Method for estimating transmitted symbol vector in an overloaded communication channel

Abstract

A computer-implemented method for estimating a transmitted symbol vector transmitted in an overloaded communication channel includes receiving a signal represented by a received signal vector corresponding to a signal superposition representing a transmitted symbol selected from a symbol constellation and transmitted from one or more transmitters. A continuous first function is defined in a search space in a convex domain, the continuous first function being a function of the received signal vector and a channel characteristic, and the continuous first function having a global minimum when the product of an input vector from the search space and a channel matrix is ​​equal to the received signal vector. A continuous second function is defined in the search space, the continuous second function being a function of an input vector from the search space, and the continuous second function having a significantly low value for each transmitted symbol vector of symbols of the constellation. The first function and the second function are combined into a third function, and a fractional programming algorithm is applied to the third function, with the purpose of finding an input vector that minimizes the third function. A mapping rule converts the found input vector into an estimated transmitted symbol vector, and the estimated transmitted symbol vector is output to a decoder for decoding into an estimated transmitted symbol from the constellation.

Description

Technical Field

[0001] The present invention relates to the field of digital communications in overloaded channels. Background Art

[0002] It is estimated that by 2030, more than 100 billion wireless devices will be connected through emerging networks and paradigms such as the Internet of Things (IoT), fifth generation (5G) cellular radio and their successors. This future scenario implies a significant increase in device density and, with it, a surge in resource contention. Therefore, future wireless systems will be characterized by non-orthogonal access with significant resource overload, unlike previous third generation (3G) and fourth generation (4G) systems, where spreading code overload and carrier aggregation (CA) are additional features designed to modestly increase user or channel capacity.

[0003] The expression "resource overload" or "overloaded communication channel" generally refers to a communication channel that is used simultaneously by multiple users or transmitters T, the number of these transmitters N being T Greater than the number N of resources R R At the receiver, the multiple transmitted signals will appear as one superimposed signal. A channel may also be overloaded due to a single transmitter transmitting a superposition of symbols and thereby exceeding the channel resources available in a "traditional" orthogonal transmission scheme. Thus, "overload" occurs compared to a scheme where a single transmitter has exclusive access to the channel, e.g., during a time slot, etc. as found in an orthogonal transmission scheme. For example, overloaded channels may be found in wireless communication systems using non-orthogonal multiple access (NOMA) and underdetermined multiple-input multiple-output (MIMO) channels.

[0004] Figure 1 Figure 2 and Figure 3 respectively show the basic properties of orthogonal multiple access and non-orthogonal multiple access. Figure 1 An exemplary embodiment of orderly access of transmission resources to channels of a shared transmission medium, for example in a wireless communication system, is shown. The available frequency band is divided into a plurality of channels. Any one transmitter may use a single channel or a combination of contiguous or non-contiguous channels at a time. Different transmitters indicated by different hash patterns may transmit in discrete time slots or in multiple subsequent time slots and may change the channel or channel combination they transmit on for each transmission. Note that, as Figure 1 As shown, any transmitter can use one channel resource for a longer period of time, while another transmitter can use two or more channel resources at the same time, and another transmitter can take both into account, that is, use two or more channel resources for a longer period of time. In any case, only one transmitter uses any channel resource or combination thereof at a time, and it is relatively easy to detect and decode the signals from each transmitter.

[0005] Figure 2aShown with Figure 1 The same frequency band shown, but there may not always be a temporary exclusive allocation of one or more individual channels to the transmitter. Instead, at least a portion of the frequency band may be used by multiple transmitters simultaneously, and it is much more difficult to detect and decode the signal from a single transmitter. Similarly, different hash patterns indicate different transmitters, and the circled portion indicates the situation where two or more transmitters use the resource at the same time. However, starting from the left, initially three transmitters use the temporary dedicated channel resources in an orthogonal manner, and the next moment two transmitters transmit in partially overlapping channels. The transmitter represented by the horizontal hash pattern has exclusive access to the channel shown at the bottom of the figure, and the next three channels used by the transmitter are also used by another transmitter, represented by the diagonal hash pattern in the dashed ellipse. Superposition is indicated by the diagonally crossed hash pattern. A similar situation occurs at a later moment, where each of the two transmitters uses two channel resources exclusively, while the two share the third channel resource. It should be noted that more than two transmitters can at least temporarily share some or all of the channel resources used by each of them. These situations can be referred to as partial overload or partial NOMA.

