Patent Application: US-201113995766-A

Abstract:
a process selects a precoding matrix index in a multiple in multiple out receiver used in a wireless communications system including a base station communicating with user equipments through a downlink and uplink channel . the base station applies a precoding on the transmit symbol vector based on a matrix selected from a set of predefined matrices and identified by a pmi index computed by the ue and forwarded to the base station via the uplink . the process includes estimating the mimo channel matrix h of a given set of resources blocks comprising received symbol vectors , estimating the variance σ 2 of the additive noise , and computing for each particular matrix comprised within the set of predefined matrices a cost function representative of the orthogonality of the matrix mimo channel matrix h . the process further includes comparing the values of the cost function and transmitting to the base station the index corresponding to the matrix corresponding to the best conditioned mimo channel matrix according to the comparison of the values .

Description:
the process which will be described hereinafter can be embodied in a wide number of applications . clearly , any ofdm standard supporting mimo spatial - multiplexing mode , e . g . ieee 802 . 16 , ieee 802 . 11 , 3gpp lte and 3gpp lte - a , can take advantage of the process described below . more particularly , the invention is particularly advantageous in the case of a large number of antennas and consequently in the case of the 3gpp lte - a standard . the process which will be described below with details is particularly useful for decreasing the complexity of a lattice reduction - aided ( lra ) detector which achieves high efficiency . indeed , it has been discovered by the inventors that lattice reduction - aided ( lra ) detection can be advantageously combined with a closed loop precoding technique , associated with one new precoding matrix index ( pmi ) selection criterion having the effect of improving the conditioning of the channel matrix in the perspective of the lra computation . to achieve this , the pmi selection mechanism is non longer based on the computation of the sinr ( as in the conventional capacity - selection criterion ( c - sc )), but is based on a new parameter which is representative of the conditioning of the channel matrix , in other words its orthogonality . in one particular , embodiment , the pmi selection mechanism is based on the so - called orthogonal deficiency parameter which shows great interest since it is strongly cheaper to compute than the condition number . therefore , a significant reduction of both the mean and maximal computational complexity of the lr mechanism can be expected and near - optimal detector performance can be achieved at an expected polynomial computational cost in cl case . as presented in the following , both la and sa computational complexity ubs can be decreased with an appropriate selection criterion . for the sake of clarity , theoretical considerations of the lra mechanism will be introduced ( i ), prior to the description of one particular embodiment of a process of selection of the pmi to be used in a closed loop precoding technique . the optimal maximum likelihood ( ml ) detector can be efficiently approximated by the use of several techniques such as lattice reduction aided detectors ( linear or not ), commonly referred as near - ml techniques . these detection schemes have been widely studied in the open - loop ( ol ) case , in term of computational complexity and performance while the cl case has been neglected . in term of uncoded bit error rate ( ber ) performance , the lra techniques have been shown to be near - optimal for a polynomial computational complexity . various lr algorithms have been proposed . in this patent proposal , the popular lenstra - lenstra - lovász ( lll ) algorithm ( la ) [ 2 ] and the more recent seysen algorithm ( sa ) [ 2 ] have been considered . while it classically reads : y = hx + n , where x ∈ n t and y ∈ n r denote the system input and output respectively , h ∈ n r × n t the channel matrix and n ∈ n r the awgn , the equivalent system model can then be rewritten : any lattice reduction ( lr )- aided ( lra ) detector principle lies in the consideration of a reduced channel matrix { tilde over ( h )}= ht . consequently , the introduction of the transformed signal z = t − 1 x , where { tilde over ( h )}∈ n r × n t denotes the reduced lattice generator matrix and t ∈ n t × n t the transformation matrix that has to be unimodular by definition , offers an advantage in the use of classical linear equalizers . in order to further introduce the