US20160365902A1 - Method and apparatus for channel estimation in massive mimo systems with dynamic training design - Google Patents
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/0413—MIMO systems
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/0413—MIMO systems
- H04B7/0417—Feedback systems
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B17/00—Monitoring; Testing
- H04B17/30—Monitoring; Testing of propagation channels
- H04B17/309—Measuring or estimating channel quality parameters
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
- H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
- H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
- H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
- H04B7/0621—Feedback content
- H04B7/0634—Antenna weights or vector/matrix coefficients
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
- H04B7/0686—Hybrid systems, i.e. switching and simultaneous transmission
- H04B7/0691—Hybrid systems, i.e. switching and simultaneous transmission using subgroups of transmit antennas
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/0204—Channel estimation of multiple channels
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/0224—Channel estimation using sounding signals
Definitions
- the present invention generally relates to channel estimation for a massive multi-input multi-output (MIMO) communication system.
- MIMO massive multi-input multi-output
- the present invention relates to such channel estimation with reduced computation requirements.
- massive MIMO communications Due to various advantages such as a high data-transmission rate, a high beamforming gain and a high spatial resolution, massive MIMO communications have attracted considerable interest for future deployment in mobile communication systems.
- a transmitter In a massive MIMO system, a transmitter has a very large number of transmit antennas, e.g., greater than 100.
- the large number of transmit antennas often leads to a high computation requirement and a need for a lot of training resources, e.g., orthogonal time/frequency resource, in channel estimation. It is desirable to reduce these demands in operations in mobile communication systems.
- US20130182594 discloses a reduced-complexity channel-estimation technique by grouping the transmit antennas into groups for training. By reducing the number of antennas for estimation in each group, channel estimation requires less computation. However, spatial correlations are not taken into account to improve accuracy in channel estimation. Reduced-complexity techniques disclosed by US20130272263 and US20140254702 also have an estimation-accuracy issue since channel correlations are not taken into account.
- U.S. Pat. No. 8,837,621 teaches transmitting pilot reference signals on only a subset of antennas and using spatial interpolation to obtain channel estimates for other antennas. However, high estimation error results when spatial correlations among the antennas are not adequately high.
- An aspect of the present invention is to provide a method for estimating a massive MIMO channel on which a first communication device having plural transmit antennas communicates with a second communication device having a single receive antenna.
- the massive MIMO channel has a channel covariance matrix that characterizes spatial correlations among the transmit antennas.
- the first communication device partitions the transmit antennas into plural antenna groups with each comprising a subset of the transmit antennas such that a pre-determined level of channel-estimation accuracy is attainable.
- For an individual antenna group one or more training signals for estimating a group of channels associated with the subset of the transmit antennas belonging to the individual antenna group are determined.
- the number of the antenna groups, the subset of the transmit antennas for forming the individual antenna group, and the one or more training signals for the individual antenna group are determined based on the spatial correlations, a maximum allowable total number of training signals and a transmit signal-to-noise ratio (SNR) such that the pre-determined level of channel-estimation accuracy is achievable.
- SNR transmit signal-to-noise ratio
- the number of antenna groups is determined by identifying a highest number of antenna groups under a constraint that the pre-determined level of channel-estimation accuracy is achievable.
- the identified highest number is less than or equal to the maximum allowable total number of training signals.
- the partitioning of the transmit antennas comprises the following steps.
- a first step is to computing a first channel-estimation accuracy level achieved in an absence of partitioning the transmit antennas, whereby the pre-determined level of channel-estimation accuracy may be related to the first channel-estimation accuracy level.
- a second step is as follows. Given a trial number of antenna groups, determine, for each antenna group, a candidate subset of the transmit antennas and a candidate number of the one or more training signals so as to compute a second channel-estimation accuracy level attained by partitioning the transmit antennas into the trial number of antenna groups.
- the second channel-estimation accuracy is computed based on the spatial correlations, the transmit SNR, the trial number of antenna groups, and the candidate number of the one or more training signals for each antenna group.
- the second step is repeated for different trial numbers until the second channel-estimation accuracy level achieved for one trial number is better than the pre-determined performance level.
- the number of antenna groups is determined to be the aforesaid one trial number.
- the fourth step is to determine, for each antenna group, the subset of the transmit antennas for forming this antenna group to be the candidate subset therefor associated with the aforesaid one trial number.
- the disclosed method is implementable in a base station comprising plural radio antennas, a radio transceiving unit and one or more processors.
- FIG. 1 is a flowchart for exemplarily illustrating the method disclosed in the present invention.
