box minimizations in terms of time.

Description

 METHOD OF SPHERICAL DECODIFICATION OF SIGNS OF COMMUNICATION SYSTEMS OF MULTIPLE INPUTS AND MULTIPLE OUTPUTS (MIMO) OF MAXIMUM VEROSIMILITY

DESCRIPTION

OBJECT OF THE INVENTION

The present invention relates to a method of spherical decoding of signals of communication systems of multiple inputs and multiple outputs (MIMO) of maximum likelihood, in which a method of dimensions by box minimization is applied which accelerates spherical decoding; and which aims to reduce the number of cash minimizations and simplify each of said minimizations, reducing the computation time and therefore the temporary cost of decoding.

In general, the invention is applicable in the telecommunications industry and more particularly in wireless communications. In addition the invention is applicable in the field of cryptography.

BACKGROUND OF THE INVENTION

In the last decade, one of the most significant technological developments that led to the new generation of wireless broadband is communication through multi-input and multi-output systems (multiple-input multiple-output, MIMO). The recent interest aroused by MIMO technologies is not only limited to the world of research but has also had a dramatic impact on the wireless communications industry, proof of this is the adoption of MIMO techniques in many wireless standards such as LTE , WiMAX and WLAN. MIMO systems increase maximum transmission rates and improve the reliability and coverage of current wireless communications without the need to use additional bandwidth or transmission power. This is undoubtedly a huge advantage, since spectral resources are very scarce and expensive. On the other hand, keeping the transmission power as low as possible is a crucial factor in the battery life of the wireless communication devices and therefore it is necessary to minimize the consumption of the stages that make MIMO communication possible. In short, for all the reasons described above and for many others, MIMO is a field that attracts a large part of the highest level of international research.

Figure 1 shows the block diagram of a typical MIMO communications system composed of a transmitter 1 equipped with M antennas for sending signals to a receiver 2 equipped with N antennas, through a MIMO channel 3 that generates a mixture of the transmitted signals, which is due to the appearance of multiple paths between each pair of transmitter-receiver antennas. The number of transmitting antennas is never greater than that of receiving antennas, that is, N≥ M. The receiver comprises a detector that processes the mix of received signals and estimates what the transmitted data were, generally following some probabilistic rule, obtaining the decoded signal. It has been shown that the use of MIMO communication systems complicates the receiver and, especially, the data detection stage. Therefore, it is very important to achieve low complexity MIMO receivers that maintain a low detection error rate. There are different types of detectors, with different error rate properties and calculation complexity. The so-called "suboptimal" detectors are computationally efficient, but their error rate may not be acceptable, especially in the presence of a lot of noise in the transmission. The detectors with the lowest error rate are the so-called optimal detectors or of maximum likelihood, that in the decoding they obtain the signal with greater probability of being the one sent. The best known maximum likelihood detectors are those based on spherical decoding, which is described below to facilitate understanding of the invention.

5 Maximum likelihood detectors in general, and spherical decoding in particular, are very computationally expensive, that is, the computation time they require is high, especially when the noise in the communications channel is considerable. In addition, the cost of detecting a signal by these methods is quite unpredictable, depending on the noise of the channel. The invention described below is a modification of the spherical decoding method aimed at reducing the cost of decoding calculation, and which has the additional effect that the detection complexity of a signal is practically independent of noise.

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DESCRIPTION OF THE INVENTION

In order to achieve the objectives and solve the aforementioned drawbacks, the invention provides a new decoding method.

20 spherical signals of communication systems of multiple inputs and multiple outputs (MIMO) of maximum likelihood, in which there is a transmitter with a plurality of transmitting antennas M for sending signals through a MIMO channel to a plurality of antennas N of a spherical decoding receiver in which a dimension method is applied by

25 continuous minimization that accelerates spherical decoding; and where it is known that the receiver's input data is:

- a matrix of H and E ^NxM channels, with N rows and M columns, that is, the number of rows is equal to the number of receiving antennas and the number of 30 columns is equal to the number of transmitting antennas, where the number of Receiving antennas is greater than the number of transmitting antennas N> M.

- the constellation: D = {d _lt ..., d _L } set of L symbols, all of them in R. - the received signal and E ^N ;

From said input data, the receiver obtains the maximum likelihood signal, that is the decoded signal, which is selected from among all the M component signals that fulfill each of the M components of the signal belonging to the constellation D. The maximum likelihood signal means that one of these M component signals that, after being filtered by the H-channel matrix, has the minimum distance to the received signal and.

The conventional spherical decoding method comprises a preprocessing stage and a search stage. In the preprocessing stage, a new R ε R ^MxM channel matrix is obtained and a new received signal z ε R ^{M is also obtained} , by orthogonal transformation of the H channel matrix and the received signal y; where the new matrix of channel R is triangular superior by means of which the search stage is simplified by allowing to organize the search sequentially.

Furthermore, in the preprocessing stage a first auxiliary signal sck is obtained, by solving a conventional triangular equation system described below to facilitate the understanding of the invention. Next, it is verified whether the condition that said first auxiliary signal sck has all its components within a box defined by the maximum and minimum values of the constellation D is fulfilled, so that if it is verified that said condition is met, then obtains an initial radius whose value is the distance between the sck signal after being quantized and filtered by the matrix R, and the received signal z. For him On the contrary, if this condition is not checked, then in the preprocessing stage an initial signal xO is selected which is used to calculate a second auxiliary signal, by solving a minimization problem with conventional restrictions, and in addition an initial radius is obtained as the distance between the signal being after being quantized and filtered by the matrix R, and the signal received z.

In the search stage it is known that in the first instance the square of an initial radius is established as the smallest total distance obtained so far, and then partial signals are listed (s¿, s¿ ₊₁ , "-, SJV _Í -I, s _M ) and complete signals (s ₁ , s ₂ , - -, s _M _ ₁ , s _M ), on which a feasibility test is applied, to decide whether each of the partial signals listed it is feasible or not, and when a certain partial signal (s¿, s¿ ₊₁ , ·· ·, s _M _ _lt s _M is feasible, the following signals are selected, selected between partial signals and complete signals, called successors , of said partial signal, and when a certain partial signal (s¿, s¿ ₊₁ , - -, s _M _ _lt s _M ) is not feasible it is discarded and no partial signal or complete signal is enumerated, successor of said partial signal.

Each time in the enumeration a complete signal is obtained that, after being filtered by the R channel matrix, its distance to the received signal z is less than the smallest total distance obtained so far, said complete signal is saved as a candidate for maximum likelihood solution, and the smallest total distance obtained so far becomes that distance to the received signal z. When the enumeration ends, the resulting candidate signal is the maximum likelihood signal corresponding to the decoded signal.

In the feasibility test, where it is decided whether a partial signal (s¿, s¿ ₊₁ , ·· ·, s _M -i _> S _M ) is feasible or not, it is first checked whether the partial distance of said partial signal is less than the smallest total distance obtained so far. In the case of not performing said check, that is when the partial distance of the partial signal is not less than the smallest distance obtained from the received signal, then said partial signal is established as not feasible. On the contrary, if said check is carried out, that is, when the partial distance of the partial signal is less than the smallest distance obtained from the received signal, then an initial signal xO is used which is used as the initial signal to apply a method of minimization with conventional restrictions, whereby the second auxiliary signal scr¿ associated with the partial signal (¾ ½, -,% _ _!, ½) is obtained. Next, said second auxiliary signal scr¿ is used to calculate a conventional continuous minimization dimension c, and the dimension c is added to the partial distance of the partial signal 0¿, s¿ ₊₁ , ···, s _M _ _lt s _M ). Next, it is verified whether said sum is greater than the smallest total distance obtained so far in which case the partial signal is declared not feasible; and if the sum is less than the smallest distance obtained so far, the partial signal is declared feasible.

Basically, the invention brings two improvements to spherical decoding. Making the second improvement requires having made the first improvement.

