WO2010000075A1

WO2010000075A1 - Computation of extrinsic information in a branch-and-bound detector

Info

Publication number: WO2010000075A1
Application number: PCT/CH2008/000298
Authority: WO
Inventors: Christoph Studer; Andreas Burg; Helmut BÖLCSKEI
Original assignee: Eth Zurich
Priority date: 2008-07-03
Filing date: 2008-07-03
Publication date: 2010-01-07

Abstract

The computational complexity associated with detection in multiple-input multiple-output (MIMO) systems often dominates the complexity of the MIMO receiver. Soft-input soft-output detection can significantly improve the error rate performance in iterative MEvIO systems. Branch-and-bound (BB) based detection techniques aim at reducing the computational complexity by transforming MIMO detection into a graph-search problem. The method described in this document computes extrinsic information directly in the BB detector to enable extrinsic LLR clipping, which significantly reduces the computational complexity. As an example, we describe the application of the proposed method to the single tree-search sphere decoding algorithm.

Description

Computation of Extrinsic Information in a Branch-and-Bound Detector

⁵ T E C H N I C A L F I E L D

The invention relates to a method and device for branch-and-bound based soft-input soft-output decoding in a multiple-input multiple-output system.

¹⁰ B A C K G R O U N D A RT

Multiple-input multiple-output (MIMO) techniques have emerged in various wireless communication standards due to the high spectral efficiency offered by spatial multiplexing. Iterative detection and decoding can significantly improve the error rate ^ performance of MEMO wireless systems.

1. ITERATIVE MIMO SYSTEMS

The relevant blocks of a MIMO system using an iterative MEVIO detector are shown 20 in Fig. 1. The channel encoder obtains binary-valued information (denoted by the bit vector b) and computes coded bits X_jj,. The MIMO mapper obtains the coded bits and maps them to multi-dimensional data vectors (denoted by s). The iterative MIMO decoder consists of a soft-input soft-output (SISO) detector for MEMO systems and a channel decoder. The SISO detector obtains the received symbol vector 25 (denoted by y), channel state information, and soft-information from an external device (e.g., the channel decoder). The SISO detector computes extrinsic information, e.g., in the form of extrinsic log-likelihood ratios (denoted by L?_b) of the corresponding bits X_jJ1. The channel decoder computes estimates of the data bits (b) and produces a priori information Lf _b for SISO detector. The SISO detector can

30 compute new extrinsic outputs. The number of iterations (i.e., how many times the detector and the channel decoder are used), significantly affects the error rate performance of the iterative MEMO decoder.

₃₅ 2. SOFT-INPUT SOFT-OUTPUT MEMO DETECTION

The computation of soft-output information with the use of soft-inputs is a computational complex task and poses significant challenges in practical implementations. One of the most promising candidate for high-performance low-complexity soft- input soft-output MIMO detection is to use branch-and-bound (BB) techniques. The key idea of BB-based MIMO detection is to transform the MIMO detection problem into a graph-search problem that can efficiently be solved by pruning of unnecessary branches in the graph. Prominent examples of BB-based MIMO detectors are the sphere decoder, k-Best algorithms, or M-algorithms.

D I S C L O S U R E O F T H E I N V E N T I O N

The present invention relates to a low-complexity method to compute extrinsic soft- outputs using a branch-and-bound (BB) based MIMO detector by processing channel observations and a priori information.

The key objective of the described method is to reduce the computational complexity associated with extrinsic soft-output computation. This objective is achieved by a method for generating extrinsic soft-outputs using a branch-and-bound detector in a MIMO system and using path traversal in a graph for identifying a multidimensional transmit vector, said method comprising the steps of a) feeding a priori information L^A to the detector, with j and b together specifying a bit in said transmit vector L^A and said a priori information comprising values Lf _b being indicative of a probability that said bit is 1, b) traversing paths of the graph, each path representing a possible transmit vector, c) for at least part of the nodes x^ of a path being traversed, checking if a pruning criterion B is met,

wherein is a partial distance for the node,

_X ^MAP j_{s an es}tχ_mate of a most likely transmitted vector, d) and wherein in criterion B a contribution of a priori information Lf _b is, for all bits in considered differently depending on if the bit j, b in yfi⁾ is equal to the bit j, b in x^MAP, e) and terminating the traversal of said path if said pruning criterion is met. The method enables to identify influences of the detection algorithm to the final extrinsic soft-output information at an early stage in the detection phase, i.e., already during the BB procedure, and allows to compute the pruning criterion accordingly. Advantageously, this is used for clipping the magnitude of the extrinsic LLRs in or- der to lower the computational complexity of the BB procedure.

