GB2576178A - Non-orthogonal spreading sequence design for multi user shared channel - Google Patents

Abstract

The invention creates pools of spreading sequences for use in non-orthogonal multiple access (NOMA) systems. A base set of, preferably orthogonal, complex spreading sequence vectors is created 204. From these a set of hyperplanes is created 206, preferably each hyperplane is created from a pair of base set vectors. Non-orthogonal sequence vectors are created in the hyperplanes 208, preferably as linear combinations of the base vectors defining the hyperplane. Vector cross correlation amongst the pool is determined and used as a measure of the quality of the sequence pool 210. This may be determined using dot products.

Description

Technical Field [1] The following disclosure relates to Non-Orthogonal Multi-Access (NOMA) schemes supporting diverse services and applications in future 5G networks. The following disclosure relates, in particular, to NOMA support of grant-free transmission and of massive machine type communication (mMTC) scenarios where massive number of users are to use a limited amount of resources. In addition to NOMA support for grant free transmission of ultra-reliable low latency communication (URLLC) where latency is very important thus not necessarily have time for grantbased transmission.

Background [2] Non-orthogonal Multiple Access (NOMA) is a technology that is being developed part of the 5G wireless communications. It stems from both the increasing demand of mobile Internet as well as the Internet of Things (loT) challenging communication tasks, along with the demand for high spectral efficiency, massive connectivity, and expected increase in system throughput, and the demand for ultra-reliable transmission with very low delay.

[3] NOMA recently gained wide interest, prompting Rel-13 Study Item on downlink multi-user superposition transmission (MUST) and initial study in Rel-14 Study Item on New Radio (NR). NOMA allows multiple users to share time and frequency resources in the same spatial layer via power domain or by code domain multiplexing. NOMA claims to accommodate more users via non-orthogonal resource allocation as compared to orthogonal multiple access (OMA).

[4] In Rel. 14 NR SI, a large number of NOMA schemes were proposed and captured in 3GPP TR38.802, mainly targeting grant-free transmission for mMTC scenario. Many nonorthogonal multiple-access schemes are continually being evaluated since the Rel-14 NR study item. Evaluation results show significant benefit of non-orthogonal multiple access in terms of UL link-level:

• Sum throughput • Overloading capability • System capacity enhancement • Improved packet arrival rate at given system outage [5] The Rel-14 Study Item concluded that NR should at least target UL non-orthogonal multiple access for mMTC.

[6] The SI objectives are to study a generic NOMA scheme which can provide benefit in various aspects for scenarios like mMTC, URLLC, eMBB small packet, 2-step RACH. Therefore, more comprehensive performance evaluations were to be done to fully understand the pros and cons of different NOMA schemes.

[7] A general (high-level) block diagram for a multi-user receiver is shown in Figure 1.

[8] Uplink NOMA is promoting grant free transmission to save on signaling overhead and transmission latency, thereby reducing power consumption of devices. Signature codes, such as random spreading codes, support grant-free access. Further options for improvements and optimizations include mMTC performance metrics, URLLC baseline for performance comparison of UL transmission, and eMBB, performance metrics.

[9] Uplink NOMA schemes and categorizations thereof have been proposed and features such as long-sequence, short-sequence, bit-level, symbol-level, sparse, non-sparse, coding, spreading, and interleaving have been discussed. All NOMA features are based on spreading signals onto a larger and shared resource grid in bit and symbol level, in frequency, time, and code domain. Bit and symbol level signal processing such as spreading, repetition, scrambling, sparse resource mapping, and FEC coding are often used in NOMA.

[10] A classification of NOMA features in two categories, namely bit and symbol, is shown in Figure 2. Further details of Figure 2 are set out below • Low Density Signature (LDS), originating from synchronous Code Division Multiple Access (CDMA), • Pattern Division Multiple Access (PDMA) is one feature applying LDS by sparse Resource Element (RE) mapping, • SCMA, IGMA, constellation codebook, bit level interleaving, and symbol level signal transform matrix are applied to form distinct signatures, • Low density spreading with signature vector extension (LDS SEV), • NCMA and NCOA are based on sparse type of RE mapping, • RSMA, RDMA, and GOCA directly apply symbol-based spreading sequence; the difference between them lies in the spreading sequence applied.

[11] Further, low code-rate spreading (LCRS) implies using FEC. LSSA and IDMA set LCRS as the keynote, applying bit level spreading and symbol level repetition code.

[12] Proposed for using spreading sequences as NOMA UE’s signature are Sparse code multiple access (SCMA), Resource spread multiple access (RSMA), and Multi-User Shared access (MUSA).

[13] Other NOMA schemes are interleave-grid multiple access (IGMA), pattern division multiple access (PDMA), low code rate and signature based shared access (LSSA; which also applies bit spreading), repetition division multiple access (RDMA), and group orthogonal coded access (GOCA).

[14] “Uplink Multiple Access Schemes for 5G: A Survey”, published online June 23, 2017, classifies these schemes by UE’s signature design. The schemes are grouped into three classifying categories:

Category 1 (scrambling-based)	Category 2 (interlea ving-based)	Category 3 (spreading-based)
Uses different scrambling sequences to distinguish different UEs	Uses different interleavers to distinguish different UEs	Uses different codes to distinguish different UEs
Can be used together with low code rate FEC	Can be used together with low code rate FEC	LDS code	Non-LDS code
NOMA	IMDA	SCMA	MUSA
RMSA	IGMA	PDMA	NOCA
LSSA		LDS-SVE	NCMA
			LCRS

[15] The present disclosure is given in particular reference to category 3, spreading-based NOMA schemes. It shall serve as an enabling technique for Multi-User Multiple Access (MUSA).

Some methods in category 3, distinguishing UE’s by code, are described here for the sake of completeness:

[16] Sparse Code Multiple Access (SCMA) distinguishes UE’s by code from a pre-designed multi-dimensional codebook. Incoming data streams are directly mapped to code words taken from Code Books for each layer.

[17] Multi-User Shared access (MUSA) is a non-orthogonal multiple access scheme operating in the code domain. Each user’s modulated data symbols are spread by a specially designed sequence. Detection is done by successive interference cancellation (SIC) implementation. Each user’s spread symbols are transmitted on the same radio resource by means of ‘shared access’. The spreading sequences should have low cross-correlation and can be non-binary. Decoding of each user’s data from superimposed signal can be performed at base-station side using SIC technology. Figure 3 shows an example of MUSA with resources shared by multiple users, where each user is using a spreading code of Spreading Factor (SF), SF=4.