[0006] In different representations, Figure 2b Shown with Figure 2a Same frequency band. The difficulty of detecting and decoding signals from individual transmitters is illustrated by a grey fill pattern that does not allow identification of any single transmitter, since there is no clear temporary exclusive allocation of one or more individual channels to one transmitter and at least a portion of the frequency band is used simultaneously by multiple transmitters at least temporarily. In other words, all transmitters use all channels.

[0007] Signals from some transmitters may be transmitted using higher power than others, and may therefore be received with higher signal amplitudes, but this may depend on the distance between the transmitter and receiver. Figure 2a and Figure 2b It can help to understand the situation that exists in non-orthogonal multiple access environment.

[0008] One of the main challenges of such overloaded systems is the detection at the receiver, since the bit error rate (BER) performance of well-known linear detection methods such as zero forcing (ZF) and minimum mean square error (MMSE) is much lower than the bit error rate performance of maximum likelihood (ML) detection, which is the first choice for detecting signals in overloaded communication channels. The ML detection method determines for each transmitter the Euclidian distance between the received signal vector and the signal vector corresponding to each symbol from a predetermined set of symbols that may have been transmitted, allowing the estimation of the transmitted symbols under such challenging conditions. The symbol whose vector has the smallest distance to the received signal vector is selected as the estimated transmitted symbol. However, it is obvious that ML detection does not scale well with larger symbol sets and larger numbers of transmitters, since the number of calculations that need to be performed for large sets in the discrete domain increases exponentially.

[0009] To avoid this problem, several signal detection methods based on sphere decoding have been proposed in the past, for example, C. Qian, J. Wu, Y. R. Zheng, and Z. Wang, “Two-stage list sphere decoding for under-determined multiple-input multiple-output systems,” IEEE Transactions on Wireless Communication, vol. 12, no. 12, pp. 6476-6487, 2013 and R. Hayakawa, K. Hayashi, and M. Kaneko, “An overloaded MIMO signal detection scheme with slab decoding and lattice reduction,” Proceedings APCC, Kyoto, Japan, Oct. 2015, pp. 1-5 [Overloaded MIMO signal detection scheme using plate decoding and lattice basis reduction, "APCC Conference Proceedings", Kyoto, Japan, October 2015, pp. 1-5], which demonstrates its ability to asymptotically reach ML detection performance with lower complexity. However, the complexity of the known methods grows exponentially with the size of the transmitted signal dimension (i.e., the number of users), thus hindering its application in large-scale systems.

[0010] R.Hayakawa and K.Hayashi in “Convex optimization-based signal detection for massive overloaded MIMO systems,” IEEE Transactions on Wireless Communication, vol.16, no.11, pp.7080-7091, Nov.2017 proposed a low-complexity signal detector for massive overloaded MIMO systems that addresses the scalability issues of previous solutions. This low-complexity signal detector is called the Sum of Absolute Values ​​(SOAV) receiver, which relies on a combination of two different methods: a) by A. -El-Bey, D.Pastor, SMA and Y. Fadlallah in “Sparsity-based recovery of finite alphabet solutions of underdetermined linear system,” IEEE Transactions on Information Theory, vol. 61, no. 4, pp. 2008-2018, 2015 and b) regularization-based methods proposed by PL Combettes and J.-C. Pesquet in “Proximal splitting methods in signal processing,” Fixed-point algorithms for inverse problems in science and engineering, pp. 185-212, 2011.