The general method described in this document is applicable to a variety of extrinsic soft-output BB-based MIMO detectors. As an example, we demonstrate the application of said method using a soft-input soft-output single tree-search sphere decoder.

BRIEF DESCRIPTIONS OF DRAWINGS

The invention will be better understood and objects other than those set forth above will become apparent when consideration is given to the following detailed description thereof. Such description makes reference to the annexed drawings, wherein

Fig.1 shows the main building blocks of an iterative MIMO system. The soft- input soft-output MIMO detector computes extrinsic soft-output information using channel observations and a priori information.

Fig.2 shows simulation results for the soft-input soft-output single tree-search sphere decoder (SISO STS-SD). The plot illustrates the performance/complexity trade-off of the soft-input soft-output detector depending on the (normalized) extrinsic LLR clipping level (indicated by the numbers next to the curves) and on the number of iterations /, i.e., how many times the detector and decoder are used.

MODES FOR CARRYING OUT THE INVENTION 3. OUTLINE

In Sec.4, we introduce the notation, provide definitions, and describe the system model. In section Sec.5, we provide a brief review of sphere decoding (SD). Sec.6 introduces the general idea of the method to compute extrinsic LLRs within the BB- based MIMO detector. Sec.7 illustrates the application of the described method using a single tree-search (STS) sphere decoder. Simulation results are shown in Sec.8. Further comments are given in Sec.9 and conclusions are given in Sec.10. 4. NOTATION, DEFINITIONS, AND SYSTEM MODEL

4.1. Notation

Matrices are set in boldface capital letters, vectors in boldface lowercase letters. The 5 superscripts ^τ and ^H stand for transpose and conjugate transpose, respectively. We write A_i:j for the entry in the ith row and jth column of the matrix A and b{ for the ith entry of the vector b = [6_X 62 • • • b^ }^τ- I_N denotes the N x N identity matrix. We call an N x M matrix A, where N > M, satisfying A-^A = I_M. unitary. \O\ denotes the cardinality of the set O. The probability of an event Z is denoted by P[Z]. x is the binary complement of £ G {+1, —1}, i.e., x = —x.

4.2. Definitions

In the context of the present applications and claims, the following definitions are used.

15

MIMO Multiple-input multiple-output (MIMO) is understood to be a communication system that can be described by a linear input-output relation according to

20 y = Hs + n

wherein s is a multi-dimensional transmit data vector of dimension M_τ > 1, H is a complex-valued MIMO channel matrix of dimension M_R x M_τ, n is a noise vector of dimension M_R > 1, and y is the received data vector of dimension M_R. In par- „_<. ticular, the input-output relation might represent a MIMO wireless communication system. However, MIMO may also describe channels with inter-symbol interference (ISI) or multiple access (MAC) channels, for example.

Soft-Outputs Soft-outputs (soft-output information) are understood to be any 30 set of values that allows to derive the estimated probabilities or an approximate of a binary-valued random variable. In particular, soft-outputs might be log-likelihood ratios (LLRs) according to

_ . /P[z = +1]\ where the binary-valued random variable x takes on values from the set {+1, -1} and b denotes the basis of the logarithm. If the basis b is omitted, the natural logarithm, i.e., with b = e, is assumed. However, it might, e.g., also be that soft-output information can also be represented as the ratio of probabilities

P[x = -1] or the difference of probabilities

D = P[x = +1] - P[x = -I] .

Soft-Input Soft-Output Soft-input soft-output (SISO) is understood to be a technique to compute soft-output information using soft-input information and possibly received data. In particular, it may describe a device (e.g., a decoder or a detector) that obtains soft-input information in the form of a priori LLRs and computes either intrinsic or extrinsic soft-output LLRs, for example.

Extrinsic Information Extrinsic information of a binary- valued random variable is understood to contain only new information that has been generated from a soft- input detector. Extrinsic information does not contain the part of information that has been fed into the detector with the exception of the data received through the communication channels. However, the soft-input information fed into the detector is often required to compute new extrinsic information. In the context of iterative de- coding, e.g., extrinsic information corresponds to the information that is exchanged between two or more decoders or detectors. For log-likelihood ratios, extrinsic LLRs are denned as

T B _ r D T A

where Lf_b is the intrinsic information for the bit j, b computed from received data and all available a priori information L^A (i.e., Vj, b), Lf _b denotes the a priori information of the particular bit j, b, and Lf_>b is the extrinsic LLR (soft-output information) of the bit j, b.