This first improvement is characterized in that after applying the feasibility test and verifying that a partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt s _M ) is feasible, since its partial distance is less than the Shortest total distance obtained so far, as described, includes:

- calculate the first auxiliary signal sck _t = (s _lt s ₂ , ^■■ ·, s¿_i) associated with the partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt s _M ), - check if the first auxiliary signal sck _t associated with the partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt s _M ) has all its components within the box defined by the maximum and minimum values of the constellation,

- when such verification is checked, that is when there is a condition that all the components of the first auxiliary signal sck _t they are inside the box, then the partial signal (s¿, s¿ ₊₁ , ·· ·, s _{M →} s _M ) is declared feasible;

- on the contrary, when said verification is not verified, that is, there is no prior condition that all the components of the first auxiliary signal sck _t are inside the box, then the second auxiliary signal scr? associated with the partial signal is calculated (s¿, s¿ ₊₁ , ·· ·, s _M _ _lt s _M ), and then the continuous minimization dimension c is determined, using the feasibility test, if the partial signal (s¿, s¿ ₊₁ , - -, s _M _ _lt s _M ) is feasible or not. Therefore, the described method limits the number of minimizations in box, using the position of the first auxiliary signal sck _t relative to the box defined by the constellation, so that it is not always necessary to calculate the second auxiliary signal scr¿. Consequently, with this first improvement proposal, the number of cash minimizations made in the state of the art is reduced.

The second improvement proposed by the invention is characterized in that after checking the feasibility of a partial signal (s¿, s¿ ₊₁ , ·· ·, s _M _ _lt s _M ) for an ith component, with i <M , which verifies that its partial distance is less than the lowest total distance obtained so far, and for which the first auxiliary signal sck _t associated with said partial signal has any of its components outside the box defined by the maximum and minimum values of the constellation, so the second auxiliary signal scr¿ associated with the partial signal (s¿, s¿ ₊₁ , ·· ·, s _M _ _lt s _M ) has to be calculated, according to the method of the First improvement, and also the continuous minimization level c must be calculated, also includes:

- obtain the initial signal xO for the continuous minimization method with restrictions, such as the first i - 1 components of the second auxiliary signal scr _{i + 1} = (s _1; έ ₂ , ···, s¿-i) when at check the feasibility of a predecessor partial signal (s¿ ₊₁ , ·· ·, s _M _ _lt s _M ) of a partial signal (s¿, ·· ·, s _{M - 1} , s _M ) the second was calculated auxiliary signal scr _{i + 1} = (s _1; s ₂ , ^■■ ·, yes) associated with the partial signal (s _{í + lJ} ···, s _M _ _lt s _M ), and

- obtain the initial signal xO for the continuous minimization method with restrictions, such as the first i-1 components of the first auxiliary signal sck _{i + 1} : (s ^, ···, s¿-i), when checking the feasibility of the predecessor partial signal (s¿ ₊₁ , ···, s _M _ _lt s _M ) the second auxiliary signal scr _{i + 1} was not calculated, and therefore the first auxiliary signal sck _{i + 1} = ( yes, s _{2 <} ···, i) associated with the partial signal (s¿ ₊₁ , -, s _M _ ₁ , s _M ).

Therefore, by means of this second proposal, the initial signal for the box minimization method is selected, using the auxiliary signals scr¿ and / or scki obtained by examining the feasibility of the predecessor partial signal, which minimizes the temporal cost of each of Cash minimizations.

Additionally the invention is characterized in that:

- the preprocessing step comprises storing the first auxiliary signal sck, and storing the second auxiliary signal being when it has been calculated,

- use the first auxiliary signal sck and the second auxiliary signal to be stored, in the possible minimizations that are applied to verify the feasibility of partial signals of the form (s _M ) with i = M,

- after checking the feasibility of a partial signal (s _M ) with i = M, which verifies that its partial distance is less than the lowest total distance obtained so far, and for which the first auxiliary signal sck _M associated with said signal partial has some of its components outside the box defined by the maximum and minimum values of the constellation, so the second auxiliary signal scr _M associated with the partial signal (s _M ) and the continuous minimization dimension c have to be calculated , also includes:

- obtain the initial signal xO for the continuous minimization method with restrictions, such as the first M— 1 components of being, when the auxiliary signal was calculated in the preprocessing stage, and - obtain the initial signal xO for the method of continuous minimization with restrictions, such as the first M-1 components of sck, when in the preprocessing stage the second auxiliary signal was not calculated and only the first auxiliary signal sck was calculated.

5 This additional characterization allows to complement the advantages described for the first and second improvement, obtaining a more efficient method, in which the temporal cost of spherical decoding is practically independent of noise.

It should also be noted that the proposed method can be applied i or simultaneously (and with cumulative improvements) along with other well-known optimizations for spherical decoding (Schnorr-Euchner sorting, column array ordering, etc.)

It is common for the signal to be sent in the form of complex numbers, and for decoding methods to be written directly in complex form. The proposed method can also be adapted to spherical decoding methods for complex data; On the other hand, it is well known that the problem of complex decoding can be written as a problem in terms of real numbers.

In addition, it has been proven that the algorithm for minimization in box 20 proposed in the book Ake Bjórck, "Numerical Methods for Least Squares Problems", SIAM, Philadelphia, 1996 section 5.2, page 203, is perfectly adapted for the resolution of minimization problems of the invention, although other algorithms could also be used.

In general, spherical signal decoding methods also have application in the field of cryptography; The proposed method can also be used in that field.

Next, to facilitate a better understanding of this descriptive report and forming an integral part of it, a series of figures are attached in which, with an illustrative and non-limiting nature, represented the object of the invention.

BRIEF STATEMENT OF THE FIGURES

5 Figure 1.- Shows a conventional generic block diagram of a MIMO communications system with M transmitting antennas and N receiving antennas, which has been described in the background section of the invention. Figure 2 shows a conventional flow chart of the preprocessing stage of the spherical decoding.

Figure 3.- Shows a conventional flow chart of an improvement in the preprocessing stage of spherical decoding.

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 Figure 4.- Shows a conventional flow chart of the search stage of spherical decoding.

Figure 5.- Shows a conventional flow chart of the feasibility test 20 that is included in the search stage of the previous figure.

Figure 6.- Shows a flow chart of the improved conventional preprocessing stage with respect to the preprocessing of Figure 2, with respect to which it also includes a technique for obtaining a good approximation of the radius.

Figure 7.- Shows a conventional flow chart of the feasibility test of the partial signals with a continuous minimization level that replaces and improves the test of Figure 5.

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Figure 8.- Shows a flow chart of the new preprocessing stage according to the invention. Figure 9.- Shows a flow chart of the new feasibility test that includes the search stage according to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Below is a description of the invention based on the figures mentioned above.

First, to facilitate the understanding of the invention, the mathematical representation of the problem of signal decoding in conventional MIMO systems is described, which is shown in Figure 1 and which was described in the background section of the invention.

The transmission of data from the M transmitting antennas to the N receiving antennas is mathematically modeled by an HGE ^NXM matrix, with N rows, corresponding to the number of receiving antennas and M columns, corresponding to the number of transmitting antennas, being N> M, called channel matrix, and is known to the receiver. The sending of an M-dimensional signal s = (s ^ - ^ M ^ SM) through the channel is simulated as the product of the channel matrix by the signal sent: H · s ε Ε ^Ν . Therefore, the result of a signal s being filtered by the channel matrix is the signal H ^■ s £ l ^N. When a signal is sent through the channel, it is not only filtered by the channel matrix, but is transformed by noise. As a consequence, the received signal and £ E ^N could be written as y = H · s + v; where v GE ⁿ is the noise (unknown).

Furthermore, it is known that the components (S ^ - ^ SM ^ SM) of the signal sent s GE ^M belong to a discrete, finite set D = {d _1; d _L } called constellation or alphabet The elements of the constellation D are called symbols and therefore D is formed by the symbols. For example, the constellation 4-PAM (pulse amplitude modulation) is the set {-3, - 1, 1, 3}, represented in Figure 3, which will be described in greater detail 5 later.

The objective of the problem is to find the maximum likelihood solution ("Máximum Likelihood Solution", or ML Solution hereafter). This is the signal s = (s ₁ , -, s _M _ ₁ , s _M ) G ffi ^M which verifies that the distance between said signal, filtered by the channel matrix H {H · se E ^N ) and the received signal ioy G l ^N is the minimum, among all the possible signals composed of constellation symbols D. Mathematically it is expressed as s = arg min _s || H · s— y || , where s (i) GD, i = 1, M.

It should be noted that any spherical decoding algorithm consists of two stages: a preprocessing stage, followed by a search stage.

The conventional basic version of the spherical decoding for obtaining the ML signal, whose preprocessing stage is shown in the flowchart of Figure 2 (d1 1) and comprising, is described below.