- FIG. 2 depicts a flowchart illustrating one general flow of steps for performing the partitioning of the transmit antennas.
- FIG. 3 depicts a flowchart illustrating the steps of partitioning of the transmit antennas according to one embodiment of the present invention.
- FIG. 4 depicts a first communication device sending individual sets of training signals one-by-one to the second communication device according to a partitioning of transmit antennas into plural antenna groups, whereby a massive MIMO channel is estimated.
- An aspect of the present invention is to provide a method for estimating a massive MIMO channel. The method is developed based on the following observations.
- h an N ⁇ 1 complex channel-gain vector of the massive MIMO channel
- A is a diagonal matrix having eigenvalues of R as diagonal elements
- Q is a matrix containing eigenvectors of R.
- y is a transmit signal-to-noise ratio (SNR) and Q(1:m) is an N ⁇ m matrix composed of m eigen-vectors corresponding to the m largest eigenvalues of R.
- SNR transmit signal-to-noise ratio
- Q(1:m) is an N ⁇ m matrix composed of m eigen-vectors corresponding to the m largest eigenvalues of R.
- n is an m ⁇ 1 noise vector.
- MMSE minimum mean-square error
- MSE mean-square error
- the inventors have made the following observations that form the basis in developing the present invention. If the N transmit antennas are partitioned into G groups of adjacent antennas, and if the correlation between any two antenna groups is neglected, the estimation of the massive MIMO channel can be done by independently carrying out channel estimation for each antenna group.
- the overall complexity in performing estimation of the massive MIMO channel is only O(N 3 /G 3 ) roughly. If the number of antenna groups for dividing the N transmit antennas is large, a significant reduction in computation requirement results. It is therefore desirable to have G as large as possible. However, a higher value of G leads to an increased estimation error due to neglecting the mutual correlation among the G antenna groups.
- the inventors have observed that due to a large number of transmit antennas, the antenna spacing among the transmit antennas of a massive MIMO system is much shorter than the antenna spacing for a mobile communication system using a low number of transmit antennas, e.g., 8 as is commonly used in a present-day Long Term Evolution (LTE) system.
- LTE Long Term Evolution
- a high spatial correlation results in the largest eigenvalue more dominant than other eigenvalues as compared to the case of low spatial correlation, leading to more accurate channel estimate under the same value of m. This observation is usable as follows in the design of antenna grouping.
- the largest value of G is determined and selected under a given m value such that the resultant performance loss is within this tolerable loss. This approach is adopted in the present invention.
- N g be the number of adjacent antennas in the g th antenna group
- m g be the number of training signals used in channel estimation for this antenna group, where 1 ⁇ g ⁇ G and N g ⁇ m g .
- the signal from the N g transmit antennas of the g th antenna group arrives at the second communication device.
- the received signal denoted as an m g ⁇ 1 matrix y g , is given by
- h g is the N g ⁇ 1 complex-channel gain vector of the N g transmit antennas
- n g is an m g ⁇ 1 noise matrix
- S g is an N g ⁇ m g matrix representing the training signals for the g th antenna group, given as follows.
- R g E ⁇ h g h g H ⁇ extracted from R and then get
- a g is a diagonal matrix having eigenvalues of R g as diagonal elements
- Q g is a matrix containing eigenvectors of R g .
- ⁇ g is the estimate of h g .
- An estimate of h obtained from ⁇ g , 1 ⁇ g ⁇ G, is denoted by ⁇ tilde over (h) ⁇ and is given by
- ⁇ g,i is the i th largest eigenvalue of R g .
- the present invention provides a method for estimating a massive MIMO channel on which a first communication device having plural transmit antennas communicates with a second communication device having a single receive antenna.
- the first communication device is usually a base station (BS) while the second communication device may be a user equipment (UE) such as a mobile phone or a tablet having wireless-communication capability.
- BS base station
- UE user equipment
- the first or the second communication device used herein is not limited only to a BS or a UE.
- the massive MIMO channel has a channel covariance matrix that characterizes spatial correlations among the transmit antennas.
- FIG. 1 is a flowchart exemplarily illustrating a flow of steps used in the method as generalized from the embodiment described above.
- the method comprises a step 120 of partitioning, by the first communication device, the transmit antennas into plural antenna groups each comprising a subset of the transmit antennas such that a pre-determined level of channel-estimation accuracy is attainable.
- the pre-determined level of channel-estimation is set with a value of ⁇ . Then the first communication device determines, for an individual antenna group, one or more training signals for estimating a group of channels associated with the subset of the transmit antennas belonging to the individual antenna group in a step 130 .