Branch-and-Bound Detector A branch-and-bόund (BB) detector is understood to be a method to decode digital information that is represented by a graph. The graph consists of nodes and branches. Each path in the graph represents a possible data vector (output). Nodes correspond to partial data vectors. Branches are associated with bits (of part of the data vector) and branch metrics. The BB detector traverses the graph and checks during traversal whether parts of the graph can be pruned. 5 Pruning parts of the graph is performed whenever a pruning criterion is met. During graph-traversal, the BB detector searches for the most likely transmitted data vector (and eventually associated metrics) and/or data vectors (and/or associated metrics) with particular properties. The traversal in the graph can be stopped if no more parts of the graph are remaining. In particular, sphere decoding algorithms are a prominent example of BB-based MIMO detection algorithms and represent the detection problem by a tree and perform the traversal on this tree.

4.3. Reference System j _- A multiple-input multiple-output (MIMO) system with M_τ transmit and M_R > M_τ receive streams is considered. The coded bit-stream to be transmitted is mapped to (a sequence of) M_τ-dimensional transmit symbol vectors s G o^Mτ, where O stands for the underlying complex scalar constellation and \O\ = 2^Q. Each symbol vector (data vector) s is associated with a label vector x containing M_TQ binary values

20 chosen from the set {+1, —1} where the null element (0 in binary logic) of GF(2) corresponds to +1. The corresponding bits are denoted by x^, where the indices j and b refer to the bth bit in the binary label of the jth entry of the symbol vector s = [si S₂ • • • s_Mτ ]^τ. The associated complex baseband input-output relation is given by

25

(1) y = Hs + n

where H stands for the M_R X M_T channel matrix, y is the Mβ-dimensional received signal vector, and n is an i.i.d. circularly symmetric complex Gaussian distributed 30 M_β-dimensional noise vector with variance N₀ per complex entry.

35 5. SOFT-INPUT SOFT-OUTPUT SPHERE DECODING

5.1. Max-Log LLR Computation as a Tree Search

Coherent SISO detection for MIMO systems requires computation of soft-outputs in 5 the form of LLRs [HtB(B]

for all bits j = 1, 2, . . . , M_τ, b = 1, 2, . . . , Q, in the label x. Transforming (2) into a tree-search problem and, for example, using the sphere decoding algorithm, e.g., [FP85, SE94, BBW⁺05, SBB08], allows efficient computation of the LLRs. To this end, the channel matrix H is first QR-decomposed according to H = QR, where the M_R x MT matrix Q is unitary and the M_τ x M_τ upper-triangular matrix _j 5 R has real-valued positive entries on its main diagonal. Left-multiplying (1) by Q^H leads to the modified input-output relation

(3) y = Rs + Q^Hn

_„ where y = Q^y. Noting that Q^n is also i.i.d. circularly symmetric complex

Gaussian and using the max-log approximation on (2) leads to the intrinsic max-log LLRs [HtB(B]

where X^ _b and X^ _b are the sets of symbol vectors that have the bit corresponding to the indices j and b equal to —1 and +1, respectively.

In the following, we consider an iterative MIMO decoder as depicted in Fig. 1, where a soft-input soft-output MEvIO detector computes intrinsic LLRs according to (4) from the received channel matrix H, the signal vector y, and the a priori probabilities (a priori information) in the form of the a priori LLRs

and delivers soft-outputs in the form of extrinsic LLRs

to a subsequent SISO channel decoder. Slightly abusing our notation, we define the set that contains all a priori information belonging to a symbol vector, i.e., lA for j = 1, 2, . . . , M_τ and b = 1, 2, . . . , Q, as ZΛ

For each bit, one of the two minima in (4) corresponds to

(6) _λ ^MAP ^ -Uly - Rs^{MAP 2} - log P[s^MApT

N₀ which is associated with the MAP solution (i.e., the metric associated with the most likely transmitted vector) of the MIMO detection problem

(7) s^MAP = arg mm ( -U|y - Rs||² - log P[s] ) . ss6£θθ^MMrτ 1 ¹^o J

The other minimum in (4) can be computed as

where the (bit-wise) counter-hypothesis x^^p to the MAP hypothesis denotes the binary complement of the 6th bit in the label of the jth entry of s^MAP. With the definitions (6) and (8), the intrinsic max-log LLRs in (4) can be written (Vj, b) in com- pact form as I

We can therefore conclude that efficient max-log optimal soft-input soft-output MIMO detection reduces to efficiently identifying s^MAP, λ^MAP (Vj, b).