[0011] Although the SOAV decoder is found to outperform other state-of-the-art schemes in terms of superior BER performance with significantly lower complexity, a shortcoming of SOAV is that the l0-norm regularization function adopted to capture the discreteness of the input signal is replaced by the l1-norm approximation, leaving the possibility of further improvement.

[0012] It is therefore an object of the present invention to provide an improved method for estimating a transmitted symbol vector, in particular in an overloaded communication channel. Summary of the invention

[0013] The inventors recognize that since the symbols used in digital communications are ultimately transmitted as analog signals in the analog domain (i.e., the continuous domain), and attenuation, intermodulation, distortion, and various errors inevitably modify the signal from the transmitter through the analog communication channel to the receiver, the "detection" of the transmitted symbols in the receiver is still first of all an "estimation" of the transmitted signal, which is independent of the method used, and because the signal is represented by the signal amplitude and the signal phase in most cases (if not all cases), it is specifically an estimation of the vector of the transmitted signal. However, in the context of this specification, the terms "detection" and "estimation" are used interchangeably unless the corresponding context indicates the difference between them. Once the vector of the estimated transmitted signal is determined, it is converted into an estimated transmitted symbol and ultimately provided to a decoder, which maps the estimated transmitted symbol to the transmitted data.

[0014] In the context of this specification and claims, a communication channel is characterized by a set or matrix of complex coefficients. A channel matrix may also be represented by a capital letter H. A communication channel may be established in any suitable medium, for example, a medium that carries electromagnetic waves, sound waves, and / or light waves. It is assumed that the channel properties are completely known and constant during each symbol transmission, i.e., although the channel properties may vary over time, each symbol transmission experiences a constant channel.

[0015] The expression "symbol" refers to a set of discrete symbols c i These discrete symbols form a symbol constellation C, or more generally, an alphabet for composing a transmission. A symbol represents one or more data bits and represents the minimum amount of information that can be transmitted at a time in a system using constellation C. In a transmission channel, a symbol can be represented by a combination of analog states (e.g., the amplitude and phase of a carrier). Amplitude and phase can, for example, be referred to as complex numbers or ordinate values ​​on the abscissa in a Cartesian space and can be viewed as vectors. A vector whose elements are symbols taken from C is represented herein by the lowercase letter s. Each transmitter can use the same constellation C to transmit data. However, the transmitter can also use different constellations. It is assumed that the receiver knows the constellation used in the corresponding transmitter.

[0016] A convex domain is a domain where any two points can be connected by a straight line that lies entirely within the domain, i.e. any point on the straight line is a point in the convex domain. A convex domain can have any dimension, and the inventors recognize that the concept of a straight line may be difficult to visualize in domains of 4 or more dimensions.

[0017] Throughout the following description, the terms "component" or "element" may be used synonymously, especially when referring to vectors.

[0018] As mentioned before, one of the constraints in a typical ML detection scheme is that the symbol c of the constellation C i This prevents the use of, for example, known efficient fractional programming (FP) algorithms to find the signal vector, and hence the symbol with the minimum distance to the vector of the received signal. The strong interest is usually expressed by performing separate calculations on the symbols of the constellation C in the equations describing the detection. Some schemes attempt to enable FP algorithms to estimate the most likely transmitted symbols and replace the separate calculations on the symbols by describing the discreteness of the constellation C with an l1 norm, which is continuous and can therefore be passed through the FP algorithm to find the minimum. However, using the l1 norm introduces a large amount of estimation error, which is generally undesirable.

[0019] The detection scheme of the overloaded system of the method presented in this paper does not rely on a loose relaxation of the l0 norm by means of the l1 norm. Instead, in the method of the present invention, a function f2 is adopted as a tight l0 norm approximation, which allows to optimize non-convex fractional objectives with an efficient and robust FP framework, which has low computational requirements and has been shown to outperform SOAV through simulations.