[18] Symbols of each user are spread by a spreading sequence, as described in figure 3. Multiple spreading sequences constitute a pool of pre-generated sequences from which each user can randomly pick one thereby improving the performance via interference averaging. Spread symbols are transmitted over the same time-frequency resources. The spreading sequences should have low cross-correlation and can be non-binary. At the receiver, SIC is used to separate in the code-word level data from different users. MUSA is proposed also for loT aiming at Grant-free access strategy. MUSA handles massive number of users. The method assumes an SIC or Maximum Likelihood (ML) detector. It eliminates the need for control message overhead. To reduce the complexity of the SIC receiver implementation, a simple downlink synchronization could be performed.

[19] Figure 1 shows the MUSA Transmitter and Receiver structure of the multiple access structure to support Multi-User transmission with K simultaneous users in order to identify placement of spreading code in the Transmitter / Receiver structure. On the transmitter side, the data bits d_k of user k are encoded by an encoder with code rate R, generating the coded bits ck = [c/c(l), c/c(2), ..., c/c(/V)], where N is the length of the coded bits ck. Then ck’s are modulated by a modulator, for example, a x-QAM Modulator, where x is the size of quadrature amplitude modulation (QAM) constellation. As an example, x = 4 for x-QAM, quadrature phase shift keying (QPSK) is producing the modulated symbols mk = |m/c(l), ..., ^mk(.^N/i_Og2(%))] [20] The spreading with a complex spreading sequence (code) (see blocks “Complex spreading” in figure 4), is done with a code sk of short length L and is carried out to get the spread symbols as follows: tk , where tk are the transmitted spread symbols.

[21] Other NOMA spread sequence schemes include the following.

[22] For Welch bound equality spread multiple access (WSMA), the spreading sequences are based on the Welch bound equality (WBE). WBE is a design metric, for the signature vectors is the total squared cross-correlation T_c = Σ_ί;· |s/s₇j . Lower bound on the total squared crosscorrelation of any set of K vectors of length N, is K²/N < T_c. WBE bound on the total squared cross-correlations of the vector set with B_Weich = . p- In Multi-layer Generation of Spreading

Code for multi-layer transmission with M >2, there are multiple ways in generating the spreading codes, namely layer-specific or UE-specific WBE sequences.

[23] Non-orthogonal Coded Multiple Access (NCMA) using “Grassmannian Sequences” is a multiple access (MA) scheme based on the resource spreading by using non-orthogonal codewords composed of the codewords obtained by Grassmannian line packing problem, where there is a lower bound and upper bound of the cross correlation between codeword pairs.

[24] Non-Orthogonal Coded Access (NOCA) using LTE-defined low correlation sequences taken as the baseline for spreading based non-orthogonal multiple access.

[25] Known NOMA schemes may exhibit one or more of the following properties.

[26] Typically, Multi User Interference (MUI) between the non-orthogonal sequences is relatively high, thus having an impact on the usable bandwidth and/or throughput. Further, it is typically not possible to generate a flexible size non-orthogonal sequence pools data-base and it is typically not possible to generate gradually graded non-orthogonal sequence pools to be stored in a data base, thereby giving the gNodeB a cell design tool for different traffic levels.

[27] Therefore, there exists a need for flexible spread pool generation and for a traffic management tool.

[28] The present disclosure provides, over the known prior art at least two distinct advantages by flexible spreading sequence generation and by flexible traffic management tool provision.

[29] Flexible spread pool generation is based on orthogonal base code set where crosscorrelation is zero such as in ‘CDMA-like’ direct spread, guaranteeing zero MUI caused by spreading sequence.

[30] Further, larger pools are generated as an extension to the orthogonal base set by way of gradual MUI degradation. Pools are designed in a graded fashion where the smallest size is purely orthogonal and as pool size grows by design demand so is MUI worsening gradually.

[31] With respect to the traffic management tool, the spreading sequence pools size can be used upon need as a code cover for expected traffic load. Pool size could be matched with expected uplink traffic by gNodeB or operators, thereby providing an improved tool for traffic management.

[32] Traffic volume overload can be controlled by choosing a “best match” to the nonorthogonal spreading pool of choice by sequences parameters, such as pool size and pool quality figure.

[33] “Flexible codebook design for limited feedback downlink systems via smooth optimization on the Grassmannian manifold”, Ahmed Medra and Timothy N. Davidson IEEE Transaction Vol. 62 No. 5 2014, describe a flexible approach to the design of Grassmannian codebooks based on smooth optimization algorithms for the Grassmannian manifold. This stems from the problem of Packing Lines, Planes in Grassmannian Spaces (see “Packing Lines, Planes, etc.: Packings in Grassmannian Spaces” John H. Conway, Ronald H. Hardin, N. J. A. Sloane, Experimental Mathematics, 1996).

Summary [34] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

[35] In a first aspect, there is provided a method of generating spreading sequences in the form of a pool of complex sequences, comprising creating the pool of complex sequences including creating a sequence base set and constructing a plurality of hyperplanes from the base set, constructing non-orthogonal vectors in each hyperplane of the plurality of hyperplanes, and assigning a quality figure to the sequence pool based on a pool cross correlation measure.

[36] In a second aspect according to aspect 1, the sequence base set has a size of N. Optionally, the sequence base set is orthogonal and complex.

[37] In a third aspect according to the preceding aspect, the sequence base set defines ) dimensional orthogonal hyperplanes space.

[38] In a fourth aspect according to any one of the preceding aspects, creating the sequence base set comprises generating complex Hadamard codes. Optionally, the complex Hadamard codes in the normalized de-phased matrix form [F_N] = e^ljk27l/N correspond to log-Hadamard matrices.

[39] In a fifth aspect according to any one of the preceding aspects, constructing the plurality of hyperplanes from the base set comprises choosing a plurality of pairs of orthogonal vectors from the sequence base set, each pair of orthogonal vectors of the plurality of pairs of orthogonal vectors defining a hyperplane of the plurality of hyperplanes.

[40] In a sixth aspect according to the preceding aspect, n orthogonal base vectors of the plurality of pairs of orthogonal vectors construct Knyperpianes = (n - 1).

[41] In a seventh aspect according to any one of the preceding aspects, the pool of complex sequences has a size of M.

[42] In an eight aspect according to any one of the two preceding aspects, the method further comprises generating a total number of M sequences of the pool of complex sequences, with

M North J^- Z^/iyperpianes * /'r, with N_orth being the number of orthogonal sequences, Kftyperpianes being the number of hyperplanes, and L_r being the number of sequences of hyperplanes.