20 1) (d 1 1 1) Calculate the QR decomposition of the H-channel matrix. In this process, two matrices Q and E ^NXN and R and E ^NXM are calculated so that their matrix product Q · R is equal to H ; where Q is an orthogonal matrix (which verifies that the product of Q by its transposition Q ^T is the identity; Q · Q ^T = I, and therefore the inverse of Q is its transposition Q ^T ) and R is a matrix

25 triangular upper. The new channel matrix R £ E ^MxM , is a superior triangular matrix, with M rows and M columns, is obtained as the first M rows of R.

2) (d1 12) The signal received and is projected on the matrix R, this is done by multiplying Q ^T by y. Selecting the first M components of (Q ^T - y) we obtain the new received signal, which is called z GE ^m . Therefore the problem s = arg min _S || H · s - y || it becomes the mathematically equivalent problem (with the same solution) s = arg min _s \\ R · s - z \\, where s (i) ED, i = 1, ..., M Then the stage of search represented in figure 4 (d12) and figure 5 (d18).

The upper triangular structure of the new R channel matrix allows to organize the search sequentially, first looking for a value for the M-th component of the sent signal, using the M-th row of the R matrix; then a value is searched for the Μ-1 -th component of the signal, and so on. The selection of values for the ith component of the ML solution signal is said to be done in the ith layer.

The R · s - z operation can be written in detail as:

Then, the distance \\ R · s - z \\ ² , where s = ^••• , s _M _ ₁ , s _M ) is written in detail as

\\ R ^■ s— z \\ ² =

···, s _{M - 1} , s _M )

⁼ ( ^r l, l ^'S l + ^r l, 2 ^{' s} 2 + ^r l, 3 ^'s 3 + I ^"r l, M' ^S M ~ ^z l) + ( ^r 2.2 ^'s 2 + ^r 2.3 ^'s 3 + + ^R 2, M ^{' S} M ~ ^z l)

+ (J3,3 · s ₃ + ··· + r _3¡M ^■ s _M - z ₃ ) ² + ···

+ ( ^r Ml, Ml ^'S M-1 + ^R Ml, M' ^S M ~ ^Z Ml) + ( ^R M, M ' ^S M ~ ^Z M)

(ec.2)

The ML signal is searched among the signals received in the form s = {s, - ^ SM- ^ SM) where the values do belong to the constellation D, discarding those whose distance to the received signal z is greater than a certain radius r ² ; this initial radius r ² must be chosen so that there is at least one signal = (s ^ --- .SM ^. SM, with s (i) GD such that

To properly describe the search in spherical decoding, a partial signal in the ith layer can be defined as a signal of M - i + 1 elements of the constellation, already selected for the components of the possible sent signal, from the layer i-th to M-th: (s¿, s¿ ₊₁ , ···, s _{M - 1} , s _M ). This partial signal has a partial distance associated, which is calculated as: partial distance ^ s¿, s¿ ₊₁ , ···, s _{M - 1} , s _M )

⁼ ( ^r t, t ^' ^ t + ^r t, t + l' ^ i + l + I ^"r i, M '·% ^{- z} i)

+ ( ^r t + l, t + l '^ i + l + I ^"R Í + l, M' ·% - Z¿ _{+ 1} ) + ···

+ ( ^r M- _l , M- _l '·% - _! + - S _M - Z _M _ ₁ ) + (r _MM · S _M - Z _M )

(ec.3)

In contrast to the partial signal concept, it is useful to define the complete signals; these are the signals that have their M components defined; they are of the form s = (s _1; ^••• , s _M _ ₁ , s _M ) and, as mentioned above, the ML signal is searched among the complete signals.

Clearly, any possible complete signal s = (S _1J S _2J "-, 5 _Í _ _1J S _ÍJ S _{Í + 1J} " - _J S _{M - 1} , S _m ) whose components from i to M are the partial signal (s¿, s¿ ₊₁ , ···, s _{M →} , s _M ) will your distance to the received signal be fulfilled || 7? -sz || ² =

s ₂ , · ^■ ·, s¿_ _! , s¿, s¿ ₊₁ , ···, s _M _ ₁ , s _M ) is greater than the partial distance associated with said partial signal.

From the above it follows that if a partial signal (s¿, s¿ ₊₁ , -, s _{M - 1} , s _M ) has an associated partial distance greater than the radius r ² then said partial signal can be discarded, since that any complete signal s obtained from said partial signal will have an associated total distance greater than the radius r ² .

In addition to facilitate the understanding of the search stage it is useful to define the predecessor signal of a given as follows; given a partial signal in layer i (i <M) (s¿, s¿ ₊₁ , -, s _M _ _lt s _M ), its predecessor signal is the signal (s _{í + lJ} -, s _M _ _lt s _M ), in the i + í layer. The concept is also valid for complete signals: the predecessor signal of a complete signal>i> ^S 2>"'> ^S MI> ^s w¡) the partial signal (S2, · · ·, SJIÍ-I» · ¾).

Similarly, the successor signals of a given signal are defined as follows; given a partial signal in layer i (i> 1) (s¿, s¿ ₊₁ , -, s _M _ ₁ , s _M ), its successor signals are the L possible signals of i + 1 components, so (YES ^ YES. YES ^, - - -, s _{M - 1} , s _M ) and where s _¿--1 is one of the elements of the constellation.

The search stage of any spherical decoding algorithm has two stages: A) enumeration of the possible partial and complete signals, and B) feasibility test of each partial signal.

A) The enumeration of the partial signals is done sequentially by the different "dimensions" or layers of the signal s, from the last (the Mth) to the first. The diagram in Figure 3 aims, by means of a simple example, to give an idea of how this enumeration proceeds.

Figure 3 shows how the enumeration of the possible signals would be in a case with M = 5 and constellation £> = {- 3, -1, 1, 3}. In this example, some partial signals have been designated arbitrarily as feasible and others as not feasible, to explain how the enumeration proceeds depending on whether the partial signals found are feasible or not. Instead of the arbitrariness mentioned, the feasibility test must be applied as will be described later.

The enumeration begins with the layer i = M (M = 5 in the example), and considers all possible constellation values for position M of the signal. Each of the elements of the constellation constitutes a partial signal of level M. To each partial signal of level M the feasibility test is applied, and those that are feasible are still explored, generating its successor signals of level M - 1; the feasibility of each one of these is checked, and again only those that are proven feasible are still explored (generating successors).

The partial signals considered in layer 5 are then (-3), (-1), (1) and (3) Each of these partial signals is subjected to the feasibility test. In this example, we assume that the partial signals (3) and (1) are non-feasible (partial signals not feasible are slightly obscured), while partial signals (-3) and (-1) are feasible. First, the partial signal (-3) is scanned, moving on to the next layer (i = 4).

In layer 4, the partial signals that have the value already assigned (-3) in the fifth component are considered, and all possible constellation values for the fourth component are considered: These partial signals are: (-3, -3), (-1, -3), (1, -3), and (3, -3), and the feasibility test would be applied to all of them. Of these, only the partial signal (-1, -3) is considered (arbitrarily in the example) feasible, and is the only one for which the next layer is passed, i = 3.

The method continues to generate partial signals until it reaches layer i = 1. In this layer the signals are no longer considered "partial", but "complete" because they already have the desired number of components (M = 5). In this last level, the feasibility test is not applied, but the distance to the received signal is calculated (calculating || R · s - z \\) and that complete signal having minimum distance || R · s - z \\ among those that have reached the last layer (i = 1).

After finishing the four "complete" signals, successors of the partial signal (1, 1, -1, -3), return to the previous layer to complete the enumeration of the successor signals of the signal (1, -1 ,-3). The superscript of each partial and complete signal indicates the order in which the partial and complete signals are traversed in the search method of Figure 4 (d12), assuming that the constellation elements are traversed in the natural order (from less than higher). Note, for example, that the signal predecessor of the signal in layer 4 (3, -1) is the signal in layer 5 (-1); or, similarly, the signal predecessor signal (-3,1, 1, -1, -3) is the signal (1, 1, -1, -3). Note also that a partial signal (of level i <M) or a complete signal is examined only if its predecessor signal is feasible. Note that the 4 successor signals of the partial signal (-1, -3) are (-3, -1, -3), (-1, -1, -3), (1, -1, -3) and (3, -1, -3).

