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`subset restriction would be signaled with a conventional bitmap, N =NH• Nv = 64 bits would be
`used.
`
`"Similar rows embodiment"
`
`In one embodiment, by using compressing of the CSR signalling, a scheme is designed
`
`5
`
`taking into consideration the hypothesis that precoders (k, l) with adjacent l-indices (i.e.
`(k, l 0 - 1), (k, l 0 ) and (k, l 0 + 1)) are likely to have the same restriction setting, meaning that if
`(k, l 0 ) is restricted , (k, l 0 + 1) is likely to be restricted as well and vice versa . The scheme works
`as follows :
`
`10
`
`First, a bitmap of NH bits are sent, indicating the codebook subset restriction for the
`"row" of precoders where l = 0 (c.f. Figure 4), i. e the precoders (k, l) = (0,0), (1,0), ... , (NH -
`1,0).
`
`Then , the codebook subset restriction for the second "row" of precoders, where l = 1 is
`sent. If the restriction is the same as for the previous row of precoders, a '1 ' is sent. If the
`
`restriction for this row differs from the restriction of the previous row, a 'O' is sent, followed by a
`
`15
`
`bitmap indicating the restriction for this row.
`
`The previous step is then repeated for each of the Nv "rows" of precoders.
`
`This embodiment is illustrated with an example, considering the codebook subset
`restriction setting illustrated in Figure 4, i.e. the restriction of precoders with indices (k, l) =
`(0,4), (3,5), ( 4,5), (7,4) should be signaled .
`For l = O:
`No precoders with l-index O should be restricted, therefore the bitmap '00000000' is
`
`20
`
`sent.
`
`25
`
`sent.
`
`sent.
`
`sent.
`
`30
`
`For l = 1:
`The restriction of this row is identical to the restriction of the previous row, the bit '1' is
`
`For l = 2:
`The restriction of this row is identical to the restriction of the previous row, the bit '1' is
`
`For l = 3:
`The restriction of this row is identical to the restriction of the previous row, the bit '1' is
`
`For l = 4:
`The restriction of this row is not identical to the restriction of the previous row, therefore
`
`the bit 'O' is sent. The bitmap indicating the restriction for this row should now be sent.
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`35
`
`Precoders (0,4) and (7,4) should be restricted. Therefore, the bitmap '10000001 ' is sent.
`For l = 5:
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`The restriction of this row is not identical to the restriction of the previous row, therefore
`
`the bit '0' is sent. The bitmap indicating the restriction for this row should now be sent.
`
`Precoders (3,5) and (4,5) should be restricted. Therefore, the bitmap '00011000' is sent.
`For l = 6:
`The restriction of this row is not identical to the restriction of the previous row, therefore
`
`5
`
`the bit '0' is sent. The bitmap indicating the restriction for this row should now be sent. No
`
`precoder should be restricted. Therefore, the bitmap '00000000' is sent.
`For l = 7:
`The restriction of this row is identical to the restriction of the previous row, the bit '1' is
`
`10
`
`sent.
`
`The string of bits to be signaled is thus
`
`0000000001110100000010000110000000000001', consisting of 39 bits. Generally, the number
`
`of bits required with this scheme is
`
`15
`
`20
`
`Nbits = M ·NH+ Nv - 1
`Where M is the number of times the rows change and a bitmap for a row has to be
`transmitted, M = 4 in the example. Analyzing the above expression, we note that 1 :::; M :::; Nv.
`This means that for some of the 2N = 2NwNv possible codebook subset restrictions , the number
`of bits required to signal the codebook subset restriction with this scheme is smaller than N,
`while for others, such as when M = N v , the number of bits required is larger than N.
`It should be noted that this is a small example for the sake of illustrating the
`embodiment. If a larger codebook is used, say NH = Nv = 30 , and M = 4 the number of bits
`required with this scheme would be Nbits = M ·NH+ Nv - 1 = 149 compared to N =NH· Nv =
`900 in the case of just transmitting the entire bitmap; this is hence a substantial reduction in the
`
`number of required bits.