[43] In a ninth aspect according to any one of the preceding aspects, constructing the nonorthogonal vectors in each hyperplane of the plurality of hyperplanes comprises defining a constraint of least projection as a minimum vector on vector cross-correlation, generating linear combination factors a = cos θ and β = sin0 are generated, wherein θ is the angle between the vectors determined by the criterion of constraint of least projection.

[44] In a tenth aspect according to any one of the preceding aspects, the method further comprises constructing a non-orthogonal vector V_non-orthogonai based on a, β as: A' = a- a_r + _____„ . . . . _____„ _____„ . π <Z 0.2 + ··· + CT ’ CL_n, Β β ' b-^ + β />2 + + β b_n, V-non—orthogonal A ' e + B ' e ².

[45] In an eleventh aspect according to any one of the preceding aspects, assigning a quality figure to the sequence pool further comprises forming a list of sequences in the pool of complex sequences in an ordered labels format, optionally orthogonal sequences being listed first and non-orthogonal sequences being listed thereafter; constructing a cross-correlation matrix, where each entry in the cross-correlation matrix is determined as a dot product (l/, I/); grading the pool of constructed vectors based on a measure of sequence cross-correlation, optionally the measure including Cross_correlation = Average (COL_average.), where i = 1. . . M and COL_averagei = average of each column of the cross-correlation; and assigning the quality figure to the sequence pool as the inverse of pool cross-correlation as (Pool_Cross_Correlation)^_1.

[46] In a twelfth aspect, there is provided a non-transitory computer readable medium containing a computer program configured to implement the method of generating spreading sequences in accordance with any one of the preceding aspects.

[47] In a thirteenth aspect according to the preceding aspect, the non-transitory computer readable medium comprises at least one from a group consisting of: a hard disk, a CD-ROM, an optical storage device, a magnetic storage device, a Read Only Memory, a Programmable Read Only Memory, an Erasable Programmable Read Only Memory, EPROM, an Electrically Erasable Programmable Read Only Memory and a Flash memory.

Brief description of the drawings [48] Further details, aspects and embodiments of the invention will be described, by way of example only, with reference to the drawings. Elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. Like reference numerals have been included in the respective drawings to ease understanding.

[49] Figure 1 shows a general block diagram for a multi-user receiver in accordance with prior art examples;

[50] Figure 2 shows a classification of NOMA features in accordance with prior art examples;

[51] Figure 3 shows an example of MUSA with resources shared by multiple users, where each user is using a spreading code of SF=4, in accordance with prior art examples;

[52] Figure 4 shows a Multi-User Multiple Access transmitter and receiver structure in accordance with prior art examples;

[53] Figure 5 shows a general structure of the transmitter side;

[54] Figures 6 to 10 show example sequences;

[55] Figure 11 shows a table illustrating the calculated average MUI for N=4, r=2;

[56] Figure 12 shows a table illustrating the calculated average MUI for N=4, r=2;

[57] Figure 13 shows a diagram illustrating sequence pools as per orthogonal base (OB) and r, request sequences per hyperplane;

[58] Figure 14 shows a diagram illustrating a summary of sequence pool qualities per orthogonal base and requested sequences per hyperplane;

[59] Figure 15A shows an gNodeB cell design tool Table for choosing sequence pool for SF = 4;

[60] Figure 15B shows an gNodeB design tool Quality figure for SF = 4;

[61] Figure 16 shows an gNodeB cell design tool for choosing sequences for users in the cell;

[62] Figure 17 shows a table illustrating an gNodeB design tool for SF = 4; and [63] Figure 18 shows a flow chart for a method of generating spreading sequences.

Detailed description of the preferred embodiments [64] Those skilled in the art will recognise and appreciate that the specifics of the examples described are merely illustrative of some embodiments and that the teachings set forth herein are applicable in a variety of alternative settings.

[65] The present disclosure pertains to the UE-specific design of MA signature of symbol level spreading as shown in block 140, Symbol-level Spreading/Scrambling/lnterleaving. In Rel.15 NR joint modulation and spreading codebook could be used as the MA signature, as shown in Figure

5. Such design of modulation and spreading can reduce the inter-user interferences by symbollevel spreading.

[66] The design target of the spreading sequence is to lower the inter-user interferences by using low cross-correlation or low-density property among sequences. Some typical sequences proposed by companies are QAM-based sequences, WBE/GWBE/Grassmannian sequences, ZC like sequences, chirp sequences, and sparse sequences. The sequences used are taken from the following pools used for the symbol level linear spreading scheme, using spreading factor (SF) of 2, 3, 4, 6 and 8.

Linear spreading codebook for SF=2 (the table is repeated for the simulation with more than 6 UEs)

Linear spreading codebook for SF=3 (the table is repeated for the simulation with more than 9 UEs)

ω²

1

-I j ω² ω²

ω² ω² [67] Figures 6 to 10 show tables illustrating example sequences. An example of a QPSK sequence with SF = 4, pool size = 64, is given in the table of Figure 6. An example of BPSK or {+1/-1} sequence with SF = 6, pool size = 16 is given in the table of Figure 7. An example Codebook of Grassmannian sequences for Spreading Factor: N = 4 serving K users is given in the table of Figure 8. An example Codebook of Grassmannian sequences for Spreading Factor: N = 4 serving K=2, 3, 4, 6 users is given in the table of Figure 9. An example of 64QAM-quantized Grassmannian Sequence based codebook for Spreading Factor: N = 4 is given in the table of Figure 10.

[68] The starting point for the approach to the design of Grassmannian codebooks (see background section above) is the problem of finding a codebook such that the minimum distance between codeword pairs is maximized. That is finding a codebook T = {F,} ₁ that solves raax mm

F.vG- ,v where d(Fi,Fj) is a measure of the distance between the subspaces spanned by its arguments.

[69] As a comparative example, the generation of spreading code at a UE (layer) is summarized in R1-1803620.

[70] According to Qualcomm, the spreading factor may be K and the number of distinct spreading codes may be N. Then the n-th spreading code can be denoted by S_n = [s_n(l) s_n(2) ··· s_n(O; 1 <n< N, N > K >2 (Eq. 1). An example of closed-form construction would be s_n(/c) = --Lexp )) w(/c), with 1 < k < K, 1 <n< N (Eq. 2), where w(/c) is a perfect sequence satisfying J]£₌₁w(/c)w*(/c + /) = Κδ(ί).