As can be seen in the example, in the i-th layer partial signals are considered in which their components from i + 1 to M (s¿ ₊₁ , -, SM.-J_. SM) have values already assigned or selected in layers i + 1 through M, and in the ith layer the different elements of the constellation are tested for the ith component of the partial signal. We will distinguish the components with value already assigned from those with value to be assigned using a top bar, that is, if the ith component of the signal s has an assigned value, we denote it as yes, while if it still does not have an assigned value we denote it as yes

The method is detailed in the flowchart of Figure 4 (d12), which is described in detail below:

1 - Initially (d121) the layer counter i is initialized with the initial value M (to start processing the layer M); the minor variable _dist_obtenida is initialized with the value r ² .

2- The feasible partial signals and the complete signals whose distances are smaller than the minor variable _dist_obtended are traversed in a tree. When all partial and total signals have been explored; that is to say i is equal to M (d122) the method tries to access the layer M + 1, which does not exist; This indicates the end of the method (d123).

3- For the first layer to be examined (i = M), we start searching among the elements of the constellation by starting the constellation enumeration (d124), verifying if the enumeration has been completed (d125), and in case if it is not complete, a new constellation element is selected (d127). In this first layer, the elements of the constellation s _{M are selected} those that verify that the partial signal (s _M ) is feasible, test (d131).

4- If said partial signal (s _M ) is not feasible (d131), it means that this partial signal should not be scanned further and should be discarded, so it is returned to

(d125) and, if elements of the constellation remain to be explored, the following element is selected.

5- If said partial signal (s _M ) is feasible, then said current partial signal will continue to be scanned, setting the element s _M = s _M , and preparing the exploration of the new layer: the partial distance is saved and decremented the layer counter i = i - 1 (d132).

6- Next, we begin to examine the layer i = M - 1; (d124, d125, d127) in the same way as was done for the first layer. At this moment, the elements s _{M - 1} belonging to the constellation will be selected and that verify that the partial signal (s _{M - 1} , s _M ) is feasible again, test (d131).

7- If the partial signal (s _{M - 1} , s _M ) is not feasible, this partial signal can be discarded, and the next element of the constellation for layer M— 1 is scanned. 8-If the signal partial (s _{M - 1} , s _M ) is feasible, then the current partial signal will continue to be scanned, setting the element s _{M - 1} = s _{M - 1} and the layer counter is decremented (i = i - 1) (d132).

9-If given the selected element s _M all possible checks are checked values for s _{M - 1} and none of the partial signals (s _M -i,%) is feasible, that means that no complete feasible signal can be obtained from the partial signal s _M ); in this case, after examining the last element of the constellation for the layer i = M - 1, the choice in (d125) is positive, the layer counter (i = i + 1), (d126) is increased by returning to the layer M, the element s _M is discarded and an attempt is made to select a new value for s _M (dl27).

10- This process of enumerating candidate partial signals is repeated for all layers until (and including) the last layer (i = 1). As in the previous layers, the layer i = 1 is now traversed; in the layer i = 1 partial signals are no longer obtained, but complete signals are obtained.

1 1 - If in layer i = 1, for some element of the constellation s _{1 it} is verified that the distance of the complete signal obtained is less than the best distance obtained so far:

, s _M _ ₁ , s _M ) <minor _dist_obtenida

(d130), then s _x = s ₁ is selected and the signal (s _1; ···, s _M _ _lt s _M ) becomes the best candidate signal to be ML solution, of those found so far. The lower value _dist_obtenida is updated, taking as a new value distance {s _lt ^■ · ^■ , s _M _ ₁ , s _M ). (dl28) 12-The process continues with the enumeration and will end when there is no possible signal within the smaller radius sphere _dist_obtenida; at that time, the optimal solution obtained is the ML solution. Note that the minor variable _dist_obtenida decreases each time a better solution is found. The order in which the elements of the constellation are traversed (order in which each new element of the constellation is selected, in (d127) influences the performance of the method. In the previous example the most common ordering has been described which, according to the description consists of touring the elements of the constellation from least to greatest according to a tree configuration, and which is known as Fincke-Pohst sorting. There are also other ordinations, such as Schnorr-Euchner ordination is known to be more efficient. The invention proposed below works equally beneficial for any arrangement of the constellation elements.

It is also possible to change the way partial signals are traversed; the search stage (d12) runs through the tree of partial and complete signals looking first in depth and then in width. There are other ways to travel the tree, first in width and then in depth. The invention proposed below can be applied equally beneficial to any of these tree travel techniques.

B) Feasibility test of partial signals In the basic spherical decoding algorithm, the feasibility test of a partial signal consists only of checking whether the partial distance associated with said partial signal is less than the smallest distance obtained so far. In addition, if a partial signal is feasible, in the feasibility test the necessary (convenient) calculations are made to continue exploring said signal.

In the case of the basic algorithm, said calculations consist in that, each time a certain element is selected in the ¿, yes, it is computationally convenient to correct the received signal z by canceling the effect of the selected element s¿, on said received signal z. This effect is canceled by subtracting the ith column of the matrix R multiplied by the selected element s from the z signal. For this, a corrected signal will be used for each layer we call zaux _t . In the first layer (i = M), for a certain selected element s _M , zaux _M is a signal of M— 1 components that is calculated as: zauxii) - z (l) Y \, M ' ^S M ^'

z ux _M ^ ∑) = z (2) - τ _2Μ '$ Μ> zaux _M (M - 1) = z (M - 1) - r _M _ _1M · s _M

 (ec.4)

In the next layer (i = M— 1), with s _M already selected, a new element of the M-1 layer would be selected, be it s _{M - 1} . To obtain zaux _M _ _lt the signal of M— 2 components corrected after canceling the effects of s _M and s _M _ _lt the following operation is performed:

ziuXyi- ^ i) = zaitx _M (2) - _2: Μ-Ι '$ Μ-Ι> ^ zaux _M _ ₁ M - 2) = zaux _M (M - 2) - r _M _ ₂ , Mi' ·% -ι

In general, suppose the elements have already been selected (½, ^■ ··,% _ _! ,%), The corresponding corrected signal zaux _{i + 1} has been calculated and in the ith layer the element s¿ is selected. Then the corrected signal zaux of i - 1 components is calculated as follows:

zaux¿ (l) = zaitx¿ ₊₁ (l) - r _x ¿· s¿;

zaitx¿ (2) = zaux _{i + 1} () - r _2i · s¿; zauxiii— 1) = zaux _{i + 1} i— 1) - r. ^ ¿· s¿

(ec.6) Equally it can be verified that zaux _t can be written as: zaitx¿ (l) - z (l) r _{1 (} ¿· s¿ · s¿ ₊₁ ··· r _1¡M · s _M ;

zaitx¿ (2) = z (2) - r _{2 i} · s¿— r _{2 i + 1} · s _{i + 1} - r _2M · s _M ; zauXiii— 1) = z (i— 1) - TÍ_ _1: Í · s¿— r¿_ _{1 (} £ ₊₁ · s¿ ₊₁ - ··· - r¿_ _liM · s _M

Given a partial signal in the i + í layer (s¿ ₊₁ , ^■ ··, _ _! ,%), If the partial distance corresponding to this partial signal is calculated and stored, it is possible to easily calculate the partial distance corresponding to any partial signal of level i obtained by adding the element s¿ to the partial signal (s _{i + 1} , -,% -i,%) as follows: partial distance s _it s _{i + 1} , ^■ · ^■ , s _M _ _lt s _M ) = partial distance (s _{i + 1} , ^■ ··, $ Μ-Ι · $ Μ) + {zaux _{i + 1} (V) - r¿ ¿· s¿) (ec. 8)

5 With the help of figure 5 (d18) the feasibility test mentioned is detailed.

As mentioned above, in this case the partial distance of the partial signal to be checked is checked (d181); If the partial distance is greater than the smallest distance obtained so far, the signal is not feasible (d182). io If the partial distance is less than the smallest distance obtained so far, the zaux _t signal (d183) is updated, as shown in equation 6, and the partial signal is feasible (d184).

Furthermore, the use of spherical accelerated decoding methods by continuous minimization is known in the state of the art.

15 In this regard, we now need to consider two conventional associated auxiliary problems, the problem of continuous minimization and the problem of continuous minimization restricted or "in cash".