`
`Finally, it is pointed out that all possible codebook subset restriction configurations can
`
`25
`
`be represented by this encoding/decoding scheme, thereby providing full flexibility.
`"Similar columns" embodiment
`
`In another embodiment, the scheme discussed in the previous embodiment is modified
`
`by instead taking into consideration the hypothesis that precoders (k, l) with adjacent k-indices
`(i.e. (k 0 - 1, l), (k 0 , l) and (k 0 + 1, l) ) are likely to have the same restriction setting, meaning
`that if (k 0 , l) is restricted, (k 0 + 1, l) is likely to be restricted as well and vice versa. The
`construction of the string of bits to be signaled would then work similarly as in the previously
`
`discussed embodiment, except that the precoders "columns" k will be used instead.
`
`In another embodiment an extra initial bit is inserted where '1' indicates that encoding is
`done under the assumption that precoders (k, l) with adjacent l-indices (i.e. (k, l 0 -
`1), (k, l 0 ) and (k, l 0 + 1) ) are likely to have the same restriction, hence the encoding is done row
`wise, whereas a '0' indicates that precoders (k, l) with adjacent k-indices (i.e. (k 0 -
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`1, l), (k 0 , l) and (k 0 + 1, l) ) are likely to have the same restriction setting , hence encoding is
`done column wise.
`
`In another embodiment an initial bit is inserted where '1' indicates that no precoders are
`
`restricted, a '0' indicates that some precoders are restricted and the '0' is followed by a number
`
`5
`
`of bits representing the codebook subset restriction .
`
`Accordingly, different "compression" techniques (whether based on similar rows ,
`
`columns, or otherwise) may be adopted for different groups of precoders in the same codebook,
`
`where the particular technique is indicated to the device so that the device can decode the
`
`signaling. Alternatively, the same "compression" technique may be adopted for each of the
`
`10
`
`groups of precoders, but the network evaluates different possible techniques to identify the one
`
`that provides the best compression and then adopts that approach (and indicates it to the
`
`device).
`
`Of course, the embodiments shown in Figure 2, and variations thereof, may be used for
`
`signaling a restricted subset of precoders in any given codebook, whether Kronecker structured
`
`15
`
`or not. Moreover, the signaling may be rank-specific, meaning that different signaling restricts
`
`different rank-specific codebooks.
`
`According to other embodiments shown in Figure 5, a method is implemented in a
`
`network node 10 (e.g., a base station) for signaling to a wireless communication device 14
`
`which precoders in a codebook are restricted from being used (e.g. , which Kronecker product
`
`20
`
`precoders are restricted). As shown, the method includes generating codebook subset
`
`restriction signaling that, for each of one or more groups of precoders, jointly restricts the
`
`precoders in the group, e.g., with a single signaling bit (Block 210). In at least some
`
`embodiments, this signaling (i) is rank-agnostic so as to restrict precoders irrespective of their
`
`transmission rank; and/or (ii) jointly restricts a group of precoders by restricting a certain
`
`25
`
`component that those precoders (i.e., the precoders in the group) have in common. Regardless,
`
`the method then includes sending the generated signaling to the wireless communication device
`14 (Block 220).
`
`Consider embodiments that jointly restrict a group of precoders by restricting a certain
`
`component that those precoders (i.e., the precoders in the group) have in common. Precoders
`
`30
`
`have a certain component in common if the precoders are derived from or are otherwise a
`
`function of that same component. In one embodiment, for example, a group of precoders W(b)
`
`that have a certain component b in common are jointly restricted by restricting that component
`
`b. Restriction of this component b may be signaled for instance in terms of one or more indices
`
`for the component (e.g., m where the component is indexed as bm or (k, l) where the
`
`35
`
`component is indexed as bk,l , with m, k, and l being indices for a Kronecker-structured
`
`codebook as described above) .