[71] The generation of spreading codes can be defined in a complex vector derived from Grassmannian line packing problem. Here, the spreading code can be Grassmannian Sequence or M-QAM quantized Grassmannian Sequence. Details can be seen in R1-1802229.

[72] The spreading sequence can be a Grassmannian Welsh-bound Equality (GWBE)

SPS =— (ΣΙλ)² sequence satisfying ¹ ' , where Pk is layer power, and where the power difference is a key point to optimize the spreading sequence and can let the gNB have more flexibility to configure the signature pool for different grouped users. Detailed sequences can be found in R1-1802497. The idea of flexible grouping is described here as a key point to optimize the spreading sequence and can let the gNB (gNodeB) have more flexibility to configure the signature pool for different grouped users.

[73] According to the present disclosure, there is provided a flexible generation method for spreading sequences, which generates non-orthogonal pools of spreading sequences as follows:

• Flexible size sequence pools are generated by design parameter, • Multi-user Interference (MUI) is inherently minimized, and • Sequence pools are graded with a quality figure.

[74] The Quality Figure is proportional to the inverse of cross-correlation number. The crosscorrelation number is an average cross-correlation measured between all sequence pairs of the pool.

[75] A key concept of the present disclosure is the building of a sequence pools database according to a competitive greedy guideline. According to this guideline sequences are added by least worsening the MUI condition.

[76] According to this concept, the generator first establishes an orthogonal base set of sequences. Then, the base set is extended into larger non-orthogonal sequence sets using a principle of constraint of least projection. The guideline of least projection adds non-orthogonal sequences in a LEAST-MU I way. The method according to the present disclosure guarantees that the sequences of a given pool are of least MUI for its size.

[77] In accordance with the present disclosure, a mechanism is defined that generates Graded sequence pools attributing a quality figure to each pool. The flexible selection and assignment of a sequence pool to uplink users provides a network design tool to gNodeB.

[78] Pools are graded with the intention to support gNodeB grant-free and Grant-based cell management. Cell management takes into account the expected traffic level and the receiver known capability of MU interference susceptible level and selects a sequence pool to best match these conditions.

[79] gNodeB may use this database of pools as a cell management tool by way of selecting and assigning a desired pool to a projected number of users in a cell taking the frequency and time resources into account.

[80] The assignment of a pool of sequences should be decided by the following cell parameters: system parameters (i.e. available resource elements to be granted to a group of users; and receiver strength to match the Quality Figure of the chosen sequence pool) and environment conditions (i.e. expected traffic level).

[81] The advantages of this invention over prior art entail at least flexible spreading sequence generation and by flexible traffic management tool provision.

[82] Flexible spread pool generation is based on orthogonal base code set where crosscorrelation is zero such as in ‘CDMA-like’ direct spread, guaranteeing zero MUI caused by spreading sequence.

[83] Further, larger pools are generated as an extension to the orthogonal base set by way of gradual MUI degradation. Pools are designed in a graded fashion where the smallest size is purely orthogonal and as pool size grows by design demand so is MUI worsening gradually.

[84] With respect to the traffic management tool, the spreading sequence pools size can be used upon need as a code cover for expected traffic load. Pool size could be matched with expected uplink traffic by gNodeB or operators, thereby providing an improved tool for traffic management.

[85] Traffic volume overload can be controlled by choosing a “best match” to the nonorthogonal spreading pool of choice by sequences parameters, such as pool size and pool quality figure.

[86] Without the proposed configuration and/or parameter, Multi User Interference (MUI) between the non-orthogonal sequences would be significantly higher than achievable MUI in accordance with the present disclosure. Further, it would not be possible to generate a flexible size non-orthogonal sequence pools data-base, and it would not be possible to generate gradually graded non-orthogonal sequence pools to be stored in data base, thereby giving the gNodeB a cell design tool for different traffic levels.

[87] Solutions in the prior art, so far as can be reasonably derived from known contributions to the prior art, are solutions using evenly spaced sequences. Evenly spaced sequences mean having equal MUI between spreading sequences. On the other hand, the concepts according to the present invention allow for the generation of graded sequence pools with MUI from perfect to poorer MUI in a gradual manner. An obvious usage of pools is one size of sequence pool with one MUI property that is enforced on the cell without flexible choice.

[88] It appears that is not possible, based on prior art solution and/or starting from any one of the prior art solutions discussed above, to use orthogonal hyperplanes generated from an orthogonal vector base set to generate non-orthogonal sequences, or to set the principle of constraint of least projection, in order to generate the non-orthogonal sequences in each hyperplane in a good to poorer cross-correlation property.

[89] In accordance with the present disclosure there is provided a method of generating spreading sequences comprising the following steps.

[90] In a first step a pool of complex sequences is created, the pool having a size of M sequences.

[91] First, an orthogonal sequence base set is created. A base set of orthogonal sequences of size N is generated, where N sets the size of the sequence which is the Spread Factor (SF). The orthogonal set should be complex and orthonormal. For the purpose of creating an example of orthonormal sequences, generation of Complex Hadamard codes may be followed. An example of complex Hadamard codes in the normalized de-phased matrix form [F_w] = _ey^k27r/^w corresponds to log-Hadamard matrices. Examples of orthogonal sequences by complex Hadamard codes in the normalized de-phased matrix are given below. For N=4 F₄ =

1	1	1	1-
1	i	-1	—i
1	-1	1	-1
-1	—i	-1	i-

and for N=6

1 1	1	1	1	1
1 0,5 + 0.866/	-0.5 + 0.866/	-1	-0.5-0.866/	0.5 + 0.866/
1 -0.5 + 0.866/	-0.5- 0.866/	1	-0.5 + 0.866/	-0.5 - 0.866/
1 -1	.1	-1	1	-1
1 -0.5 - 0.866/	-0.5 - 0.866/	1	-0.5 -0.866/	-0.5 + 0.866/
1 0.5 0.866/	0.5 · 0.8667	1	-0.5 + 0.866/	0.5 + 0.866/

[92] Second, non-orthogonal sequences are generated from the orthogonal base set, in a gradual fashion, as follows, by constructing hyperplanes. A pair of orthogonal vectors is chosen from the base set F_N, where each pair of orthogonal vectors defines a hyperplane in a hyperplane space. A base set of N-Orthogonal vectors defines dimensional orthogonal hyperplanes space. A combination of 2 orthogonal vectors out of n, Q) = _2!(·”ί₂₎, hyperplanes, n orthogonal base vectors set constructs K_hyperpi_anes = (n - 1). In an example of n=12 orthogonal vectors /12\ ii result in ( j = 12 * — = 66 hyperplanes.