The auxiliary problem of continuous minimization (PA1) aims to find the sck e RM signal that verifies that the distance between the R · 20 scfce R ^M signal and the received signal ze RM is the minimum:

sck = arg min _s \\ R · s— z \\, where sck (i) GR, i = 1, ..., M

This is not a discrete problem, as in the case of basic spherical decoding, but it is a "continuous" problem (the components of sck can be any real number) and its solution is easily obtained by solving the system of linear equations triangular R · sck = z. The auxiliary problem of continuous minimization in box (PA2) aims to find the signal to be G ^M which verifies that the distance between the signal R · be <≡ ^M and the signal z <≡ ^M is the minimum distance, and which also verifies that the components of being are real numbers contained between the minimum and maximum of the constellation:

ser = arg min _s \\ R · s— z \\;

where min (D) <= scr (i) <= max (D) and be (i) G R, i = Ι,.,. Μ

This is also a continuing problem, but with the restriction that it must be contained in the "box" defined by the maximum and minimum constellation values. There are different methods to solve this problem. Being a relatively complex problem, computer programs already written for this purpose are usually used to solve it. These programs start from an initial signal xO and proceed by taking steps in which the initial solution moves towards the final solution. If an initial solution close to the final solution is provided to the chosen program, these programs can be considerably faster. They can work without an initial solution (in this case, the program selects an initial solution xO randomly), but the calculation cost to obtain the solution will usually be much higher. In the state of the art, a modification of the method of spherical accelerated decoding by elevation by continuous minimization is known; which we call modification 1.

 Said modification 1 to improve the performance of spherical decoding, aimed at obtaining a good estimate of the initial radius r, has been described in document [1] Xiao-Wen and Qing Han, "Solving Box-Constrained Integer Least Squares Problems" IEEE Transactions on

Wireless Communications, vol. 7, no. 1 (2008), 277-287.

In this modification 1 for the search of Figure 4 (d12) to be successful, the initial radius r must be chosen so that there is at least one signal s = (SL, · · ·, s _M _ ₁ , s _M ), with s (i) GD such that

···, s _M _ ₁ , s _M ) <r ² . If not There was no signal verifying this condition, search (d12) would not find any solution.

On the other hand, for the search to conclude in a reasonable time, the initial radius must be as small as possible. A well known technique for selecting an initial radius is based on finding a signal that is a reasonable approximation to the ML solution and taking its distance from the signal received as the initial radius.

It is well known that the solution of the continuous auxiliary problem described (PA1) sck can be used to obtain a possible signal, rounding (quantizing) each component of the sck signal to the closest value of the constellation D. The signal obtained is called zf ( "zero-forcing"), which is one of the possible signals sent. Since it is possible that zf is close to the ML solution, and it is certainly a possible feasible signal, the value \\ R · zf - z is usually used as the initial radius r (for the search algorithm). This radio is sure that a signal is within the sphere (the possible zf solution).

This technique to obtain an initial radius is performed in the preprocessing stage, obtaining a new preprocessing method that includes the one described with the help of Figure 2 (d1 1) and also includes the technique described below with the help of Figure 6 (d21) to obtain a good approximation of the radius.

Thus, the preprocessing stage shown in the flow chart of Figure 6 (d21) contains the stages (d1 1 and d1 12) described in Figure 2, which have been referred to as (d21 1 and d212). Next, sck is obtained by solving a system of triangular equations R- sck = z (d213) (PA1).

However, in situations with a lot of noise, this radius estimate produces unsatisfactory results. A typical characteristic of these situations is that the sck signal is "far" from any possible signal s, what which can be detected by examining whether the components of the sck signal are contained in the range defined by the minimum {mD) and maximum (MD) values of the constellation.

To clearly define this situation, we will say that a signal s is in the box if all its components s (i) are contained in the interval [mD, MD], and we will say that s is outside the box if any of its components s (i) has a value outside the range [mD, MD] (d214).

If the sck solution of the auxiliary problem of continuous minimization (PA1) is out of the box, then the initial radius is obtained using zf and by quantifying (rounding) sck the radius r is obtained as r = \\ R · zf - z \\ (d215).

If the sck solution of the auxiliary problem of continuous minimization (PA1) is outside the box, then the solution is of the auxiliary problem of continuous minimization in box (PA2) (which, by definition, is inside the box) is often a better approach to the ML solution that the sck signal.

Consequently, if sck is out of the box, instead of calculating the initial radius using zf, the initial radius will be calculated using the following method:

1-get to be by some method of minimization in box (d216), solving (PA2). 2-round (quantize) each component of the signal be the closest value of the constellation D, the resulting signal will be called zfr (d216).

3-Then, the initial radius is calculated as r = \\ R · zfr - z \\ (d217). This technique was proposed in the document [1] mentioned above. Also known in the prior art is the spherical decoding method with dimension by continuous minimization; which we call modification 2.

Such modification 2 to improve the performance of the spherical decoding search stage was proposed in document [2] M. Stojnic, H. Vikalo, and B. Hassibi, "Speeding up the Sphere Decoder with H ^A ∞ and SDP inspired lower bounds. ", IEEE Transactions on Signal Processing, vol. 56, no. 2 (2008), 712-726. These modifications 2, as proposed below, only affect the feasibility test of each partial signal. Therefore, the enumeration method remains the one described with the help of Figure 4 (d12), changing the feasibility test (d131). The test in Figure 5 (d18) is replaced by that in Figure 7 (d28), which is explained below.

Suppose we are examining the i-th layer and in it we are examining the partial signal s = (s¿, s¿ ₊₁ , ···, s _{M - 1} , s _M ). Recall that the partial distance associated with said partial signal is calculated as: partial distance ^ s¿, s¿ ₊₁ , ···, s _{M - 1} , s _M )

⁼ ( ^r t, t ^' ^ t + ^r t, t + l ^' ^ i + l + I ^"r i, M ^' ·% ^{- z} i

+ ( ^r t + l, t + l ^' + ^{■ "} + ^T i + 1, M ^' ·% -

+ ( ^r Ml, Ml '·% -! + - S _M - Z _M _ ₁ ) + ~ M, M ^{' S} M ^z M

(ec.10)

While the distance of any total signal s obtained from the previous partial signal will be calculated as: distCLHCiCL (SL, S2, ■■■, S _i, S¿, Sj + _!, " ^■ , S ^ _- ^, S ^)

⁼ ( ^r l, l ' ^s l + ^r l, 2 ^{' s} 2 + I ^"r l, M ^' ·% ~ ^z l)

+ ( ^r 2.2 ^'s 2+ ^r 2.3 ^{' s} 3 + + ^r 2, M ^' ·% ~ ^■ ¾) +

+ ( ^r tl, tl ' ^s tl + ^r tl, t' ^s i + I ^"r il, M ^' ·% ~ ^z il)

+ ( ^r t, t ' ^s t + ^r t, t + l' ^ t + l + I ^"r t, M '·% ^{- z} i)

+ ( ^r t + l, t + l '^ t + l + I ^"r i + l, M ^' ·% ~ ^z i + l) +

+ ( ^r M- _l , M- _l '·% - _! + - ·% - Z _M _ ₁ ) + (r _MM · S _M - Z _M )

(ec.11) or equivalently distance S ₂ , ..., S _i, S¿,, ···, S ^ _, s ^)

⁼ ( ^r l, l ' ^s l + ^r l, 2 ^{' s} 2 + I ^"r l, M ^' ·% ~ ^z l)

+ ( ^r 2.2 ^'s 2+ ^r 2.3 ^{' s} 3 + I ^"r 2, M ^' ·% - Z ₂ ) +

+ ( ^r tl, tl ' ^s tl + ^r tl, t' $ i + I ^"r il, M ^' ·% ~ ^z tl)

+ partial distance ^ s¿, s¿ ₊₁ , ···, s _{M - 1} , s _M )

(ec.12)

We will name the difference between

and partial distance (s _it s _{i + 1} , ^■ · ^■ , s _M _ _lt s _M ) as remainder (s _lt s ₂ , ..., s¿_i): remainder (s _lt s ₂ , ..., Sj_ _! )

⁼ ( ^r l, l ' ^s l + ^r l, 2 ^{' s} 2 + I ^"r l, M ^' ·% ~ ^z l)

+ ( ^r 2.2 ^'s 2+ ^r 2.3 ^{' s} 3 + I ^"r 2, M ^' ·% - Z ₂ ) +

+ ( ^r í-l, í-l ' ^s tl + ^r tl, t' $ i + I ^"r il, M ^' ·% ^{- z} tl)

(ec.13)

Note that remainder s ₁ , s ₂ , .... s ^) is necessarily a real number greater than or equal to 0, and that trivially it is verified

= partial distance ^ s¿, s _{i + 1} , ^■ · ^■ , s _{M - 1} , s _M )

+ remainder (s _lt s ₂ , ..., Sj_!).