`
`Note that embodiments herein contemplate a precoder having one or more different
`
`"components" at any level of granularity (e.g., component(s) at a high level of precoder
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`factorability and/or component(s) at a lower level of precoder factorability). For example, a
`
`precoder may comprise one or more different components b at one level of granularity. At a
`
`finer level of granularity, though, each of these components b may in turn be derived from or
`
`otherwise be a function of multiple sub-components xH and x v such that b(xH,xv ). In this case,
`
`5
`
`a group of precoders W(xH,xv) that have a certain component xH or xv in common may be
`
`jointly restricted by restricting that component xH or xv. Restriction of this component x H or x v
`
`may be signaled for instance in terms of an index for the component (e.g. , k or l where the
`
`component xH is indexed as x~ and the component xv is indexed as xt, with xH and x v being
`
`horizontal and vertical beamforming vectors, respectively, and with k and l being indices for a
`
`10
`
`Kronecker-structured codebook as described above).
`
`In some embodiments, a precoder at one level of granularity consists of one or more
`
`different components that are referred to as one or more so-called "beam precoders". Each
`precoder Win this regard consists of one or more beamforming vectors b 0 , bi, ... , bx that are
`referred to as beam precoders. One or more embodiments herein jointly restrict a group of
`
`15
`
`precoders W that have a certain beam precoder in common, by restricting that beam precoder.
`
`With restriction of precoders Was a whole founded on restriction of one or more of their
`
`constituting beam precoders, these embodiments advantageously generate the CSR signaling
`
`in terms of beam-specific restrictions (i.e., restrictions of certain beam precoders), rather than in
`
`terms of precoder-specific restrictions (i.e. , restrictions on precoders Was a whole). In some
`
`20
`
`embodiments, the device 14 shall assume that a precoder Wis restricted if one or more of its
`
`beam precoders are restricted. In other embodiments, each beam precoder must be restricted
`
`for the device 14 to assume that the total precoder W is restricted.
`
`In one embodiment, a beam precoder is the beamforming vector used to transmit on a
`
`particular layer, where different scaled versions of that beamforming vector are transmitted on
`
`25
`
`different polarizations. Different layers are transmitted on different beam precoders. A precoder
`
`W in this case can be expressed as:
`w =a. [ ho
`]
`bL-1
`b1
`~L-1bL-1
`~oho ~1b1
`Here, W is a N x L precoder matrix, where N is the number of transmit antenna ports, L
`
`the transmission rank (i.e. the number of transmitted spatial streams), b 0 , b1, ... , bL-i are!!_ x 1
`2
`beamforming vectors (denoted beam precoders), ~ 0 , ~ i , ••• , ~L-i and a are arbitrary complex
`numbers. Another precoder W of the same codebook as W above can be expressed as:
`
`30
`
`W = a . [ b1
`b2
`]
`bL
`~LbL .
`~1b1 ~2b2
`For example, by signaling b0 , only the former precoder is restricted and by signaling b 1 both
`precoders will be restricted.
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`In some embodiments, the first!!_ antenna ports are mapped to antennas with one
`2
`
`polarization while the latter!!_ antenna ports are mapped to antennas with the same positions as
`2
`the first antennas, but with an orthogonal polarization. In such embodiments, for each column of
`
`W (i.e. the precoder for each spatial layer), a beam precoder h is transmitted on one
`
`5
`
`polarization and a scaled version of the same beam precoder <ph is transmitted on a second
`
`polarization. Such scaling may impact the phase, amplitude, or both the phase and amplitude of
`
`the beam precoder.
`
`In another embodiment, a beam precoder is the beamforming vector used to transmit on
`
`multiple different layers, where the layers are sent on orthogonal polarizations. In this case, a
`
`10
`
`precoder W can be expressed as:
`
`W = a . [ ho
`]
`ho
`ho
`(()oho
`(()1ho
`(()L-1ho
`Accordingly, it should be noted that the beam precoders for each spatial layer
`h 0 , h1, ... , hL-i may be different beam precoders, or, some subsets of the beam precoders may
`be identical, for example h 0 may be equal to h 1 .