[93] In a second step, non-orthogonal vectors are constructed in each hyperplane.

[94] A Constraint of least projection is defined as minimum vector on vector cross-correlation which is directly proportional to desired non-orthogonal vectors per hyperplane. In a given hyperplane, each generated non-orthogonal vector is a linear combination of the two orthogonal axis vectors, A,B, where A = a_r + a₂ -I-----h a_n and B = + b₂ -I-----h b_n, where · ^an3 and b_i,b₂ ··· b_n are the orthogonal vector’s components.

[95] Linear combination factors a = cos θ and β = sin θ are generated, where θ is the angle between desired vectors determined by the criterion: constraint of least projection. Then θ:= 2L where r is the request number for non-orthogonal vectors per hyperplane. The constraint of least projection is defined by min(/l_fe,S_i), where k ψ I and k,l e [1,2, •••r], where {x,y) is shorthand for “dot product” between x and y.

[96] A non-orthogonal vector is to be constructed using a, β as follows: A' = a a_± + a a₂ + _____„ . . . . _____„ _____„ . π • ·· + <Z CL_n, Β — β ' b·^ β ' b₂ ~\~ ··· ~\~ β ' b_n, Vnon-orthogonal — A ' 6 + B 6 ².

[97] L_r is the number of non-orthogonal vectors created per hyperplane.

[98] This generates the total number of sequences M, where M = N_orth + K_hyperpi_anes * L_r, where N_orth is the number of orthogonal sequences, K_hyperpi_anes is the number of hyperplanes, and L_r is the number of sequences of hyperplanes.

[99] In a third step, a quality figure is assigned to sequence pools based on a cross correlation measure. The quality figure represents the average of all interference projections of all sequences on every sequence in the pool normalized to the number of sequences.

[100] Grouping all sequences into graded pools is achieved as follows.

[101] A list of all M constructed sequences is formed in an ordered labels format: Label Sequences: 1 . . . M, as noted here, with a) orthogonal sequences being listed first, and then b) non-orthogonal sequences being listed.

[102] A cross-correlation matrix (dot product) is constructed, with Matrix entry = {v_b V/, where {a, b) = dot product a b.

[103] The pool of constructed vectors is graded, according to a measure of sequence crosscorrelation. COLjweragei = average of each column (this represents a measure of projection of all vectors on one listed vector), and pool Cross_correlation = Average (COL_averag_e,), where i = 1. . . M (this average of averages represents a measure of cross-correlation for all sequences of the pool). The Pool Quality Figure is set as the inverse of Pool Cross-correlation: Pool Quality figure = (Pool_Cross_Correlation)^_1.

[104] Examples of graded non-orthogonal sequence pools are described below.

[105] Example 1 [106] Figure 11 shows, in a first example in accordance with embodiments of the present disclosure, a table illustrating the calculated average MUI for N=4, r=2:

Orthogonal base: 4

Number of hyperplanes: 6

Requested non-orthogonal sequences per hyperplane: 2

Total number sequences: 16

Cross-correlation average: 0.406094,

Standard deviation: 0.052156 [107] 16 constructed sequences are listed in figure 11, each entry in the cross-correlation matrix being determined as (7,, Vj), where (a, b) is the dot product a b.

[108] Example 2 [109] Figure 12 shows, in a second example in accordance with embodiments of the present disclosure, a table illustrating the calculated average MUI for N=4, r=2:

Orthogonal base: 4

Number of hyperplanes: 6

Requested non-orthogonal sequences per hyperplane: 4

Total number sequences: 28

Cross-correlation average: 0.41058,

Standard deviation: 0.042804 [110] 28 constructed sequences are listed in figure 12, each entry in the cross-correlation matrix being determined as {v_b Vj), where (a, b) is the dot product a b.

[111] In an example of a large pool (not shown in the figures due to size), the following parameters apply:

Sequence Pool (N=14, r=10)

Orthogonal base: 14

Number of hyperplanes: 91

Requested non-orthogonal sequences per orthogonal hyperplane: 10

Total number of sequences: 924

Cross-correlation average: 0.11954 [112] The Pool Quality is determined as (Cross_Corr_average)^_1 = 8.3654.

[113] Comparative Example [114] The following comparative example is based on the suggestion by ZTE for a nonorthogonal Grassmannian and Welch-bounce sequence pool. This comparison clearly illustrates a significant advantage of the inventive concepts in accordance with the present disclosure by comparing the average MUI for the same Spreading Factor.

[115] The Grassmannian and Welch-bounce code was determined for spreading factor = 4, sequence pool size = 8 with minimum cross-correlation. For performance comparison ZTE Grassmannian and Welch-bounce non-orthogonal sequence pools were selected from the table shown in figure 8.

[116] The Grassmannian non-orthogonal sequence pool is duplicated here for convenience, showing vectors 1 to 8 in corresponding columns 1 to 8 (from left to right):

-0.2381-0.8369Ϊ	>0.6599-0.12221	-0.6557-0.17761	-0.1561+0.08611	-0.1374+0.1275i	-0.1849+0.3859i	-0.2426-0.2248i	-0.1703-0.0604i
-0.2381-0.8369Ϊ	;0.4906+0.0221i	0.3934+0.2749i	-0.3453-0.2068i	-0.5596+0.0272i	0.0616+0.0315i	-0.3027-0.3133i	-0.7664+0.1256i
-0.2381-0.8369Ϊ	:0.0425+0.3856i	0.044-0.3295i	-0.3979+0.0525i	-0.5272-0.2195i	0.0649-0.877i	-0.2452+0.4427i	-0.0149-0.4727i
-0.2381-0.8369Ϊ	ίθ·3968-Ο.Ο25ϊ	-0.3444-0.28Hi	-0.7817-0.1845i	0.2417+0.5162i	0.1956-0.0203i	0.4625-0.4805i	0.0794-0.3663i

[117] An average MUI was calculated on ZTE Grassmannian code. The average MUI on each vector from all other 7 vectors was determined by cross-correlation as

Vector 1: 0.5916

Vector 2: 0.7169

Vector 3: 0.6064

Vector 4: 0.5433

Vector 5: 0.5063

Vector 6: 0.7363

Vector 7: 0.6117 and

Vector 8: 0.7246 [118] The total average MUI was determined as 0.630 (std. dev. 0.087).