(ec.14)

Therefore, from the distance condition _lt ---, s _{M - 1} , s _M ) <r ² Y of (ec.14), we have the partial distance condition ^ s¿, s _{i + 1} , ^■ · ^■ , s _{M - 1} , s _M ) + remainder (s ₁ , s ₂ , .... s ^) <r ²

Taking into account that (s¿, s¿ ₊₁ , -, s _{M - 1} , s _M ) have already been selected and have assigned values, then it can be considered that the distance is a function of the elements (s _lt s ₂ , .... s ^).

Given the partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt s _M ), if its partial distance is less than the minor variable _dist_obtained, this partial signal is feasible in the test (d18). The proposal in document [2] is to try to obtain a positive number c> 0 that is a lower bound of remainder s ₁ , s ₂ , .... yes ^: that is, for any combination of values (yes, s _2. -, YES-I), with s _k ED, k = 1, ..., i - 1, it is fulfilled that

0 <c <remainder (s _lt s ₂ , .... s ^).

In this case, the partial distance condition i, s _{i + 1} , ^■ · ^■ , s _{M - 1} , s _M ) <r ² can be substituted

By condition: partial distance ^ s¿, s _{i + 1} , ^■ · ^■ , s _M _ ₁ , s _M ) + c <r ² (ec.15)

This new condition is more restrictive (it causes more partial signals that do not comply with it) and therefore causes more partial signals to be eliminated. Consequently the search ends earlier. The larger the c (keeping the lower bound of remainder (s ₁ , s ₂ , ..., s¿_i)), the better the performance of the method.

Various techniques are proposed in the document [2] to calculate the lower bound c. One of them, on which the present proposed invention is based, is based on applying continuous minimization techniques to the expression rest distance (s _lt s ₂ , ..., Sj_!).

First, to raise the problem of continuous minimization, we rewrite the term rest distance: distance (s _lt s ₂ , ..., Sj_!)

⁼ ( ^r i, i ' ^s l + ^r l, 2 ^{' s} 2 + l ^{~ r} l, M ^' ·% ^{- z} i)

+ ( ^r 2.2 ^'s 2 + ^r 2.3 ^{' s} 3 + I ^"r 2, M ^' ·% ^{- ■} ¾) +

+ ( ^r í-l, í-l ' ^s tl + ^r tl, t' $ i + I ^"r il, M ^' ·% ^{~ z} il)

⁼ ( ^r l, l ' ^s l + ^r l, 2 ^{' s} 2 + l ^"r l, tl ' ^s t-l + ^r l, t' $ i + I ^{" r} l, M ^' ·% ^{~ z} l)

+ (0 · s ₂ + r _2i2 · s ₂ + ··· + r _2¡i _ ₁ ^■ s _i _ ₁ + r _2fi · s¿ + ··· + r ₂ ^■ s _M - z ₂ f + · ··

+ (o · sL + or · s ₂ + ^■■■ + ^■ Yes ^ + r ^ i · s¿ + ··· + n_ _{l M} ^■ s _M

- Zi-x?

(ec.16)

Recall the calculation of the corrected signal zaux assuming that the values have been assigned (s¿, s¿ ₊₁ , -, s _{M - 1} , s _M ). Using the expression (ec.7), you can verify that the distance (s _lt s ₂ , ..., S _j _!)

= (ίΊ, ι · ¾ + Γ _1Ι2 · s ₂ + ··· + r ₁ , ¿_ ₁ · s _¿ --1 - zaux¿ (l))

+ (θ · s ₂ + r _2¡2 ^■ s ₂ + ··· + r _2fi _i · s _¿ --1 - zaux¿ (2)) + ···

+ (θ · s _x + 0 · s ₂ + ^■■■ + ri_ _ _x ^■ s _¿ --1 - zauxi (i - 1))

(ec.17) Written matrixally, if we define the matrix R _Í - _Í - I-. _Í -I as the submatrix formed by the first i - 1 rows and i - 1 first columns of the R matrix:

Restoration (s ₁ , s ₂ , ..., s¿-i) Rl: í-l, l: í-l

(ec.1 8)

Remember that each s¿ must belong to the constellation D. The constellation D is made up of real values and therefore has a maximum value M _D and a minimum value m _D. One way to obtain a lower elevation value ^ s ^ s ₂ , .... If ^) consists in calculating the minimum value of the expression on the right side of (ec.1 8), restricting the possible values of s¿ to which they can take can be any real number in the interval [m _D , M _D ] .

The problem to solve then is:

scr¿ = argmin _{Si S2 S¡ 1} where s¿ G

[m _D , M _D ] (ec.1 9)

Note that scr¿ is a vector or signal with i - 1 components. We will name scr¿ as the second auxiliary signal associated with the partial signal (s¿, s¿ ₊₁ , ···, s _{M - 1} , s _M ).

Once the second auxiliary signal, scr¿, solution of (ec.19) has been calculated, the continuous minimization dimension c can be obtained by means of the expression:

(ec.20) The problem (ec.19) is a problem of continuous minimization with box-type restrictions, such as the continuous auxiliary problem (PA2). Assuming that we have a method to efficiently solve problems of this type, it is possible to modify the feasibility test (d131) in 5 the enumeration method of Figure 4 (d12) to obtain a potentially more efficient alternative method.

A detailed description of the feasibility test in Figure 7 (d28) follows.

1 - As in the test of figure 5 (d18), it is started by checking if when the io partial distance corresponding to the partial signal (s¿, s¿ ₊₁ , ···, s _{M - 1} , s _M ) is less than less _dist_obtenida. (d281)

2- If it is not, the signal is not feasible and the test ends (d282).

3- If the partial distance corresponding to the partial signal (s¿, s¿ ₊₁ , "-, s _M _ ₁ , s _M ) is less than less _dist_obtended, proceed to

15 calculate the new corrected signal zaux _t (d283).

4- Next, the problem of continuous minimization (ec.19) is solved by obtaining the second auxiliary signal scr¿ associated with (s¿, s¿ ₊ - ^, ···, s ^ _- ^, s ^), which is used to calculate dimension c (d284), using equation (ec.20).

5- Next, it is checked whether the partial distance s¿, s _{i + 1} , ···, s _M _ ₁ , s _M ) 20 plus the dimension c is less than less _dist_distined (d285).

6- If it is not fulfilled that partial distance (yes, s _{i + 1} , ---, s _M _ ₁ , s _M ) + c <smaller _dist_obtended, then this partial signal is not feasible and the test ends. (d286).

7- If the partial distance is fulfilled (yes, s _{i + 1} , ---, s _M _ ₁ , s _M ) + c <25 smaller _dist_obtended, then the current partial signal is feasible and the test ends. (d287).

The method composed of the preprocess of Figure 6 (d21) and the search of figure 4 (d12) with feasibility test of figure 7 (d28) constitutes the known method with modifications proposed by other authors, closer to the invention.

Next, the novelties that the invention brings to the state of the art, described up to this point, are described.

The invention provides modifications to the method described with the help of Figures 4 (d12), 6 (d21) and 7 (d28), and which will finally be integrated into the method described in Figures 8 (d31), 4 (d12) and 9 (d38).

The modifications of the invention basically affect the i or feasibility test for partial signals, since the new preprocessing stage represented in Figure 8 (d31) undergoes changes with respect to that represented in Figure 6 (d21) and are the following:

1) The number of minimizations in box is limited, using the position of the auxiliary signal sck _t relative to the box defined by the constellation.

15 2) The initial signal is selected for the box minimization method, using the scr¿ and / or sck _t auxiliary signals obtained by examining the feasibility of the predecessor partial signal.

The already described described method composed of figures 4 (d12), 6 (d21) and 7 (d28), is very efficient in terms of nodes explored, but not in terms of

20 computing time, because of the temporary cost of cash minimizations. The proposals of the invention are aimed at reducing the number of cash minimizations and the cost of each of said minimizations, so that the algorithm obtained with the new method is globally more efficient. It is important to understand that the number of partial signals

The explorations should not change substantially from the method described to that proposed by the invention. However, the computation time cost of the invention is much better (smaller).

The modifications proposed below are those of Figures 4 (d12), 6 (d21) and 7 (d28), and will therefore be described from said algorithm. The first proposal of the invention is to limit the number of minimizations in the box, using the position of the sck signal relative to the box defined by the constellation.

This first proposal aims to reduce the number of cash minimizations that were described with the help of Figure 7 (d28), in (d284); In that phase of the method, the second auxiliary signal scr¿ of the minimization problem restricted to the box is calculated (ec.1 9), and then scr¿ is used to calculate the c-dimension as in equation (ec.20).