We next define the partial symbol vectors (PSVs)

^{■ ■ ■} SM_T ]^Γ and note that they can be arranged in a tree that has its root just above level j = M_τ and leaves, on level j = 1, which correspond to symbol vectors s. The binary- valued label vector associated with s^w will be denoted by x^(j). The distances

d(_S) = -U|y - Rs||² - logP[s]

in (6) and (8) can be computed recursively if the individual symbols S₃ (j = 1, 2, , . , M_T) satisfy P[s] = JT^ P[s₃]. In this case, we have

which can be evaluated recursively as d(s) = d_\, with the partial distances (PDs)

d₀ = d_J+1 + Ie₃ ] , j = M_τ, M_r - 1, . . . , 1,

, _<- the initialization d_Mτ+i — 0, and the distance increments (DIs)

(10)

N₀ ^yj - logpy .

The dependence of the PDs d₃ on the symbol vector s is only through the PSV s ω

20

Thus, the MAP detection problem and the computation of the max-log MAP intrinsic LLRs has been transformed into a path traversal in a graph (or tree in this particular example): PSVs and PDs are associated with nodes, branches correspond to DIs. For brevity, we shall often say "the node s^" to refer to the node corre- 25 sponding to the PSV Φ\ We shall furthermore use d(s^) and cϋ(x^) interchangeably to denote d₃. Each path from the root node down to a leaf node corresponds to a symbol vector s G O^Mτ . The solution of (6) and (8) corresponds to the leaf associated with the smallest metric in O^Mτ and X^_b ³'^b ' , respectively. The soft- input soft-output single-tree search sphere decoder (SISO STS-SD) uses elements of ³⁰ the Schnorr-Euchner SD with radius reduction [AEVZ02, BBW+05], briefly summarized as follows: The search along paths in the weighted graph (tree) is constrained to nodes which lie within a radius r around y and (tree) traversal is performed depth-first, visiting the children of a given node in ascending order of their

PDs. A node s^ with PD d₃ can be pruned along with the entire subgraph (subtree) 35 originating from this node, whenever the pruning criterion

(11) d_j ≥ r²

is met. In order to avoid the problem of choosing a suitable starting radius, we initialize the algorithm with r = oo and perform the update r² <— d(s) whenever a valid leaf node s has been reached. The complexity measure of BB -based MIMO . detectors usually corresponds to the number of nodes visited by the decoder including the leaves, but excluding the root. 0

6. DIRECT COMPUTATION OF EXTRINSIC LLRS

Due to the large dynamic range of LLRs, fixed-point implementations need to constrain the magnitude of the LLR values to enable fixed-point hardware implemen- - tation. Evidently, clipping of the LLR magnitude leads to a degradation in terms of error rate performance. It has been noted in [YeeO5, SBB08] that incorporating LLR clipping into the graph-traversal (or tree search) is very effective in terms of reducing complexity of max-log based soft-output sphere decoding. In addition, as demonstrated in [SBB08], LLR clipping, when built into the tree search also allows0 to tune the decoding algorithm in terms of complexity versus performance by adjusting the clipping level. In the soft-input soft-output case, we are ultimately interested in the extrinsic LLRs Lf _b and clipping should therefore ensure that

< L_max (Vj, b). Note that soft-output detectors usually derive intrinsic LLRs L^® _b first and then compute extrinsic LLRs after the BB procedure using (5). 5 In order to enable clipping of the extrinsic LLRs, the BB detector needs to employ am method to directly compute extrinsic LLRs in the graph-search procedure. To this end, we start by writing the extrinsic max-log LLRs as Λ MAP \ MAP _™MAP , 1

^Λi,& ~ ^λ ' ^xj,b - ⁺¹

\ MAP Λ MAP -MAP _ i

where the quantities \ MAP _ Γ A -MAP _ . I \ MAP , r A ,JVIAP _ I Λj,b + ^,b > ^Xj,b - ^{~ l} will be referred to as the extrinsic metrics. For the following developments it will be convenient to define a function /(•) that transforms an intrinsic metric λ with associated a priori LLR L^Λ and binary label x to an extrinsic metric Λ according to

With this notation, we can rewrite (13) more compactly as Λ)f₆ ^AP = / fc^AP, Lf_fi, xf_b ^AP) .