useful vocabulary , the notation is defined as the set of complex integers such that = + with i 2 =− 1 , and the vector x is withdrawn independently from a quadrature amplitude modulation ( qam ) ξ . by discrediting in a first time any precoding step at the transmitter , let us only consider the lra detectors problematic in reception . in particular , the simplified block - diagram of a lra - zero forcing ( zf ) is depicted in fig2 . the quantization operation to the n t - th dimensional integer lattice , q ξ n t {•} the mapping of the estimates onto the corresponding symbols belonging to the ξ n t constellation and { tilde over ( x )} the estimation of the transmit signal . in order to quasi - achieve the full diversity in reception , various lr algorithms have been proposed . let us evoke the optimal ( the orthogonality is maximized ) but with exponential computational complexities minkowski and korkine - zolotareff algorithms . it has been shown that these solutions are only feasible in the 2 × 2 mimo case , which does not match with lte requirements . as an alternative , the widely popular la can approach the optimal performance while having a polynomial complexity in mean [ 2 ]. more recently , the sa has been presented as an alternative that offers better performances but for a higher computational complexity [ 2 ]. the la transforms an input basis h into a lll - reduced basis { tilde over ( h )}. it consists in a local approach that lies on satisfying two conditions of orthogonality and norm reduction , respectively : is a factor selected to achieve a good performance / quality trade - off [ 4 ]. the parameter is chosen as as commonly suggested , and { tilde over ( h )} i ={ tilde over ( h )} i − σ j = 1 i − 2 {[ μ i , j ] h j }. for sake of vocabulary , a basis that respects the condition ( 1 ) is said to be lovász δ — reduced and the condition ( 3 ) is said to size - reduced . the sa consists in a global approach that lies on the minimization of the seysen orthogonality measure : s ( { tilde over ( h )} )= σ i = 1 n t ∥{ tilde over ( h )} i ∥ 2 ∥{ tilde over ( h )} i # ∥ 2 , both the la and the sa have been briefly presented , their performance and subsequently their ber performance with many detectors have been introduced in several publications and make the la algorithm more convenient for implementation than the sa . consequently , the la is particularly considered in the following of the patent proposal and some algorithmic details such as some optimizations will be further presented . let us introduce the qr decomposition ( qrd ) of h that reads h = qr , where the matrix q ∈ has orthonormal columns and r ∈ is an upper - triangular matrix with real diagonal entries . it has been shown that the qrd outputs of h are possible starting points for the la , and it has been introduced [ 2 ] that the sorted qrd ( sqrd ) provides better starting points since it finally leads to a significant reduction of the mean computational complexity and of the corresponding variance . also , another classical result consists in directly considering the complex la that offers an average complexity saving of nearly 50 % compared to the straightforward real model system extension with negligible performance loss . this algorithm will be considered , unless otherwise indicated . through these points , the computational complexity upper bound ( ub ) has been shown [ 2 ] to be distinguished between the pre - processing step : c sqrd = 10 n r n t 2 − 4 n r n t − 1 . 5 n t 2 + 1 . 5 n t , this is the key point since its estimation is a difficult task . in particular , the number of iterations depends on the condition number of the channel matrix [ 5 ] and is consequently unbounded . nevertheless , the expected k ( and consequently the expected total computational complexity ) has been shown to be polynomial : e ⁢ { k } ≤ n t 2 ( log δ ⁡ ( n t n r - n t + 1 ) + 2 . 240 log e ⁢ t + n t , as a conclusion , the worst - case computational complexity in the open loop ( ol ) case is exponential in the number of antennas . this restrictive aspect may be overstepped though the consideration that the computational complexity in mean is polynomial in the number of antennas . this way , a thresholded version of the algorithm offers convenient results . any modification or consideration aiming at bounding the computational complexity of any lr algorithm is essential for supporting the interest of all a family of lra detectors . it will now be described with reference to fig8 , one particular embodiment of a process for selecting the pmi index to be reported in uplink to the base station . the process starts with a step 100 wherein the mimo channel matrix h is estimated . generally speaking , channel estimation is well known by the skilled man and will not be further elaborated . it suffices to recall that the estimation of the channel is based on the use of so - called reference signals ( or pilots ) which , when periodically transmitted — allows the user equipment ( ue ) for performing the estimation of the channel matrix . furthermore , it should be noticed that the channel estimation can be performed on one particular resource block or , alternatively , on a sequence of consecutive resources blocks in accordance with different parameters . then , in a step 200 , the process proceeds with the computation , for each particular matrix comprised within said set of predefined matrix ( assumed to be known at both the base station and the ue ), a cost function fi ( wi , h ), depending on the channel ( estimated in step 100 ) and any tested precoding matrix ( wi ). step 200 thus entails the computation of a sequence of fi values , with i varying from 1 to n ( assuming that the given codebook comprises n distinctive matrices ). in the conventional so - called capacity - selection criterion ( c - sc ), it is the signal to interference plus noise ratio snri — depending on wi , h , σ 2 n — which is computed for each particular matrix composing the codebook , and the selection of the higher value of the sinri returns the value of the index corresponding to the maximal capacity . the invention deviates from such known mechanism ( and particularly recommended by the 3gpp standard ) by using a different cost function which advantageously combine with a lra based mimo receiver , the new cost function only depending on h and wi — more particularly depends on w i h — and no longer being related to the signal to noise ratio . the new cost function which is proposed as an alternative to the recommended standard snri mechanism , is now based on a parameter which is closely related to the orthogonality of the matrix hw i , such as for instance the condition number . in particular , the cost function is chosen so as to be maximized or minimized with the orthogonality of the matrix hw i however , it should be noticed that the condition number is generally complex to compute and requires a significant amount of digital processing resources . in one very advantageous embodiment , the process uses a different cost functions , is which is based on the so - called orthogonal deficiency ( od ) which is a parameter defined in algebra and also representative of the orthogonality of the matrix wh . o ⁢ ⁢ d ⁡ ( w ⁢ ⁢ h ) = 1 - det ⁡ ( h h ⁢ h ) ∏ i = 1 n t ⁢ ⁢  w ⁢ ⁢ h i  2 since the general expression ( wh ) h wh = hw h wh clearly rewrites h h h , due to the unitary criterion in the codebook design . the od parameter is easier to compute than the condition number , thus reducing complexity of the receiver . when the process has completed the computation of the cost function for all matrices included in the predefined codebook , the process then proceeds to a step 300 wherein the value of the cost function fi showing the best conditioning is being determined . in the particular case of the orthogonal deficiency , the process proceeds with the determination , in step 300 , of the minimum value among all values of odi ( hw i ) being computed . once identified , the process proceeds to a step 400 wherein the corresponding index is returned to the base station through uplink 2 for the purpose of determining the proper precoding matrix to be used by the latter base station . the cumulative density function ( cdf ) of the od is depicted in fig3 in the ol case , and in the cl case for both ml - sc and c - sc in a 2 × 2 ( a ) and a 4 × 2 ( b ) mimo precoding schemes . it can be noticed that an appropriate precoding bounds strictly below 1 the od of the effective channel in the case of a 4 × 2 mimo system , by noting that the bound depends of the used codebook and of the selection criterion . as depicted in fig5 ( left ), there is no more bounding of the od strictly below 1 in 2 × 2 mimo precoding scheme , i . e . its maximal value by definition is reached . also , it must be noted that the od bounds depend on the snr in the c - sc case only . another promising point lies in the observation that this bound does not depend on the snr in the case of the ml - sc , which offers an advantage over sphere decoding - like techniques . in particular : since the od criterion and the condition ( 1 ) in the lll - based lr algorithm ( namely the orthogonality criterion ) are closely linked , the skilled man would expect that a precoding step prior to the lr step would induce a promising computational complexity reduction , at least in mean . the cdf of