[0020] In the following, the theoretical basis of the detection scheme of the present invention will be explained with reference to an exemplary underdetermined wireless system having N T transmitters and N R <N T receiving resources, so that the system overload ratio is γ≡NT / N R Given, and following the well-known signal realization, the received signal can be modeled as

[0021] y=Hs+n, (1)

[0023] in,

[0024] is the transmitted symbol vector, where each element is from base 2 b The constellation set C is sampled, where b represents the number of bits per symbol, is a matrix with zero mean and covariance The cyclically symmetric additive white Gaussian noise (AWGN) vector is The flat fading channel matrix between the transmitter and the receiver side is described.

[0025] In traditional detectors, maximum likelihood (ML) detection can be used to estimate the transmitted signal vector s of the received signal y. ML ML detection requires determining the received signal vector y and the symbol c of the constellation C i The distance between each symbol vector s. The number of calculations increases with the number of transmitters T N T Increase exponentially.

[0026] The discreteness of the target set of the ML function prevents the use of efficient FP algorithms to estimate the transmitted signal vector of the received signal y These algorithms are known to be effective for finding the minimum in functions with continuous inputs.

[0027] According to the present invention, the discrete target set of ML functions is first converted into sufficiently similar continuous functions that can be solved by the FP algorithm.

[0028] To this end, an alternative representation of the discrete ML function

[0029]

[0030] satisfy

[0031]

[0032] It is first transformed into a penalized mixed l0-l2 minimization problem, which maintains ML-like performance for the following approximation constraints:

[0033]

[0034] Where w and λ are weight parameters. Symbol indicates that as long as the weights w and λ are properly optimized, the approximation is still possible to achieve performance close to ML. T is the number of transmitters and can also be expressed as N T express.

[0035] In order to solve the intractable non-convexity problem of the l0 norm without resorting to the l1 norm, the l0 norm is replaced by an asymptotically compact expression:

[0036]

[0037] Here, x is an arbitrary sparse vector of length T.

[0038] Then, the l0 norm in the penalized mixed l0-l2 minimization problem is replaced by a close approximation of the l0 norm, and the constraint |s j -c i |≤t ij The slack variable t ij , thus generating

[0039]

[0040] Satisfaction|s j -c i |≤t ij .

[0041] (5b)

[0042] Among them, now α<<1.

[0043] Since the ratio in equation (5a) Due to the concave-on-convex structure due to the convex non-negative numerator (nominator) and the concave (linear) positive denominator, the conditions required for the convergence of the quadratic transform (QT) are satisfied, as known from the following literature: K. Shen and W. Yu, "Fractional programming for communication systems-Part I: Power control and beamforming," IEEE Trans. Signal Process., vol. 66, no. 10, pp. 2616-2630, May 2018, so that equation (5a) can be reformulated as the following convex problem:

[0044]

[0045] Satisfaction|s j -c i |≤t ij .

[0046] (6b)

[0047] in,

[0048] Because β ij The convergence of the equation can be achieved by iteratively updating β ij and solve for a given β ij The equations of are solved by means of FP. The equations obtained by converting the initial non-convex optimization problem into a convex optimization problem can be efficiently solved using known algorithms such as the augmented Lagrangian method.

[0049] Therefore, according to the present invention, it is estimated that the transmitted symbol vector transmitted in an overloaded communication channel characterized by a complex coefficient channel matrix H The computer-implemented method of includes receiving a signal represented by a received signal vector y in a receiver R. The received signal vector y corresponds to a symbol c selected from one or more transmitters T. i The signal of the transmitted symbol vector s of the constellation C is superimposed, plus any distortion and noise added by the channel.

[0050] In case of more than one transmitter, the transmitters T are synchronized in time, i.e. a common time base is assumed between the transmitters T and the receiver R, so that the receiver R receives symbol transmissions from different transmitters T substantially simultaneously, e.g. within a predetermined time window. Assuming that the transmitter T transmits a series of symbols one after another, receiving a symbol simultaneously or within a predetermined time window means that all time synchronized transmitted symbols are received at the receiver R before receiving a subsequent symbol. This may include an arrangement in which the transmitter T adjusts its transmission start time such that a propagation delay that depends on the distance between the transmitter T and the receiver R is compensated. This may also include providing a time gap between the transmission of subsequent symbols.