`In yet another embodiment, a beam precoder is the beamforming vector used to transmit
`
`15
`
`on a particular layer and on a particular polarization. That is, a beam precoder may be defined
`
`in a slightly different way than the definition above. The definition of a beam precoder may for
`
`example allow different beam precoders to be transmitted on the different polarizations of the
`
`same layer, such as
`
`w = a . [ ho
`]
`h2
`h2L-2
`(()L-1h2L-1 ·
`(()oh1
`(()1h3
`In still another embodiment, the beam precoders may be defined by disregarding the
`
`20
`
`polarization as
`
`W = a· [h 0
`hL-1] .
`h 1
`Note that the beam precoders h 0 , h1, ... , hL-i may be chosen explicitly from a set of
`beam precoders (a codebook) or they may be implicitly chosen when selecting the (total)
`
`25
`
`precoder W from a codebook X. It should be noted that the selection of the (total) precoder W
`
`may be made with one or several PM ls. In the case where selection of the total precoder Wis
`
`made with several PM ls, the resulting beam precoders for each layer may be a function of only
`
`a subset of the PM ls or they may be a function of all PM ls.
`
`Irrespective of the particular way a beam precoder is defined, though, one or more
`
`30
`
`embodiments herein jointly restrict a group of precoders W that have a certain beam precoder in
`
`common, by restricting that beam precoder. That is, in some embodiments, codebook subset
`
`restriction (CSR) may be signalled based on the set of possible beam precoders h, instead of
`
`CSR signalled on the set of possible (total) precoders W. In some such embodiments, the
`
`device 14 shall assume that a precoder W is restricted if one or more of the beam precoders
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`h 0 , h 1 , ... , hL-i of each layer are restricted . In other such embodiments, each layers' beam
`precoder must be restricted for the device 14 to assume that the total precoder W is restricted .
`
`Consider a specific example for an STX codebook with transmission rank 2 . In some
`
`embodiments, this codebook is defined as shown in Figure 6 . Defined in this way, each
`
`5
`
`precoder W is formed in part from a beam precoder vm (note the notation shift from
`
`h 0 , h 1 , ... , hL-i to vm ). The beam precoder index mis the same for some precoders W, including
`for instance precoders whose subcodebook index i 2 is equal to 0, 1, 8, 9, 12 or 13 (since for
`those precoders m = 2i1 ). This means that those precoders W have the same beam precoder
`vm in common. Accordingly, some embodiments herein jointly restrict a group of precoders W
`
`10
`
`that have a particular beam precoder vm in common, by restricting that beam precoder vm, e.g. ,
`
`with a single bit. Restriction of this beam precoder vm may be signaled for instance in terms of
`
`index m (e.g., beam precoders indexed with a particular value of mare restricted) . Signaling in
`
`this case may constitute a bitmap, with different bits in the bitmap respectively dedicated to
`
`indicating whether or not different beam precoders are restricted from being used. For example,
`
`15
`
`signaling may constitute a bitmap of m values, with different bits in the bitmap respectively
`
`dedicated to indicating whether or not beam precoders indexed with different of m values are
`
`restricted from use.
`
`In alternative embodiments not shown in Figure 6, the beam precoder vm is replaced by
`
`beam precoder vk ,l, which is a Kronecker product of a vertical beamforming vector xv with index
`
`20
`
`k and a horizontal beamforming vector x H with index l. For example, as noted above, these
`
`beamforming vectors may comprise OFT vectors. Regardless, restriction of beam precoder vk ,l
`
`may be signaled in terms of the index pair (k, l). Signaling in this case may constitute a bitmap
`
`of (k, l) value pairs, with different bits in the bitmap respectively dedicated to indicating whether
`
`or not beam precoders indexed with different (k, l) value pairs are restricted from use.