Let us now consider the problem of continuous, unrestricted minimization (PA1) for the same subproblem (with matrix R. _Í -XI. _Í -I and received signal zauxj). We will call the solution for this scfc¿ subproblem. As mentioned in describing (PA1), scfc is easily obtained by solving the triangular system of linear equations:

(ec.21)

Sck _t is referred to as the first auxiliary signal associated with the partial signal (s¿, s¿ ₊₁ , - -, s _M _ _lt s _M ). The calculation cost of the first auxiliary signal sc / c¿ for a partial signal {s _it s _{i + 1} , ---, s _M _ _lt s _M ) is normally considerably less than the calculation cost of the second auxiliary signal for the same partial signal.

Once sck is calculated, it can be checked easily and efficiently if scki is in the box defined by the constellation. Recall that a signal s is in the box if all its components s (i) are contained in the interval [mD, MD] where mD and MD are respectively the minimum and maximum values of the constellation D.

If scki is in the box, then it would coincide with scr¿, so it would no longer be necessary to calculate scr¿. Also, in that case, the value of dimension c would be 0, with which it would have no effect. Therefore, it only makes sense to use box minimization if sck _t is "out of the box".

Therefore, the first proposal includes the following steps for the feasibility test, which are described with the help of Figure 9 (d38) 1 -As in the tests of Figure 5 (d18) and 7 (d28), we start checking if when the partial distance corresponding to the partial signal (s¿, s¿ ₊₁ , "-, s _M _ ₁ , s _M ) is less than less _dist_obtained. (d381).

2- If it is not, the signal is not feasible and the test ends (d382).

3- If the partial distance corresponding to the partial signal (s¿, s¿ ₊₁ , "-, s _M _ ₁ , s _M ) is less than less _dist_obtained, the new corrected signal zaux _t (d383) is calculated. and the first auxiliary signal sck _t (d384) is calculated by solving the system of triangular equations (ec. 21).

4- If the first auxiliary signal sck _t is in the box (d385), the first auxiliary signal of sck _t is stored in memory for possible use as an initial signal χθ for minimization problems in layer i - 1, the partial signal It is feasible and the test ends (d386).

5- If the first auxiliary signal sck _t is not in the box, the second auxiliary signal scr¿ is obtained by solving the problem of continuous minimization (ec.19), for which the one obtained with the i-1 is used as the initial signal first components of the second auxiliary signal associated with the predecessor signal scr _{i + 1} (if scr _{i + 1} was calculated) or with the first i - 1 components of the first auxiliary signal associated with the predecessor signal sck _{i + 1} (if scr _{i + 1} was not calculated). Once the second auxiliary signal scr¿ is obtained, scr¿ is used to calculate the c dimension, using ec. (twenty). (d387)

6- Next, it is checked whether the partial distance s¿, s _{i + 1} , ···, s _M _ ₁ , s _M ) plus the dimension c is less than less _dist_obtained (d388).

7- If it is not fulfilled that partial distance (yes, s _{i + 1} , ---, s _M _ ₁ , s _M ) + c < minor _dist_obtenida then this partial signal is not feasible and the test ends. (d389)

8-If it is fulfilled that partial distance (yes, s _{i + 1} , ---, s _M _ ₁ , s _M ) + c <better _dist_obteined, then the current partial signal is feasible, the auxiliary signal scr¿ is saved 5 for possible use as an initial signal xO for minimization problems in layer i - 1 and the test ends. (d390)

This proposal has the effect of reducing the number of cash minimizations.

An additional effect of this proposition is as follows: Suppose that the method is considering the partial signal (s ^ S Si + !, -,

Then, it is ensured that the partial signal predecessor (s¿, s¿ _+1, - _Í -I SA, SA _i) ^is applied ^na feasibility test, and therefore be calculated SCK _t (solving (ec.21)) and possibly also scr¿ (if scki is out of the box).

15 It is important to note that, when processing a partial signal, the feasibility of the predecessor partial signal will necessarily have been previously checked, and in that case at least one of the auxiliary signals sck _t or scr¿ corresponding to the predecessor partial signal will have been calculated . This fact is necessary to be able to apply the second proposal of the invention

20 described below.

The second proposal of the invention consists in making the selection of the initial signal for the minimization in box.

Assume that a partial signal is being examined (s¿, s¿ ₊₁ , -, s _M _ ₁ , s _M and that it is necessary to apply box minimization. This second proposal aims to minimize the time cost of each one of the minimizations in box, and it is obtained by means of a careful election of the initial signal that is used for the minimization in box.

The restriction that the components of the second auxiliary signal scr¿ are contained between mD and MD ensures that scr¿ is contained in a "box", which gives name to the problem. The "faces" of the box are the subsets of the box that limit with the outside: that is to say, they are the vectors or signals of the box that, for at least one component, fulfill that their value is MD or mD. The fact that the solution of the unrestricted problem sck _t is out of the box guarantees that the solution of the restricted problem, scr, will be on one side of the box; that is to say; at least one component j meets scr¿ (/) = MD or ^scr ij ^{= m} D -

In general, box minimization methods are iterative methods that start from an initial signal (usually random) located in the box, which we will call χθ. These methods carry out iterations that bring the initial signal xO closer to the final solution, scr¿.

We will name the face of the box where the scr¿ solution is the optimal face. If the initial signal χθ is not on the optimal face, the continuous minimization processes "move" the signal χθ from face to face towards the optimum face, and therefore towards the scr¿ solution; If there is a lot of distance between the optimal face and the face on which the initial signal χθ is, then the minimization process can be made too long and expensive. Therefore, it is very important to select the initial signal χθ so that it is on the optimum face, or "near" it.

It has been proven experimentally that the box minimization problems that arise when examining partial signals of layer i are strongly related to the problems that arose in the previous layer (i + 1). In particular, suppose the feasibility of the partial signal (s¿, s¿ ₊₁ , - -, s _{M - 1} , s _M ) is being examined, and that, after evaluating its partial distance, it is found to be less than the minor variable _dist_obtenida. According to the first proposal, sck _t would now be calculated (solving the system of triangular equations ec.21) and it would be checked if sck _t is in the box; suppose then that sck _t is out of the box and, therefore, the next step is to solve the box minimization problem (ec.19), getting scr.

Previously, in the previous layer i + 1, the predecessor partial signal of the current one will have been examined: (s _{í + lJ} -, s _{M - 1} , s _M ); when examining this partial signal in the i + 1 layer, the auxiliary signal sck _{i + 1} will have been calculated with certainty, and possibly also the auxiliary signal scr _{i + 1} .

It has been proven experimentally that it is very likely that the solution of the new minimization problem in layer i, to obtain scr¿, is on the same side of the box as the first i-1 components of the second auxiliary signal scr ^, which It was obtained by solving the problem of minimization of the i + 1 layer. Therefore, it is proposed:

Assume that scr _{i + 1} is the solution to the box minimization problem by examining the partial signal (¾, · ^■ ·,%. _! , ¾) in the (i + 1) -th layer. Then, if in the next layer (i) when examining the partial signal (s¿, s¿ ₊₁ , -, s _M _ ₁ , s _M ) it is necessary to solve a new box minimization problem, it will be used as a signal initial χθ for this new minimization problem the first i - 1 components of scr _{i + 1} :

It is possible that for a certain partial signal (s¿, s¿ ₊₁ , ···, s _{M - 1} , s _M ) in the layer i a box minimization problem needs to be solved, but that for the partial signal predecessor (β _{ί + 1} , ···, s _M _ _lt s _M ) it was not necessary to apply cash minimization, and therefore scr _{i + 1} has not been calculated. In that case, the first i-1 components of sck _{i + 1} would be used as the initial signal, which was previously calculated when checking the feasibility of the predecessor signal s _{i + 1>} -, s _M _i, s _M ). Due to the first proposal, it is known with certainty that sck _{i + 1} was calculated.

In principle, this technique could not be applied when checking the feasibility of partial signals in the layer (i = M), since these have no predecessor signal. However, remember also that, due to the first existing proposal, in the preprocessing stage of Figure 6 (d21), before starting the search, the sck signals (analogous to the first auxiliary signal sc / c¿ are calculated) ) and, if this is out of the box, it is calculated to be (analogous to the second auxiliary signal scr¿). In the first existing proposal, sck and ser are calculated to obtain a better approximation to the initial radius. However, the signal to be (and, if it has not been calculated, the signal sck) can also be used to obtain an initial signal for the possible box minimizations in the layer i = M, that is, for the possible minimizations that may if necessary in the initial layer M) it will be taken as the initial signal xO = culated, and otherwise

will take com

The preprocessing step of Figure 8 (d31) is very similar to that of Figure 6 (d21); with the difference that the sck or ser signals, calculated in (d215), (d216) are stored in (d315) and (d316) for later use as an initial signal for minimization problems that may arise in layer M.