[0051] The method further comprises defining a convex search space comprising at least the components of the received signal vector y and all symbols c of the constellation C i Components of the transmitted symbol vector s. Further, a continuous first function f1 and a continuous second function f2 are defined in the search space. In this context, the definition may include selecting factors or variable ranges for or in other predetermined functions.

[0052] The continuous first function f1 is a function of the received signal vector y and the channel characteristic H and has a global minimum when the product of the input vector s from the search space and the channel matrix H is equal to the received signal vector y.

[0053] The continuous second function f2 is a function of the input vector s from the search space and for the symbol c of the constellation C i Each transmitted symbol vector s has a significantly low value.

[0054] According to the present invention, the first function f1 and the second function f2 are combined into a third function f3 by weighted summation, and the fractional programming algorithm FP is applied to the third function f3, with the aim of finding an input vector that minimizes the third function f3. in other words, is the optimal solution or result of applying the FP algorithm to the third function f3, where the third function f3 has a minimum value.

[0055] Once the input vector that minimizes the third function f3 is found The mapping rule is applied to it, which transforms the input vector Converted into an estimated emission vector where the index "C" indicates that each component belongs to the constellation C. In other words, if the vector has two components A and B, then the input vector that minimizes the third function f3 is Each of the components A and B of can have any value in the search space. These values ​​are converted into an estimated transmit vector The values ​​A' and B' for symbol c of constellation C i , each value can only have a value that appears in any one of the transmitted symbol vectors s. These components can be selected, for example, by selecting the symbol c of the constellation C. i The closest value of the corresponding component of any transmit symbol vector in the transmit symbol vector s is mapped respectively.

[0056] After mapping, the estimated transmitted symbol vector is output to a decoder to obtain the data bits of the transmitted message.

[0057] In one or more embodiments, the second function f2 has an adjustable factor that determines the gradient of the function near a significantly low value at each vector of symbols of the constellation. The adjustable factor can help the FP algorithm converge faster and / or skip local minima that may be far from the optimal solution or at least a better solution.

[0058] In some embodiments, the adjustable factor may be different for different symbols of the constellation. For example, the gradient near the vector of the symbol far from the global minimum of the first function f1 may be very steep, but may only be very close to a significantly low value. Depending on the FP algorithm and the starting value used, this can help skip local minima located at a greater distance from the global minimum of the first function f1. On the other hand, the gradient near the vector of the symbol close to the global minimum of the first function f1 may be quite shallow at a certain distance to the significantly low value, and becomes steeper as the distance decreases. Depending on the FP algorithm used, this can help the function converge quickly to a significantly low value.

[0059] In some embodiments, the first function f1 is monotonically increasing starting from a global minimum. The first function can be considered as a rough guiding function of the FP algorithm, which helps the FP algorithm converge. Therefore, it is advantageous if the first function itself does not have any local minima.

[0060] The receiver of the communication system has a processor, volatile and / or non-volatile memory, and at least one interface suitable for receiving signals in a communication channel. The non-volatile memory can store computer program instructions, which configure the receiver to implement one or more embodiments of the method according to the present invention when executed by a microprocessor. The volatile memory can store parameters and other data during operation. The processor can be referred to as one of the following: a controller, a microcontroller, a microprocessor, a microcomputer, etc. And the processor can be implemented using hardware, firmware, software and / or any combination thereof. When implemented by hardware, the processor can be provided with a device configured to implement the present invention, such as an ASIC (application specific integrated circuit), a DSP (digital signal processor), a DSPD (digital signal processing device), a PLD (programmable logic device), an FPGA (field programmable gate array), etc.

[0061] Meanwhile, in the case of implementing the embodiments of the present invention using firmware or software, the firmware or software may be configured to include modules, programs and / or functions for performing the functions or operations explained above of the present invention. Furthermore, the firmware or software configured to implement the present invention is loaded into a processor or stored in a memory to be driven by the processor.