`
`25
`
`Instead of such a bitmap, restriction of one or more beam precoders vk, l in some
`
`embodiments is jointly signaled in terms of a "rectangle" defined by two (k, l) value pairs:
`namely, (k 0 , l 0 ) and (k1 , l 1 ). In this case, beam precoders vk,l with indides k 0 < k < k 1 and
`l 0 < l < l 1 are restricted .
`As yet another alternative, restriction of one or more beam precoders vk,l in some
`
`30
`
`embodiments is signaled in terms of a bitmap of k values and/or a bitmap of l values. If signaled
`
`as only a bitmap of k values, the device in some embodiments assumes that any beam
`
`precoders vk ,l with certain k values are restricted, irrespective of those precoders' l values. If
`
`signaled as only a bitmap of l values, the device in some embodiments assumes that any beam
`
`precoders vk,l with certain l values are restricted, irrespective of those precoders' k values. If
`
`35
`
`signaled as both a bitmap of k values and a bitmap of l values, the device in some
`
`embodiments assumes that only beam precoders vk,l with certain (k , l) value pairs as
`
`collectively defined by those bitmaps are restricted.
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`That said, restrictions specified in term of k and/or l values may in some sense be
`
`deemed as restrictions at a finer level of granularity than even the beam precoders themselves.
`
`Indeed, as noted above, each beam precoder vk,z, is in some embodiments a Kronecker
`
`product of a vertical beamforming vector xv with index k and a horizontal beamforming vector
`
`5
`
`xH with index l. Accordingly, signaling the restriction as k and/or l values effectively amounts
`
`to restricting (sub)components xH or xv.
`
`Consider an example of these finer-granularity embodiments where codebook subset
`
`restriction is to be applied to beam precoders with l values of 3 or 4. If this configuration of
`codebook subset restriction would be signaled with a conventional bitmap, N =NH• Nv = 64
`bits would be used. By contrast, the scheme in these finer-granularity embodiments consider
`
`10
`
`restriction of entire precoder "rows", i.e all precoders that are formed from beam precoders with
`
`the same l-index is either turned on or off. To signal the codebook subset restriction in this
`example, therefore, the bitmap '00011000' of l values, consisting of Nv = 8 bits, may be sent.
`With this scheme, a large reduction of the number of bits required to signal the codebook subset
`
`15
`
`restriction is seen. However, not all of the 2N possible codebook subset restrictions may be
`
`signaled .
`
`In a similar embodiment, the restriction is applied on the precoder "columns" k and the
`
`codebook subset restriction is signaled with a NH bit long bitmap, indicating restrictions of entire
`
`precoder "columns".
`
`20
`
`In another embodiment an extra initial bit is inserted where '1' indicates that encoding is
`
`done as above "row wise", whereas a '0' indicates is done "column wise".
`
`In yet another embodiment, the device 14 shall assume that a precoder Wis restricted if
`
`both the vertical and the horizontal precoder in the Kronecker structure are restricted. If only one
`
`of the vertical and horizontal precoders are restricted, then the device 14 shall not assume that
`
`25
`
`the resulting precoder after Kronecker operation is restricted.
`
`Thus, one or more embodiments herein advantageously exploit a codebook's Kronecker
`
`structure to generate the signaling of Figure 5 in terms of indices k, l, and/or m. In some
`
`embodiments, for example, the signaling is generated to jointly restrict, e.g., with a single bit, a
`
`group of precoders that either (i) have the same value of index k; (ii) have the same value of
`
`30
`
`index l; or (iii) have the same pair of values for indices (k , l).
`
`In some embodiments, signaling that jointly restricts a group of precoders by restricting a
`
`certain component (e.g., beam precoder) that those precoders have in common is rank(cid:173)
`
`agnostic. That is, the signaling jointly restricts the group of precoders regardless of the
`
`35
`
`precoders' transmission rank (i.e., regardless of which rank-specific codebook they belong to).