The inverse function of (14) transforms an extrinsic metric Λ to an intrinsic metric λ and is denned as

The key idea of the proposed method is to compute (12) instead of (9) directly within the BB detector, which requires to search for the MAP solution x^MAP, its metric λ^MAP, as well as all extrinsic metrics Λ^₆ ^AP (j = 1, 2, . . . , M_τ, b = 1, 2, . . . , Q). In order to obtain the pruning criterion or to compute branch-metrics, the functions (14) and (15) can be used to map intrinsic metrics to extrinsic metrics and vice versa.

To obtain (or approximate) the MAP solution (and its metric) as well as all counter-hypotheses, a variety of BB algorithms, linear detectors, and non-linear detectors exist [PNG03]. Prominent examples of BB detectors are the repeated tree- search (RTS) strategy [WG04] or the single tree-search (STS) strategy [SBB08]. In the following sections, the method is illustrated with the aid of the STS strategy.

7. EXTRINSIC LLR COMPUTATION WITH THE SISO STS-SD

We emphasize that BB-based MDVIO detection using the method described in the previous section directly leads to (clipped) extrinsic LLRs Lf _b (Vj, b) in (12) rather than to intrinsic ones (9).

7.1. List Administration

The main idea of the STS strategy is to use elements of the Schnorr-Euchner sphere decoder and to perform a search the subtree originating from a given node only if the result can lead to an update of either λ^MAP or of at least one of the Λ^°\ The SISO decoder employs the method described in Sec. 6 and maintains a list containing the current MAP hypothesis x^MAP, the corresponding metric λ^MAP, and all QM_T extrinsic metrics Λ¥₆ ^AP and performs list administration steps. Note that for hardware implementation, this list could be stored directly into a memory. The algorithm can be initialized with λ^MAP = Λ^^AP = oo (Vj, b) or with values that have been computed based on, e.g., previous detection runs or channel state information. Whenever a leaf with corresponding label x has been reached, the decoder distin- 5 guishes between two cases (list administration steps):

7.2. i) MAP Hypothesis Update

If d(x) < λ^MAP, a new MAP hypothesis has been found. First, all extrinsic metrics Λ^₆ ^AP for which x_jib = x™^AF are updated according to

A MAP , J- Λ MAP T A ,JVIAP \ Aj,b *^~ / ^^A > ^Lj,b> ^Xj,b J

followed by the updates λ^MAP <— d(x) and χ^MAP <— x. In other words, for each bit in the MAP hypothesis that is changed in the update process, the metric associated with the former MAP hypothesis becomes the extrinsic metric of the new counter- hypothesis.

7.3. ii) Extrinsic Metric Update

20 In the case where d(x) > λ^MAP, only extrinsic metrics corresponding to counter- hypotheses might be updated. For each j — 1, 2., . . . , M_τ, b = 1, 2, . . . , Q with X_jtb = xf^AP and whenever /(φc), Lf_b, xf^AP) < Λ$°\ the SISO STS-SD performs the update

7.4. Extrinsic LLR Clipping

In order to ensure that the extrinsic LLRs delivered by the algorithm indeed satisfy 30 < L_max (Vj, b), the following update rule

, λ Λ MAP + , L r _max \>, V VJj_A, oh

has to be applied after carrying out the steps in Case i) of the list administration 35 steps described before. We emphasize that for L,_mΑX = oo the decoder attains max- log optimal SISO performance, whereas for L_max — 0, only the hard-output MAP solution (7) is found. Note that the detector can also reduce the magnitude of at least a part of the

Λ^₆ ^AP or of λ^MAP whenever a new x^MAP is found, in order to impose constraints on the resulting extrinsic LLRs.