[119] The Welch-Bounce non-orthogonal sequence pool is duplicated here for convenience, showing vectors 1 to 8 in corresponding columns 1 to 8 (from left to right):

-0.6617 + 0.1004	i -0.0912 + 0.4191	i 0.4151-0.3329i 0.2736 - 0.4366Ϊ -0.4727 - 0.1234i	-0.3413 + 0.1257	: 0.4216 + 0.11871 0.4603 + 0.2142Ϊ
0.0953 + 0.4784	i -0.4246-0.0859	i 0.2554-0.3140i 0.5452 + 0.2068i 0.0592 - 0.6432i	; 0.3671-0.1430	i -0.0241 - 0.56201 0.0048 - 0.4244i
-0.4233- 0.1399	i -0.4782 + 0.3752	i -0.3808-0.1569i -0.4690- 0.2225Ϊ 0.3493 - 0.1988i	; 0.6514-0.0660	i -0.4507 + 0.09581 0.4047 + 0.16011
-0.1265 + 0.3153	i 0.4936 + 0.1233	i 0.6130-0.08731 -0.3399 + 0.0974i -0.0975 - 0.41611	; 0.2174 + 0.4864	i -0.5167 + 0.1116i -0.4908 + 0.3629Ϊ

[120] An average MUI was calculated on ZTE Welch-Bounce code. The average MUI on each vector from all other 7 vectors was determined by cross-correlation as

Vector 1: 0.6982

Vector 2: 0.6781

Vector 3: 0.6740

Vector 4: 0.8291

Vector 5: 0.4739

Vector 6: 0.6608

Vector 7: 0.7101 and

Vector 8: 0.7866 [121] The total average MUI was determined as 0.6888 (std. dev. 0.1049).

[122] Advantages derived based on the concepts in accordance with the present disclosure include at least the following.

[123] As a first advantage, inventive concepts exhibit MUI improvement of non-orthogonal sequences compared to others, the allow for the generation of sequence pools that have a definite average MUI (cross-correlation) improvement over other suggested pools. An MUI calculation was carried out to show this claim by comparing to ZTE suggested non-orthogonal sequence pools. Inventive concepts in accordance with the present disclosure allow for, as a reference, determining a total average MUI as carried out in Example 2 (see above) for SF = 4, taken from the table shown in figure 12: Orthogonal base 4, hyperplanes 6, requested nonorthogonal sequences per hyperplane 4, total number of sequences 28. According to the inventive concepts of the present disclosure, this results in a total average MUI of 0.41058 (std. dev. 0.042804) [124] A comparison to ZTE Grassmannian non-orthogonal sequence and Welch-bounce sequence pools shows a total average of 0.630 (Grassmannian; std. dev. 0.087) and 0.689 (Welch-bounce; std. dev. 0.105).

[125] Thus, the inventive concepts in accordance with the present disclosure allow for a significant improvement.

[126] As a second advantage, a sequence pool generator is provided for any spread factor from a minimum to a maximum required spread factor. The generated sequence pools shown in figure 13 may be pre-calculated and stored in a sequence pool data base. The generated data base includes sequence pool sizes and their associated quality figures. Figures 13 and 14 show generated pools data base that spans all pools designed for SF =3 up to SF=14. Figure 13 shows a diagram illustrating sequence pools as per orthogonal base (OB) and r, request sequences per hyperplane, in accordance with embodiments of the present disclosure and figure 14 shows a diagram illustrating a summary of sequence pool qualities per orthogonal base and requested sequences per hyperplane, in accordance with embodiments of the present disclosure.

[127] As a third advantage, a flexible pools size is provided for a requested spread factor. This is shown by above-described Example 1 (see table in figure 11), which shows a pool of 16 sequences for SF = 4, and by above-described Example 2 (see table in figure 12), which shows a pool of 28 sequences for SF = 4.

[128] Figure 16 shows an gNodeB cell design tool for choosing sequences for users in the cell in accordance with embodiments of the present disclosure. An example for flexible sequence pool size design is shown in figure 16 for SF = 4 as indicated by OB4 (Orthogonal Base 4, line 1602, 2nd line from bottom) the choice of 10 pools are shown available by request per hyperplane parameter on the x-axis, as shown in the diagram on figure 16.

[129] Figure 15A shows an gNodeB cell design tool Table for choosing sequence pool for SF = 4 in accordance with embodiments of the present disclosure and figure 15B shows an gNodeB design tool Quality figure for SF = 4 in accordance with embodiments of the present disclosure.

[130] In figures 15A and 15B, the OB4 (orthogonal-base 4) line was duplicated for convenience. The selection of pool size is shown in figure 15A where the size of the pool (indicated by Y) grows by design request, and its associated Quality Figure is given in figure 15B.

[131] As a fourth advantage, a cell management tool is provided. gNodeB may use the data base of the variety of non-orthogonal sequence pools with different sizes associated with the Quality Factor for a given Spread Factor. gNodeB may use this data base to match nonorthogonal sequence pools to expected Traffic levels. This advantage is exhibited by a combined data base of sequence pools, shown in figure 13 with their associated Quality figures shown in figure 14 where generated pools data base spans all pools designed for SF =3 up to SF=14.

[132] To show a cell process matching non-orthogonal pool to a given traffic level, figure 14 is partially duplicated in figure 16 showing a cell design tool data base for Spreading Factor of 3 up to 10. The Spreading Factor (x-axis) designates the amount of Resource Elements (RE) devoted to the spreading sequence. The graph shows pool sizes that may be chosen to match the expected cell traffic level.

[133] Figure 17 shows a table illustrating a gNodeB design tool for SF = 4 in accordance with embodiments of the present disclosure. The tool for cell management is exemplified in figure 15B and in its tabulated form in the table shown in figure 17 where pool size should be associated with a Quality Figure.

[134] Figure 18 shows a flow chart for a method 200 of generating spreading sequences in accordance with embodiments of the present disclosure. The method 200 of generating spreading sequences in the form of a pool of complex sequences start at step 201. In step 202, the pool of complex sequences is created. This includes creating 204 a sequence base set and constructing 206 a plurality of hyperplanes from the base set. In step 208, non-orthogonal vectors are constructed in each hyperplane of the plurality of hyperplanes. And in step 210, a quality figure is assigned to the sequence pool based on a pool cross correlation measure. The method 200 ends at step 212.

[135] Although not shown in detail any of the devices or apparatus that form part of the network may include at least a processor, a storage unit and a communications interface, wherein the processor unit, storage unit, and communications interface are configured to perform the method of any aspect of the present invention. Further options and choices are described below.