`For example, embodiments that restrict a single beam precoder h0 can be extended so that all
`precoders across all ranks that contain the restricted beam precoder h 0 are restricted. Hence,
`all precoders across all ranks that contain a certain beam precoder h0 is a precoder group that
`can be restricted jointly. According to some embodiments, therefore, an advantage of signaling
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`CSR based on beam precoders is that one does not need to signal a separate CSR for
`
`precoders with different rank (precoders with different rank are restricted with the same CSR) .
`
`This reduces signaling overhead .
`
`Signaling that jointly restricts a group of precode rs by restricting a certain component
`
`5
`
`that those precoders have in common also proves effective for restricting precoders that
`
`transmit in whole or in part towards certain angular pointing directions. Indeed, according to
`
`some embodiments herein, the network node 10 jointly restricts a group of precoders that
`
`transmit at least in part towards a certain angular pointing direction, by restricting a certain
`
`component (e.g ., beam precoder) which has that angular pointing direction. In this way, the
`
`10
`
`network node 10 avoids transmitting energy in a certain direction, by signaling to the device 14
`
`by means of CSR that the device 14 shall not compute feedback for that particular direction.
`
`More specifically in this regard, when each precoder Wis formed from multiple beam
`
`precoders, the precoder Win some sense has multiple angular pointing directions
`
`corresponding to the angular pointing directions of its constituent beam precoders (where each
`
`15
`
`beam precoder has its own azimuth and zenith angular pointing direction for example). In
`
`another sense, though, the precoder W has an overall angular pointing direction that is a
`
`combination (e.g. , average) of its beam precoders' respective directions. By restricting beam
`
`precoders that have certain angular pointing directions, embodiments herein effectively restrict
`
`precoders that transmit at least in part in those directions, and do so with reduced signaling
`
`20
`
`overhead.
`
`As an example, a set of rank-1 precoders with the same angular pointing direction but
`
`with different polarization properties, such as the whole set of rank-1 precoders
`
`[ej~~bJ [ej~~bJ [ej~~bJ
`may be restricted by restriction signaling of a single beam precoder b 0 . That is, when a
`restriction is signaled for a certain beam precoder, the restriction applies implicitly to all
`
`polarization phases of the signaled beam. Hence, the group of rank-1 precoders exemplified
`
`above is associated with a single CSR bit and is thus jointly restricted. This reduces device
`
`complexity and CSR signaling overhead, since only the beam direction needs to be signaled.
`
`In another example, the set of rank-1 precoders
`
`[ej~~bJ. [ej~\J [ej~~bJ.
`may be jointly restricted by restriction signaling of a single beam precoder b 0 . Hence, the group
`of rank-1 precoders exemplified above is associated with a single CSR bit and is thus jointly
`
`25
`
`30
`
`restricted.
`
`Restriction of precoders with certain angular pointing directions can also be
`
`35
`
`accomplished by specifying restrictions in terms of certain k and/or l values. This is illustrated
`
`with reference to Figure 7, which illustrates the angular beam pointing directions of rank-1
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`precoders in a codebook according to one example. In this example, the network node has a
`
`4x4 antenna array where no mechanical downtilt is used. The Kronecker codebook consists of 8
`vertical and 8 horizontal precoders, i.e. NH = N v = 8. In this example, codebook subset
`restriction is applied to restrict beams with pointing directions in the zenith interval [80 °, 100°]
`
`5
`
`(the interval is illustrated with dotted lines). That is, codebook subset restriction is applied in the
`angular interval 80 ° < 0 < 100°, such that the precoders with indices l-index 3 and 4 are
`restricted. The restricted beams are illustrated with an 'o' while the unrestricted beams are
`
`illustrated with an 'x'. The beam index kin the horizontal codebook and l in the vertical
`
`10
`
`codebook is written next to the beams as (k, l). To signal the codebook subset restriction in this
`example, therefore, the bitmap '00011000' of l values, consisting of Nv = 8 bits, may be sent.