5 7.5. The Pruning Criterion

Consider the node s^ on level j corresponding to the label bits x^ {i = j, i + 1, . . . , M₇-, 6 = 1, 2, . . . , Q). Assume that the subtree originating from this node and corresponding to the label bits x^_b (i = l, 2, . . . , j — l, b = 1, 2, . . . , Q) has not been expanded yet. The pruning criterion for the node s^ along with its subtree is compiled from two sets, defined as follows:

1) The bits in the partial label

s^ are compared with the corresponding bits in the label of the current MAP hypothesis. All extrinsic metrics Λ^₆ ^AP with Xj_tb = x^_b ^AP found in this comparison, may be affected ^ when searching the subtree originating from s^\ As d(pό^) is an intrinsic metric, the extrinsic metrics Λ^₆ ^AP need to be mapped to an intrinsic measure according to (15). The resulting set of intrinsic metrics, which may be affected by an update, are given by

2) The extrinsic metrics Λ^₆ ^AP foτ i = l, 2, . . . , j — l, b = l, 2, . . . , Q corresponding 25 to the counter-hypotheses in the subtree of s^ may be affected as well. Correspondingly, we define

(19) Λ(x^(Λ)

| i < j,V&}.

30 In summary, the intrinsic metrics which may be affected during the search in the subtree emanating from node s^ are given by the union of the sets (18) and (19) according to Λ(x^ij)) = {en} = A₁ (x^ω) LJ .4₂(x^). The node s^ϋ) along with its subtree is pruned if the corresponding PD d(χ^) satisfies the pruning criterion

35 (20) d(x^ω) > max_, α,. This pruning criterion ensures that a given node and the entire subtree originating from that node are explored only if this could lead to an update of either λ^MAP or of at least one of the extrinsic metrics Λ^₆ ^AP.

8. SIMULATION RESULTS

The simulation results are for a convolutionally encoded (rate 1/2, generator polynomials [133_O 17I₀], and constraint length 7) iterative MIMO-OFDM system using M_τ = M_R = 4, 16-QAM symbol constellation with Gray labeling, 64 OFDM tones, a TGn type C channel model [E⁺04], and are based on a max-log BCJR channel decoder. One frame consists of 1024 randomly interleaved (across space and frequency) bits corresponding to one (spatial) OFDM symbol. The SNR in all simulations corresponds to the SNR per receive antenna. The number of using the detector (and the SISO channel decoder) corresponds to the number of iterations /. Fig. 2 shows the performance/complexity trade-off of the SISO STS-SD (using sorted QR decomposition) employing the method of incorporating extrinsic LLR computation in combination with extrinsic LLR clipping as described in the previous sections. Reducing the LLR clipping level also reduces the complexity of the decoder. Increasing the number of iterations I improves, in general, the SNR operating point. We emphasize however, that the trade-off between (tree-search) complexity and error rate performance can be adjusted with the extrinsic LLR clipping parameter L_max and the number of iterations /. This enables to choose (e.g., with the aid of the corresponding simulation results) the most efficient combination of L_max and / in order to optimize the performance/complexity trade-off of the iterative MIMO decoder.

9. FURTHER COMMENTS

9.1. Comment 1

Note that in the above example, we have used (20) as pruning criterion. However, in general, any suitable pruning criterion of the form

J3(d(x^), L^A, x« , x^MAP)

can be used, wherein in criterion B the contribution of a priori information Lf _b is, for all bits in x^(Λ, considered differently depending on if the bit j, b in x^ is equal to the bit j, 6 in χ^MAP is to be interpreted such that the influence of Lf _b on the result of B depends on if X_j:b — x^_b ^A¥ or X_jj, Φ ^^Ap ■ However, this is of course not applicable for the bits x_i}b for i — j — 1, j — 2, . . . , 1, b = 1, 2, . . . , Q. For those bits, different criteria depending on χ^MAP might be applied. 5

9.2. Comment 2

In the above example, we have computed (12) using a single-tree-search algorithm. However, in general, any suitable detector can be used to obtain or approximate x^MAP, its metric λ^MAP, as well as all extrinsic metrics Λgp (J = 1, 2, . . . , M_τ, b = 1, 2, . . . , Q). To this end, a second BB detector, which is functionally different from the first BB detector (e.g., uses a different pruning criterion or different distance increments) but might also share the same hardware, can be used. Possible BB algorithms to approximate x^MAP, its metric λ^MAP, as well as all extrinsic metrics .. A.γ_b ^AP (J — 1, 2, . . . , MT, b = 1, 2, . . . , Q) are, for example, the list sphere decoder [HtB03], M-algorithms [dJW05], K-best algorithms [WTCM02]. Furthermore, the MAP hypothesis and its counter-hypotheses can also be approximated using linear detection methods or non-linear equalizers (e.g., a decision feedback equalizer).