[0062] The present method solves the difficulty of applying an efficient FP algorithm to estimate candidates for a transmitted symbol vector caused by the discrete nature of a constellation by transforming the discrete constraints present in known ML methods for determining the Euclidean distance between a vector of a received signal and a symbol vector of a constellation into a first function in a convex domain that exhibits a significantly low value for the symbol vector of the constellation. The minimum of the function in the convex domain can be found by applying known FP methods or algorithms that are more efficient than brute force calculations for finding a good estimate of the transmitted signal vector. A second continuous function in the convex domain is added to the first function that penalizes the estimation result as the distance from the received signal vector increases.

[0063] Although the invention has been described above for detecting superimposed signals from transmitters all using the same constellation C, the invention is also applicable to different transmitters using different constellations C. T , i.e. if the symbols of the constellation C are considered to be letters of an alphabet, each transmitter can use a different alphabet. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The invention will be further explained with reference to the accompanying drawings, in which:

[0065] Figure 1 shows a simplified schematic representation of orthogonal multiple access to a shared medium,

[0066] FIG. 2 shows a simplified schematic representation of non-orthogonal access to a shared medium,

[0067] Figure 3 An exemplary general block diagram of a transmitter and a receiver communicating over a communication channel is shown,

[0068] Figure 4 An exemplary flow chart showing method steps for implementing an embodiment of the present invention is shown,

[0069] Figure 5 The details of the method steps of the present invention are shown,

[0070] Figure 6 shows an exemplary and basic example of a constellation, a transmitted signal, and a received signal, and

[0071] Figure 7 A simplified exemplary graphical representation of a third function determined in accordance with the present invention is shown, which third function can be efficiently solved using fractional programming.

[0072] In the drawings, the same or similar elements may be referred to by the same reference numerals. DETAILED DESCRIPTION

[0073] As discussed further above Figure 1 and Figure 2, and will not be repeated here.

[0074] Figure 3 An exemplary general block diagram of a transmitter T and a receiver R communicating over a communication channel 208 is shown. The transmitter T may include, among other things, a source of digital data 202 to be transmitted. The source 202 provides bits of digital data to an encoder 204, which forwards the data bits encoded into symbols to a modulator 206. The modulator 206 transmits the modulated data into the communication channel 208, for example, via one or more antennas or any other type of signal transmitter (not shown). For example, the modulation may be quadrature amplitude modulation (QAM), in which the symbols to be transmitted are represented by the amplitude and phase of the transmitted signal.

[0075] Channel 208 may be a wireless channel. However, the general block diagram is valid for any type of wired or wireless channel. In the context of the present invention, the medium is a shared medium, i.e., multiple transmitters and receivers access the same medium, and more specifically, the channel is shared by multiple transmitters and receivers.

[0076] The receiver R receives a signal through a communication channel 208, for example, via one or more antennas or any other type of signal receiver (not shown). The communication channel 208 may have introduced noise into the transmitted signal, and the amplitude and phase of the signal may have been distorted by the channel. The distortion can be compensated by an equalizer (not shown) provided in the receiver, which is controlled based on channel characteristics, which can be obtained, for example, by analyzing pilot symbols with known properties transmitted on the communication channel. Similarly, noise can be reduced or eliminated by a filter (not shown) in the receiver. The signal detector 210 receives a signal from the channel and attempts to estimate which signal has been transmitted into the channel from the received signal. The signal detector 210 forwards the estimated signal to a decoder 212, which decodes the estimated signal into an estimated symbol. If the decoding produces a symbol that may have been transmitted, the symbol is forwarded to a demapper 214, which outputs a bit estimate corresponding to the estimated transmitted signal and the corresponding estimated symbol, for example, to a microprocessor 216 for further processing. Otherwise, if the decoding does not produce a symbol that may have been transmitted, the unsuccessful attempt to decode the estimated signal into a possible symbol is fed back to the signal detector to repeat the signal estimation with different parameters.The data processing in the modulator of the transmitter and the data processing in the demodulator of the receiver are complementary.