`With this scheme, a large reduction of the number of bits required to signal the codebook subset
`
`restriction is seen.
`
`In another embodiment, the device 14 shall assume that a precoder is restricted if both
`
`the vertical and horizontal precoder in the Kronecker structure are restricted. This allows to
`
`15
`
`restrict a rectangular "window" of beam former pointing angles as seen from the network node
`
`10.
`
`This can also be accomplished by signaling the restriction as a "rectangle" of precoders
`defined by the index pairs (k 0 , l 0 ) and (k 1 , l 1 ). With this scheme, precoders with indices
`k 0 < k < k 1 and l 0 < l < l 1 are restricted.
`Component-based restriction of a precoder group is just one example of embodiments
`
`20
`
`that provide for rank-agnostic CSR signalling. Other embodiments herein also provide for such
`
`rank-agnostic signaling. For example, some embodiments herein generate signaling to jointly
`
`indicate that a group of precoders which transmit in whole or in part in certain angular pointing
`
`direction(s) are restricted, by generating the signaling to (explicitly or implicitly) indicate those
`
`25
`
`angular pointing direction(s). The signaling may for instance specify an angular area or interval
`
`that is restricted, in terms of one or more angular parameters. This restriction may concern the
`
`angular pointing direction of a precoder as a whole, or the angular pointing direction of any
`
`beam precoder forming the precoder.
`
`30
`
`In one embodiment, the angular area or interval may be represented by angular points
`(¢ 0 , 0 0 ) and (¢ 1 , 0 1 ) , spanning a rectangle in the angular domain. Here, ¢ and 0 are the
`azimuth and zenith angles with respect to the eNodeB respectivly. Multiple such rectangular
`
`areas may be signaled although the present embodiment focuses on the case of a single
`
`rectangular area for simplicity. The device 14 may then calculate the angular pointing directions
`
`of the precoders in the codebook and compare them to the restricted angular area to derive the
`
`35
`
`codebook subset restriction. The device 14 may need some additional information regarding
`
`what to assume about the transmitter antenna array (which does not need to correspond to the
`
`actually used antenna array) to be able to calculate the pointing directions of the precoders.
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`Consider an exemplary embodiment where the (sub)-codebooks of the Kronecker codebook
`consist of DFT-precoders, i.e
`The horizontal codebook can be expressed as
`
`/ 2
`x~ = 1 e n MhQ"
`
`ti<+<lh
`
`[
`
`.2 (Mh-t )k+<lh ]
`- • · e 1 n M hQ"
`
`T
`
`, k = O, ... , Mh Qh - 1, where Qh is an integer horizontal
`
`5
`
`oversampling factor and Llh can take on value in the interval Oto 1 so as to "shift" the beam
`pattern (Llh =0.5 could be an interesting value for creating symmetry of beams with respect to
`
`the broadside of an array).
`
`The vertical codebook can be expressed as xi = 1 e 1
`
`[
`
`·2 11+<1v
`n MvQv
`
`·2
`• •• e 1
`n
`
`( Mv- l)l+<lv]T
`MvQv
`
`, l =
`
`0, ... , MvQv - 1, where Qvis an integer vertical oversampling factor and Liv is similarly defined as
`above.