the od is depicted in fig5 in the ol case , and in the cl case for both ml - sc and c - sc and both la and sa for a complex 2 × 2 ( a ) and a 4 × 2 ( b ) mimo precoding schemes . fig5 aims at showing that the precoding step not only offers a computational complexity reduction of the lr algorithm . the performance in term of od is also improved compared to the ol case , which shows the interest of associating both lr and precoding that are two different while complementary steps . more accurate considerations are offered in table 1 , where the expected and maximum computational complexities for both la and sa are given for 10 6 monte - carlo simulations , keeping in mind that la as well as sa is independent of snr ( only of the channel realization ). results are given with the following hypothesis : a real product requires 1 mul , a real addition requires 0 mul , a real division requires 16 mul and a real square root requires 32 mul . for the la , the computational complexity gain compared to the ol case is 26 % and 0 % in mean for c - sc and ml - sc respectively . for the sa , the gain is 10 % and 0 % in mean for c - sc and ml - sc respectively . there is no gain for the algorithm ub for both la and sa and whatever the sc , which is consistent to aforementioned highlights . consequently , there is no advantage in the use of a precoding step concerning the lr computational complexity with the 2 × 2 mimo precoding scheme . in fig5 , uncoded ber performances are plotted for both ol and cl with the appropriate sc as a function of the snr , with 10 7 monte - carlo simulations per snr value . the figure depicts the ml detector and the mmse equalizer as references . these classical performance results are compared to the lra mmse extended [ 1 ] equalizer performance . it can be observed that the lra detection schemes achieve full diversity in both ol and cl with a snr offset that depends on the employed detector . similarly to what has been previously done , the expected and maximum computational complexities for both la and sa are given in table 2 for 10 6 monte - carlo simulations . for the la , the computational complexity gain compared to the ol case is 29 % and 21 % in mean for c - sc and ml - sc respectively . for the sa , the gain is 29 % and 21 % in mean for c - sc and ml - sc respectively . for the la , the computational complexity ub gain compared to the ol case is 58 % for the c - sc . for the sa , the ub gain is 42 % for the c - sc . consequently , there is an advantage in the use of a precoding step on the lr computational complexity 2 × 2 mimo precoding scheme with the 4 × 2 mimo precoding scheme ; the ub has been importantly decreased , which is an essential aspect for implementation that confirms that the lra detectors offers promising perspectives in the achievement of near - optimum performances for a low computational complexity . in fig7 , uncoded ber performances are plotted for both the ol and the cl with the appropriate sc as a function of the snr , with 10 7 monte - carlo simulations per snr value . the figure depicts the ml detector and the mmse equalizer as references . these classical performance results are compared to the lra mmse extended equalizer performance . it can be seen that the lra detection schemes achieve full diversity in both ol and cl with a snr offset that depends on the employed detector . the precoding interest in term of performance is particularly visible is this case due to the increased channel capacity . the main advantage in the use of lra techniques , to which this invention relates , relies in providing quasi - optimal detection performances and an advantage over competition . while the expected computational complexities of all the aforementioned classical lr algorithms has been shown to be significantly decreased , the main advantage of the invention lies in exhibiting the maximal computational complexity decrease with the 4 × 2 mimo precoding scheme ; it is an essential aspect for the hardware calibration that can be done more advantageously in cl , with no performance loss , and with a reduced complexity ; the lra detectors offers promising perspectives in the achievement of near - optimum performances for a reduced computational complexity d . wuebben , r . boehnke , v . kuhn , and k .- d . kammeyer , “ near - maximum - likelihood detection of mimo systems using mmse - based lattice reduction ”. vol . 2 , pp . 798 - 802 , 2004 . l . barbero , t . ratnarajah , and c . cowan , “ a comparison of complex lattice reduction algorithms for mimo detection ”, acoustics , speech , and signal processing , international conference on , pp . 2705 - 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