[0077] Although Figure 3 The transmitter T and the receiver R of FIG. 1 appear to be well known, but the receiver R, more particularly the signal detector 210 and the decoder 212 of the receiver according to the present invention, are adapted to perform the following with reference to Figure 4 The method of the present invention is described and therefore works differently from known signal detectors.

[0078] Figure 4 An exemplary flow chart of method steps for implementing an embodiment of the present invention is shown. In step 102, a signal is received in an overloaded communication channel. The signal and the representation selected from the symbol c i The constellation C corresponds to the signal superposition of the transmitted symbols transmitted from one or more transmitters T. In step 104, a search space is defined in a convex domain, which includes at least the components of the received signal vector y and all symbols c of the constellation C. i Components of the transmitted symbol vector s. In step 106, a continuous first function f1 is defined, which is a function of the received signal vector y and the channel characteristic H. The first function f1 has a global minimum when the product of the input vector s from the search space and the channel matrix H is equal to the received signal vector y. Further, in step 108, a continuous second function f2 is defined in the search space, which is a function of the input vector s from the search space. For the symbol c of the constellation C iFor each transmitted symbol vector s, the second function f2 has a significantly low value. Note that steps 104, 106 and 108 do not need to be performed in the order shown in the figure, but can also be performed more or less simultaneously or in a different order. In step 110, the first function f1 and the second function f2 are combined into a third continuous function f3 by weighted summation. In step 112, once the third function f3 is determined, a fractional programming algorithm is applied to it, with the aim of finding the input vector that minimizes the third function f3. In step 114, the input vector φ is the result of the fractional programming algorithm. is converted into an estimated emission vector where each component has a symbol c from constellation C i The conversion may include selecting the value from the list that is closest to the estimated value. Then, in step 116, the estimated transmit vector is output to the decoder for decoding into the estimated transmitted symbol from constellation C In step 118, the transmitted symbol Can be further processed into one or more bits of transmitted data.

[0079] Figure 5 shows details of the method steps of the present invention which are performed to find an input vector which minimizes a third function f3, specifically the function according to equation 6 described further above. In step 112-1, the estimated transmitted signal vector The starting value of is used to initialize the fractional programming, and in step 112-2 for the estimated transmit vector The starting value of β is determined ij Then, in step 112-3, by solving the value β determined in step 112-2 ij The equation is used to obtain If the solution does not converge (the "No" branch of step 112-4), then based on the new candidate obtained in step 112-3 To determine the value of β ij , and repeat the equation solving process. If the solution converges (the "yes" branch of step 112-4), then Forwarded to Figure 4 Step 114, to map the estimated emission vector Its components adopt the symbol c from the constellation C i The vector s of values.

[0080] Figure 6a) shows an illustrative example and a very basic example of symbols c1 , c2, c3 and c4 from constellation C. Symbols c1 , c2, c3 and c4 may represent symbols of a QAM modulation. Figure 6 b) shows the symbol actually transmitted on the channel, in this case symbol c2. Figure 6 c) shows the actual received signal at the receiver. Due to some distortion and noise in the channel, the received signal is not exactly at the amplitude and phase of the transmitted symbol c2. The maximum likelihood detector determines the distance between the received signal and each symbol from the constellation and selects the symbol that is closest to the received signal as the estimated symbol. In a very simple example, this symbol would be symbol c2. This process requires calculations to be performed for all discrete received signal and symbol pairs from the constellation and can result in a large number of calculations that increase exponentially with the number of symbols in the constellation and the number of transmitters that may be transmitting the signal.