`
`10
`
`The pointing direction of precoder (k, l) can be calculated by first calculating the pointing
`
`angle with respect to the broadside of the antenna array:
`
`k +LI_ QvMv
`~
`2
`0 = acos(
`)
`d v QvMv
`
`l +LI _ QhMh
`2 ~ )
`¢ = asin(
`dHQhMhsin(0)
`
`15
`
`20
`
`Where dv and dH
`
`is the vertical and horizontal antenna element spacing of the array, in
`
`wavelengths, respectively. The mechanical downtilt angle f3 is taken into account in order to
`
`calculate the actual beam pointing angles as:
`<p = L(cos( 1J) sin( 0) cos(-{3) - cos( 0) sin(-/3) + j sin( 0) sin( 0))
`0 = acos( cos( <P) sin( e) sin(- /3) + cos(- /3) cos( li))
`The device 14 needs to be signaled the additional information dH, d v and f3 to be able to
`
`calculate the beam pointing direction of the precoders in the codebook. It is assumed that the
`
`device 14 already knows the parameters Qv , Mv, Qh, Mh and LI as part of the codebook structure.
`The set of parameters ¢ 0 , 00 ,¢1 , 01 , dH, d v,/3 thus parameterizes the codebook subset
`restriction in this embodiment. When signaling said parameters, several strategies may be used.
`In one embodiment, each parameter is uniformly quantized with a number of bits, over a
`predefined interval. An example is given in the table below.
`
`Parameters
`
`¢0, 00,¢1, 01
`
`dH,dv
`/3
`
`Interval
`
`Quantization bits
`
`[0,180) [deg]
`
`(0,2)
`
`(-30,30) [deg]
`
`22
`
`6
`4
`
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`In this embodiment, the number of bits required to signal the codebook subset restriction
`
`is 38. Note that this is independent of the codebook size.
`
`In another embodiment, each parameter may take a value from a fixed set of possible
`
`values. Each possible value of the parameter is encoded with a different number of bits
`
`5
`
`depending on e .g. the perceived likelihood of the parameter taking that value . For example, the
`
`horizontal array element spacing dH may be encoded as follows
`
`V
`
`Bi
`
`5
`
`alue
`
`ts
`
`0.
`
`1
`
`8
`
`1
`
`0 .
`
`0
`
`65
`
`0.
`
`0
`
`1
`
`0
`
`4
`
`0
`
`2
`
`0
`
`75
`
`0 .
`
`0
`
`011
`
`010
`
`001
`
`0001
`
`0000
`
`In this embodiment, the encoding of dH was designed to take into account dH = 0.5 is a
`common value for horizontal antenna element separation , thus encoding this value with a low
`
`10
`
`number of bits. Other, less common, values are encoded with a larger number of bits. Note that
`
`the encoding of dH in this embodiment constitutes a uniquely decodable code.
`
`In another embodiment, some of the parameters are uniformly quantized with a number
`
`of bits over a predefined interval, while other parameters are encoded with a different number of
`
`bits as in the previous embodiment.
`
`15
`
`In some other embodiments , different sets of parameters relating to the restricted
`
`angular area may constitute the parameters that define the codebook subset restriction . In one
`:-;:; 0 < 01 is restricted , and thus , 00 , 01 may be sent.
`such embodiment, only a zenith interval 0 0
`In another such embodiment, the restriction is only an azimuth interval </Jo :-;:; </J < ¢ 1 . In yet
`another such embodiment, the angle interval may be open-ended , i.e. </J < ¢ 1 constitutes the
`restriction.
`
`In other embodiments, parameters relating to the antenna array such as dH , dv and I.JI
`
`are not a part of the codebook subset restriction parameters , instead they may be already
`
`known to the UE or the UE assumes a default value of said parameters and the eNodeB
`chooses restriction angles (</Jo, 0 0 ) and (</Jv 01 )
`in such a way that the intended precoders are
`restricted when the UE calculates the restriction based on the default values of said parameters ,
`
`where the default values of said parameters may differ from the actual value of said parameters.
`
`In other embodiments, more parameters may be included in the codebook subset
`
`restriction parameters. In one such embodiment, the roll angle y of the antenna array may be
`
`20
`
`25
`
`included in the codebook subset restriction parameters.
`
`30
`
`In view of the above modifications and variations, one recognizes that there are many
`
`ways that the CSR signaling can jointly restrict precoders in a group. The signaling can be rank(cid:1