[136] The signal processing functionality of the embodiments of the invention especially the gNB and the UE may be achieved using computing systems or architectures known to those who are skilled in the relevant art. Computing systems such as, a desktop, laptop or notebook computer, hand-held computing device (PDA, cell phone, palmtop, etc.), mainframe, server, client, or any other type of special or general purpose computing device as may be desirable or appropriate for a given application or environment can be used. The computing system can include one or more processors which can be implemented using a general or special-purpose processing engine such as, for example, a microprocessor, microcontroller or other control module.

[137] The computing system can also include a main memory, such as random access memory (RAM) or other dynamic memory, for storing information and instructions to be executed by a processor. Such a main memory also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by the processor. The computing system may likewise include a read only memory (ROM) or other static storage device for storing static information and instructions for a processor.

[138] The computing system may also include an information storage system which may include, for example, a media drive and a removable storage interface. The media drive may include a drive or other mechanism to support fixed or removable storage media, such as a hard disk drive, a floppy disk drive, a magnetic tape drive, an optical disk drive, a compact disc (CD) or digital video drive (DVD) read or write drive (R or RW), or other removable or fixed media drive. Storage media may include, for example, a hard disk, floppy disk, magnetic tape, optical disk, CD or DVD, or other fixed or removable medium that is read by and written to by media drive. The storage media may include a computer-readable storage medium having particular computer software or data stored therein.

[139] In alternative embodiments, an information storage system may include other similar components for allowing computer programs or other instructions or data to be loaded into the computing system. Such components may include, for example, a removable storage unit and an interface, such as a program cartridge and cartridge interface, a removable memory (for example, a flash memory or other removable memory module) and memory slot, and other removable storage units and interfaces that allow software and data to be transferred from the removable storage unit to computing system.

[140] The computing system can also include a communications interface. Such a communications interface can be used to allow software and data to be transferred between a computing system and external devices. Examples of communications interfaces can include a modem, a network interface (such as an Ethernet or other NIC card), a communications port (such as for example, a universal serial bus (USB) port), a PCMCIA slot and card, etc. Software and data transferred via a communications interface are in the form of signals which can be electronic, electromagnetic, and optical or other signals capable of being received by a communications interface medium.

[141] In this document, the terms ‘computer program product’, ‘computer-readable medium’ and the like may be used generally to refer to tangible media such as, for example, a memory, storage device, or storage unit. These and other forms of computer-readable media may store one or more instructions for use by the processor comprising the computer system to cause the processor to perform specified operations. Such instructions, generally 45 referred to as ‘computer program code’ (which may be grouped in the form of computer programs or other groupings), when executed, enable the computing system to perform functions of embodiments of the present invention. Note that the code may directly cause a processor to perform specified operations, be compiled to do so, and/or be combined with other software, hardware, and/or firmware elements (e.g., libraries for performing standard functions) to do so.

[142] The non-transitory computer readable medium may comprise at least one from a group consisting of: a hard disk, a CD-ROM, an optical storage device, a magnetic storage device, a Read Only Memory, a Programmable Read Only Memory, an Erasable Programmable Read Only Memory, EPROM, an Electrically Erasable Programmable Read Only Memory and a Flash memory. In an embodiment where the elements are implemented using software, the software may be stored in a computer-readable medium and loaded into computing system using, for example, removable storage drive. A control module (in this example, software instructions or executable computer program code), when executed by the processor in the computer system, causes a processor to perform the functions of the invention as described herein.

[143] Furthermore, the inventive concept can be applied to any circuit for performing signal processing functionality within a network element. It is further envisaged that, for example, a semiconductor manufacturer may employ the inventive concept in a design of a stand-alone device, such as a microcontroller of a digital signal processor (DSP), or application-specific integrated circuit (ASIC) and/or any other sub-system element.

[144] It will be appreciated that, for clarity purposes, the above description has described embodiments of the invention with reference to a single processing logic. However, the inventive concept may equally be implemented by way of a plurality of different functional units and processors to provide the signal processing functionality. Thus, references to specific functional units are only to be seen as references to suitable means for providing the described functionality, rather than indicative of a strict logical or physical structure or organisation.

[145] Aspects of the invention may be implemented in any suitable form including hardware, software, firmware or any combination of these. The invention may optionally be implemented, at least partly, as computer software running on one or more data processors and/or digital signal processors or configurable module components such as FPGA devices.

[146] Thus, the elements and components of an embodiment of the invention may be physically, functionally and logically implemented in any suitable way. Indeed, the functionality may be implemented in a single unit, in a plurality of units or as part of other functional units. Although the present invention has been described in connection with some embodiments, it is not intended to be limited to the specific form set forth herein. Rather, the scope of the present invention is limited only by the accompanying claims. Additionally, although a feature may appear to be described in connection with particular embodiments, one skilled in the art would recognise that various features of the described embodiments may be combined in accordance with the invention. In the claims, the term ‘comprising’ does not exclude the presence of other elements or steps.

[147] Furthermore, although individually listed, a plurality of means, elements or method steps may be implemented by, for example, a single unit or processor. Additionally, although individual features may be included in different claims, these may possibly be advantageously combined, and the inclusion in different claims does not imply that a combination of features is not feasible and/or advantageous. Also, the inclusion of a feature in one category of claims does not imply a limitation to this category, but rather indicates that the feature is equally applicable to other claim categories, as appropriate.

[148] Furthermore, the order of features in the claims does not imply any specific order in which the features must be performed and in particular the order of individual steps in a method claim does not imply that the steps must be performed in this order. Rather, the steps may be performed in any suitable order. In addition, singular references do not exclude a plurality. Thus, references to ‘a’, ‘an’, ‘first’, ‘second’, etc. do not preclude a plurality.

[149] Although the present invention has been described in connection with some embodiments, it is not intended to be limited to the specific form set forth herein. Rather, the scope of the present invention is limited only by the accompanying claims. Additionally, although a feature may appear to be described in connection with particular embodiments, one skilled in the art would recognise that various features of the described embodiments may be combined in accordance with the invention. In the claims, the term ‘comprising’ or “including” does not exclude the presence of other elements.

Claims (13)

Claims

1. A method (200) of generating spreading sequences in the form of a pool of complex sequences, comprising:

creating (202) the pool of complex sequences including creating (204) a sequence base set and constructing (206) a plurality of hyperplanes from the base set;

constructing (208) non-orthogonal vectors in each hyperplane of the plurality of hyperplanes; and assigning (210) a quality figure to the sequence pool based on a pool cross correlation measure.

2. The method according to the preceding claim, wherein the sequence base set has a size of N; optionally wherein the sequence base set is orthogonal and complex.

3. The method according to the preceding claim, wherein the sequence base set defines dimensional orthogonal hyperplanes space.