[0081] Figure 7 A simplified exemplary graphical representation of a third function determined according to the present invention is shown, which can be efficiently solved using fractional programming. The graphical representation is based on Figure 6 a) presents the same constellation, and assumes that the same signal c2 is transmitted. The bottom surface of the three-dimensional space represents a convex search space for the amplitude and phase of the signal vector. The vertical dimension represents the value of the third function. Because the search space is convex, the third function has values ​​for any combination of amplitude and phase, even if there are actually only four discrete symbols c1, c2, c3 and c4 in the constellation. The surface with an inverted cone shape represents the result of a continuous first function on the convex search space, and has a global minimum at the location of the received signal. The four peaks protruding downward from the conical surface represent a continuous second function, which has significantly low values ​​at the phase and amplitude of the symbols from the constellation. The first function and the second function have been combined into a third function, which is still continuous and can now be subjected to a fractional programming algorithm to find the amplitude and phase that minimizes the third function. Remember that this representation is very simplified, but it is believed to help understand the present invention.

Claims

1. A computer-implemented method (100) for estimating a transmit symbol vector transmitted in an overloaded communication channel characterized by a complex coefficient channel matrix, the method comprising: - receiving (102) in a receiver (R) a signal represented by a received signal vector corresponding to a superposition of signals representing transmitted symbols selected from at least one symbol constellation and transmitted from one or more transmitters (T), - defining (104) a search space in a convex domain, the search space comprising at least components of the received signal vector and components of the transmitted symbol vector for all symbols of the at least one constellation, - defining (106) a continuous first function, the continuous first function being a function of the received signal vector and a channel characteristic, the first function having a global minimum when the product of an input vector from the search space and the channel matrix is ​​equal to the received signal vector, - defining (108) a continuous second function in the search space, the continuous second function being a function of an input vector from the search space, the second function having a significantly low value for each transmitted symbol vector of symbols of the at least one constellation, - combining (110) the first function and the second function into a third function by weighted summation, - applying (112) a fractional programming algorithm to the third function with the aim of finding an input vector that minimizes the third function, - applying (114) a mapping rule that converts the input vector into an estimated transmit vector, wherein each component has a value from a list of possible values ​​of the corresponding component of the transmit symbol vector of symbols of the at least one constellation, and - outputting (116) the estimated transmitted symbol vector to a decoder for decoding into estimated transmitted symbols from the at least one constellation, The overloaded communication channel refers to a communication channel used by multiple users or transmitters (T), and the number of users or transmitters (T) is N. T Greater than the number N of resources R R , and the continuous first function is a function of the received signal vector and the channel characteristics and has a global minimum when the product of the input vector from the search space and the channel matrix is ​​equal to the received signal vector, and the continuous second function is a function of the input vector from the search space and has a significantly low value for each transmitted symbol vector of the symbols of the constellation.

2. The method of claim 1, wherein: The second function has an adjustable factor that determines the gradient of the function around the significantly low value at each vector of symbols of the at least one constellation.

3. The method of claim 2, wherein: The adjustable factor is different for different symbols of the at least one constellation.

4. A method as claimed in any one of the preceding claims, wherein: Applying the fractional programming algorithm includes: - providing an initial estimated transmitted symbol vector, the distance of the initial estimated transmitted symbol vector from the vector of the received signal y being at least greater than the minimum distance between vectors of adjacent symbols from the at least one constellation, or - Provide a zero vector as the initial transmit symbol vector.

5. The method of claim 1, wherein: The first function increases monotonically starting from the global minimum.

6. The method of claim 1, wherein: The goal of the fractional programming algorithm is to find a value of the third function that is lower than the global minimum of the first function.

7. The method of claim 1, wherein: The first function is a Euclidean distance function centered on the vector of the received signal.

8. The method of claim 1, wherein: The second function is a function based on or closely approximating the l0 norm.

9. A receiver (R) of a communication system, the receiver having a processor, a volatile and / or non-volatile memory, at least one interface adapted to receive signals in a communication channel (208), wherein: The non-volatile memory stores computer program instructions which, when executed by the microprocessor, configure the receiver to implement the method as claimed in one or more of claims 1 to 8 .

10. A computer program product comprising computer executable instructions which, when executed on a computer, cause the computer to perform the method of any one of claims 1 to 8.

11. A computer-readable medium storing and / or transmitting the computer program product according to claim 10.

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