Claims

one . METHOD OF SPHERICAL DECODIFICATION OF SIGNS OF COMMUNICATION SYSTEMS OF MULTIPLE INPUTS AND MULTIPLE OUTPUTS (MIMO) OF MAXIMUM VEROSIMILITUDE, where there is a transmitter with a plurality of M transmitting antennas for sending signals through a MIMO channel to a plurality of NIMO channels to a plurality of NIMO channels a receiver that uses spherical decoding that is accelerated by applying a method of dimensions by continuous minimization; and where the receiver's input data is:

- a matrix of H £ E ^NXM channel, with N rows and M columns, where N≥ M.

- the constellation: D = {d _lt d _L ] set of L symbols, all of them in E.

- the received signal and the ^N ;

Calculating, from said data, the maximum likelihood signal corresponding to the decoded signal, which is selected from among all the M component signals that meet that each of the M components of the signal belongs to the constellation D understood by the maximum likelihood signal that of these signals that, after being filtered by the H-channel matrix, has a minimum distance to the received signal and; Understanding the method:

- a preprocessing step (d21) for obtaining a new RGE ^MxM channel matrix and a new received signal ze E ^M , by orthogonal transformation of the H channel matrix and the received signal and; where the new R channel matrix is triangular superior; also comprising the preprocessing stage:

• Obtain a first auxiliary signal sck, solving a system of conventional triangular equations (PA1) and • verify whether said first auxiliary signal sck has all its components within a box defined by the maximum and minimum values of constellation D, which

- if said verification is carried out, it comprises obtaining an initial radius such as the distance between the sck signal after being quantized and filtered by the matrix R, and the received signal z;

 - and if said verification is not fulfilled, it comprises selecting an initial signal xO and using it to calculate a second auxiliary signal, by solving a minimization problem with conventional restrictions (PA2), and also obtaining an initial radius such as the distance between the signal being after being quantized and filtered by the matrix R, and the signal received z. search stage (d12) comprising:

• set the square of an initial radius as the smallest total distance obtained so far, and

• list partial signals (¾% _!, · ^■■ ,% _ _! ,%) And complete signals (s ₁ , s ₂ , ···, s _M _ _lt s _M ), on which

• a feasibility test (d28) is applied, to decide whether each of the partial signals listed is feasible or not, and when a certain partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt s _M is feasible, the following signals, selected between partial signals and complete signals, called successors, of said partial signal are still listed, and when a certain partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt sM is not feasible is discarded and no partial signal or complete signal is listed, successor of said partial signal; • every time in the enumeration a complete signal is obtained so that, after being filtered by the R channel matrix, its distance to the received signal z is less than the smallest total distance obtained so far, said complete signal is saved as a candidate for maximum likelihood solution, and the lowest total distance obtained so far becomes said distance to the received signal z; Y

• When the enumeration ends, the resulting candidate signal is the maximum likelihood signal corresponding to the decoded signal, and

Understanding this feasibility test (d28), where it is decided whether a partial signal (s¿, s¿ ₊₁ , ···, s _M _ ₁ , s _M ) is feasible or not, first check whether its partial distance it is less than the smallest total distance obtained so far; Y

 • in the event that such verification is not carried out, said partial signal is established as not feasible; Y

• in the case of such a check, it comprises selecting an initial signal xO and using it as an initial signal to apply a conventional minimization method with restrictions, whereby the second auxiliary signal scr¿ associated with the partial signal (s¿, s is obtained ¿ ₊₁ , ---, s _M _ _lt s _M ) and using said second auxiliary signal scr¿ a continuous minimization dimension c is calculated; adding the dimension ca the partial distance of the partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt s _M ) and then it is verified if said sum is greater than the smallest total distance obtained so far ( ec. 15), in which case the partial signal is declared not feasible; and if the sum is less than the smallest distance obtained so far, the partial signal is declared feasible; characterized by:

- after applying the feasibility test and verifying that a partial signal (s¿, s¿ ₊₁ , ···, s _M ) is feasible, since its partial distance is less than the lowest total distance obtained so far, it comprises:

- calculate the first auxiliary signal sc / c¿ = (s ₁ , s ₂ , ---, S _j ^) associated with the partial signal (s¿, s _{i + 1} , ^■ · ^■ , s _M _ _lt s _M ),

- check if the first auxiliary signal sc / c¿ associated with the partial signal (s¿, s¿ ₊₁ , ···, s _M -i, s _M ) has all its components within the box defined by the maximum values and minimum constellation,

- when said verification is checked, the partial signal {s_i, s i + 1), ···, s ^~ _ (M - 1), s _M) is declared feasible;

- when said verification is not verified, it comprises calculating the second auxiliary signal scr ¿associated with the partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt sM, and then calculating the continuous minimization level r and deciding , via the feasibility test, if the partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt s _M ) is feasible or not.

2. METHOD OF SPHERICAL DECODIFICATION OF SIGNS OF COMMUNICATION SYSTEMS OF MULTIPLE INPUTS AND MULTIPLE OUTPUTS (MIMO) OF MAXIMUM VEROSIMILITY, according to claim 1, is characterized in that:

- after checking the feasibility of a partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt s _M ) for an i-th component, with i <M, verifying that its partial distance is less than the shortest total distance obtained so far, and for which the first auxiliary signal sc / c ¿associated with said partial signal has some of its components outside the box defined by the maximum and minimum values of the constellation, so the second auxiliary signal scr¿ associated with the partial signal (s¿, s¿ ₊₁ , ···, s _M _ _lt s _M ) must be calculated, and the continuous minimization dimension c must be calculated, It also includes:

- obtain the initial signal xO for the continuous minimization method with restrictions, such as the first i - 1 components of the second auxiliary signal scr _{i + 1} \ (s _1; s ₂ , ^■■ ·, s¿-i) when at check the feasibility of a predecessor partial signal s _{i + 1} , ···, s _M _ _lt s _M of a partial signal (s¿, ···, s _{M - 1} , s _M ) the second auxiliary signal was calculated scr _{i + 1} = (s _1; s2, ---, ^ / associated with the partial signal if + l, -; sM — 1, sM, and

- obtain the initial signal xO for the continuous minimization method with restrictions, such as the first i-1 components of the first auxiliary signal sck _{i + 1} \ (s ₁ , s ₂ , ···, s¿-i). when, when checking the feasibility of the predecessor partial signal s _{i + 1} , ---, s _M _ _lt s _M the second auxiliary signal scr _{i + 1} was not calculated, and therefore the first auxiliary signal sck _{i + 1} was calculated = (SL, s ₂ , · ^■ ·, yes) associated with the partial signal s _{i + 1} , -, s _M _ ₁ , s _M ).

3. METHOD OF SPHERICAL DECODIFICATION OF SIGNS OF COMMUNICATION SYSTEMS OF MULTIPLE INPUTS AND MULTIPLE OUTPUTS (MIMO) OF MAXIMUM VEROSIMILITY, according to claims 1 and 2, characterized in that:

- the preprocessing step comprises storing the first auxiliary signal sck, and storing the second auxiliary signal being when it has been calculated,

- use the first auxiliary signal sck and the second auxiliary signal be in the possible minimizations that are applied to check the feasibility of partial signals of the form (s _M ) with i = M.

- after checking the feasibility of a partial signal (s _M ) with i = M, which verifies that its partial distance is less than the lowest total distance obtained so far, and for which the first auxiliary signal sck _M associated with said signal partial has some of its components outside the box defined by the maximum and minimum values of the constellation, so the second auxiliary signal scr _M associated with the partial signal (s _M ) and the continuous minimization dimension c have to be calculated ,: ; It also includes:

- obtain the initial signal xO for the continuous minimization method with restrictions, such as the first M - 1 components of being, when the auxiliary signal was calculated in the preprocessing stage, and - obtain the initial signal xO for the minimization method it continues with restrictions, such as the first M - 1 components of sck, when the second auxiliary signal was not calculated in the preprocessing stage and only the first auxiliary sck signal was calculated.