4. The method according to any one of the preceding claims, wherein creating (204) the sequence base set comprises generating complex Hadamard codes; optionally wherein the complex Hadamard codes in the normalized de-phased matrix form [Fw] = el]k2n/N correspond to log-Hadamard matrices.

5. The method according to any one of the preceding claims, wherein constructing (206) the plurality of hyperplanes from the base set comprises:

choosing a plurality of pairs of orthogonal vectors from the sequence base set, each pair of orthogonal vectors of the plurality of pairs of orthogonal vectors defining a hyperplane of the plurality of hyperplanes.

6. The method according to the preceding claim, wherein n orthogonal base vectors of the plurality of pairs of orthogonal vectors construct Khyperpianes = (n - 1).

7. The method according to any one of the preceding claims, wherein the pool of complex sequences has a size of M.

8. The method according to the two preceding claims, further comprising generating a total number of M sequences of the pool of complex sequences, wherein M = North + Khyperpian.es * L-. with North being the number of orthogonal sequences, Khyperplanes being the number of hyperplanes, and Lr being the number of sequences of hyperplanes.

9. The method according to any one of the preceding claims, wherein constructing (208) the non-orthogonal vectors in each hyperplane of the plurality of hyperplanes comprises: defining a constraint of least projection as a minimum vector on vector cross-correlation; generating linear combination factors a = cos θ and β = sin θ are generated, wherein θ is the angle between the vectors determined by the criterion of constraint of least projection.

10. The method according to the preceding claim, further comprising constructing a non- orthogonal vector Vn0n-orthogonai based on a, β as: A' = a ar + a a2 -I-----h a an, B' = β b-^ + β ' b2 + + β ' bn, ^non-orthogonal = A e + B · e 2.

11. The method according to any one of the preceding claims, wherein assigning a quality figure to the sequence pool further comprises:

forming a list of sequences in the pool of complex sequences in an ordered labels format, optionally orthogonal sequences being listed first and non-orthogonal sequences being listed thereafter;

constructing a cross-correlation matrix, where each entry in the cross-correlation matrix is determined as a dot product {vb Vj)·, grading the pool of constructed vectors based on a measure of sequence crosscorrelation, optionally the measure including Cross_correlation = Average (COLaveraqe.), where i = 1. . . M and COL_averagei = average of each column of the cross-correlation; and assigning the quality figure to the sequence pool as the inverse of pool cross-correlation as (Pool_Cross_Correlation)_1.

12. A non-transitory computer readable medium containing a computer program configured to implement the method of generating spreading sequences according to any one of the preceding claims.

13. The non-transitory computer readable medium according to the preceding claim, comprising at least one from a group consisting of: a hard disk, a CD-ROM, an optical storage device, a magnetic storage device, a Read Only Memory, a Programmable Read Only Memory, an Erasable Programmable Read Only Memory, EPROM, an Electrically Erasable Programmable Read Only Memory and a Flash memory.

05 11 19

13. The non-transitory computer readable medium according to the preceding claim, comprising at least one from a group consisting of: a hard disk, a CD-ROM, an optical storage device, a magnetic storage device, a Read Only Memory, a Programmable Read Only Memory, an Erasable Programmable Read Only Memory, EPROM, an Electrically Erasable Programmable Read Only Memory and a Flash memory.

Amendments to the claims have been filed as follows

05 11 19

Claims

1. A method (200) of generating spreading sequences in the form of a pool of complex sequences, comprising:

creating (202) the pool of complex sequences including creating (204) a sequence base set and constructing (206) a plurality of hyperplanes from the base set;

constructing (208) non-orthogonal vectors for use as spreading sequences in each hyperplane of the plurality of hyperplanes; and assigning (210) a quality figure to the sequence pool based on a pool cross correlation measure.

2. The method according to the preceding claim, wherein the sequence base set has a size of N; optionally wherein the sequence base set is orthogonal and complex.

3. The method according to the preceding claim, wherein the sequence base set defines dimensional orthogonal hyperplanes space.

4. The method according to any one of the preceding claims, wherein creating (204) the sequence base set comprises generating complex Hadamard codes; optionally wherein the complex Hadamard codes in the normalized de-phased matrix form [Fw] = el]k2n/N correspond to log-Hadamard matrices.

5. The method according to any one of the preceding claims, wherein constructing (206) the plurality of hyperplanes from the base set comprises:

choosing a plurality of pairs of orthogonal vectors from the sequence base set, each pair of orthogonal vectors of the plurality of pairs of orthogonal vectors defining a hyperplane of the plurality of hyperplanes.

6. The method according to the preceding claim, wherein n orthogonal base vectors of the plurality of pairs of orthogonal vectors construct Khyperpianes = (n - 1).

7. The method according to any one of the preceding claims, wherein the pool of complex sequences has a size of M.

8. The method according to the two preceding claims, further comprising generating a total number of M sequences of the pool of complex sequences, wherein M = North + Khyperpianes * with North being the number of orthogonal sequences, Khyperplanes being the number of hyperplanes, and Lr being the number of sequences of hyperplanes.

9. The method according to any one of the preceding claims, wherein constructing (208) the non-orthogonal vectors in each hyperplane of the plurality of hyperplanes comprises: defining a constraint of least projection as a minimum vector on vector cross-correlation; generating linear combination factors a = cos θ and β = sin θ are generated, wherein θ is the angle between the vectors determined by the criterion of constraint of least projection.

10. The method according to the preceding claim, further comprising constructing a non- orthogonal vector Vnon_orthogonai based on a, β as: A' = a ar + a a2 -I-----h a an, B' = β ' b± + β ' b2 + ··· + β ' bn, VnOn-orthogonal = A e + B · e 2.

11. The method according to any one of the preceding claims, wherein assigning a quality figure to the sequence pool further comprises:

forming a list of sequences in the pool of complex sequences in an ordered labels format, optionally orthogonal sequences being listed first and non-orthogonal sequences being listed thereafter;

constructing a cross-correlation matrix, where each entry in the cross-correlation matrix is determined as a dot product {vb I/);

grading the pool of constructed vectors based on a measure of sequence crosscorrelation, optionally the measure including Cross_correlation = Average (COLaveragej), where i = 1. . . M and COL_averagei = average of each column of the cross-correlation; and assigning the quality figure to the sequence pool as the inverse of pool cross-correlation as (Pool_Cross_Correlation)_1.

12. A non-transitory computer readable medium containing a computer program configured to implement the method of generating spreading sequences according to any one of the preceding claims.