20 10. CONCLUSIONS

We have shown how extrinsic max-log LLRs can be computed within the branch- and-bound detection stage. The presented method enables clipping of extrinsic LLRs, which can significantly reduce the computational complexity of the underlying BB

„ - algorithm.

In this document, we provided an example for the application of the method to a soft-input soft-output single tree search sphere decoding algorithm. However, it is noted that the same method can also be performed within a variety of BB-based MIMO detection algorithms. In particular, the method is applicable to various vari-

30 ants of the sphere decoding algorithm.

While there are shown and described presently preferred embodiments of the invention, it is to be distinctively understood that the invention is not limited thereto but may otherwise variously embodied and practiced within the scope of the claims.

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Claims

C L A I M S

1. A method for generating extrinsic soft-outputs using a branch-and-bound detector in a MIMO system and using path traversal in a graph for identifying a multi- dimensional transmit vector x, said method comprising the steps of a) feeding a priori information L^A to the detector, with j and b together specifying a bit in said transmit vector and said a priori information comprising values L^A _b being indicative of a probability that said bit (j, b) is 1, b) traversing paths of the graph, each path representing a possible transmit vector, c) for at least part of the nodes x.^ of a path being traversed, checking if a pruning criterion B is met,

wherein d(x^) is a partial distance for the node,

_X ^MAP j_{s an es}t_imat_{e o}f _{a mos}t likely transmitted vector, d) and wherein in criterion B a contribution of a priori information L^A _b is, for all bits in

is equal to the bit j, b in x^MAP, e) and terminating the traversal of said path if said pruning criterion is met.

2. The method of claim 1 wherein the detector is a soft-input soft-output detector for multiple-input multiple-output systems.

3. The method of any of the preceding claims where the soft-input soft-output detector is a sphere decoder.

4. The method of any of the preceding claims comprising the calculation of said extrinsic soft-outputs Lf _b (Vj, 6) according to

wherein

_XUAP j_{s a} tø_t associated _with the bit j, b in x .¹MAP λ^MAP is a metric associated with the most likely transmitted vector, and Λ^_b ^AP is an extrinsic metric associated with a counter-hypothesis of χ¥_b ^AP and with L^A- _h.

5. The method of claim 4 where the detector stores x^MAP, λ^MAP and all Λ^₆ ^AP in a m meemmoorryv..

6. The methods of any of the claims 4 or 5 where the detector reduces the magnitude of at least a part of the Λ^₆ ^AP or of λ^MAP whenever a new χ^MAP is found.

10 7. The method of claim 6, where the Λ^₆ ^AP are being updated after finding a new λ^MAP or change in Λ^_b ^AP according to

Λ A M_j)6AP < .— _ m_m• / < A Λ _jM_bAP , λ X MAP

15 wherein L_max is an extrinsic log-likelihood ratio clipping parameter.

8. The method of any of the claims 4-7, where x^MAP, λ^MAP or at least parts of y^^MAP ^₆ being approximated using a second branch-and-bound detector, ™ a linear detector, or a decision feedback equalizer.

9. The method of any of the claims 4-8, wherein a list at least of said values x^MAP, λ^MAP, and Λ^_b ^AP is maintained by means of repetitive list administration steps

25 corresponding to

or

T ^A r^MApNl

wherein a function / maps intrinsic metrics to extrinsic metrics according to 35

^{/(λ) L} '^ = I A ₊ ^₁ x = ~l and said list administration steps are performed depending on a condition basing on at least said x, d(x), x^MAP, or Lf_b.

10. The method of any of the preceding claims where the detector is operated in iterations for computation of soft-outputs and where L_raax and a number of iterations / are chosen to optimize a performance/complexity trade-off of the detector.

11. Any of the preceding claims, where said pruning criterion B is

wherein Λ(pό^j^) is a set comprising a selection of the metrics λ^MAP using Lf _b as said step d).

12. The method of claim 11 where the said set A(^) corresponds to a union of the sets

A₁ (x^ω)

<T ) }

and

wherein a;,' ₆ is a bit associated with the bit j, b in x^ and a function / ^l that maps extrinsic metrics to intrinsic metrics according to

13. A device comprising means for carrying out the method of one or more of the preceding claims.