- the number of the antenna groups, the subset of the transmit antennas for forming the individual antenna group, and the one or more training signals for the individual antenna group are determined based on the spatial correlations, a maximum allowable total number of training signals and a transmit SNR such that the pre-determined level of channel-estimation accuracy is achievable.
- the spatial correlations are reflected in R
- the maximum allowable total number of training signals is given by m
- the transmit SNR is given by ⁇ , which is used in the computation of ⁇ tilde over ( ⁇ ) ⁇ .
- the number of antenna groups is determined by identifying a highest number of antenna groups under a constraint that the pre-determined level of channel-estimation accuracy is achievable.
- the identified highest number is less than or equal to the maximum allowable total number of training signals.
- the method further comprises a step 140 that the first communication device transmits the one or more training signals of the individual antenna group to the second communication device, so that complex-channel gains for the subset of the transmit antennas belonging to the individual antenna group are estimable after the one or more training signals are received at the second communication device.
- these complex-channel gains are estimated by a MMSE estimator.
- the first or the second communication device estimates the channel covariance matrix in a step 110 .
- various existing techniques are available to an ordinary skilled person for estimating the channel covariance matrix in a mobile communication system.
- FIG. 2 depicts a flowchart illustrating a flow of steps, as follows, for performing the partitioning of the transmit antennas according to one embodiment of the present invention. Dynamic design of training signals is resulted.
- the partitioning of the transmit antennas is realizable as follows.
- G, N g and m g are advantageously determined by a search process as illustrated by a flowchart depicted in FIG. 3 .
- the variables G, N g and m g denote working variables during computation.
- the computed value of ⁇ corresponds to the MSE ⁇ under the condition that no antenna grouping is used, and serves as a reference performance indicator for comparison with ⁇ tilde over ( ⁇ ) ⁇ , a performance indicator when antenna grouping is present.
- ⁇ the reference performance indicator for comparison with ⁇ G instead. Since a higher value of ⁇ tilde over ( ⁇ ) ⁇ corresponds to a lower MSE of ⁇ G as evidenced in (15), it is desired to find a maximum value of G such that the performance loss is within a tolerable limit.
- the maximum value of G is determined under the condition that ⁇ tilde over ( ⁇ ) ⁇ is greater than a certain proportion, ⁇ , of ⁇ .
- a pre-determined value of ⁇ , which is less than unity, may be selected according to the channel-estimation accuracy that is required. For example, ⁇ may be selected to be 0.95 or 0.98.
- the search for this highest value of G is performed by a loop comprising steps 340 , 350 , 355 , 370 and 375 for testing different trial values of G.
- Each execution of the loop includes evaluating a performance measure ⁇ tilde over ( ⁇ ) ⁇ for one trial value of G.
- the step 340 comprises determining candidate values of N g and m g for 1 ⁇ g ⁇ G such that (8) and (9) are satisfied. As mentioned above, a more accurate channel estimate is obtained in the presence of higher spatial correlation under a given value of m g .
- the performance measure ⁇ tilde over ( ⁇ ) ⁇ given by (16) is then computed in the step 350 .
- ⁇ tilde over ( ⁇ ) ⁇ is computed, a first test condition of ⁇ tilde over ( ⁇ ) ⁇ > ⁇ is tested in the step 355 . If the first test condition is not satisfied, the current trial value of G yields a performance loss that is not deemed to be acceptable.
- the trial value of G is then decremented by one in the step 370, and the loop is re-executed for the updated trial value of G unless this updated value is already one.
- G′, N′ g and m′ g as the final values of G, N g and m g obtained at the end of the search process, respectively.
- the m′ g training signals identified for the g th antenna group are collectively denoted by an N′ g ⁇ m′ g matrix S′ g .
- the current trial value of G satisfies the channel-estimation accuracy requirement whereas the previous one with a G value greater than the current trial value by one does not. It follows that the current trial value of G is the highest possible value that satisfies the channel-estimation accuracy requirement.
- This current value of G is assigned to G′ in a step 360 , together with assigning the trial value of N g determined in the step 340 as N′ g , and the determined trial value of m g as m′ g .
- S′ g is determined to be S g computed by (12) under the determined trial value of m g .
- the loop is re-executed for this next trial value if the second test condition has an answer of no. If the answer is yes, there is not a possible antenna-grouping arrangement to satisfy the channel-estimation accuracy requirement.
- the values G′, N′ g and m′ g are identified as those for the no-grouping situation, and a step 380 is executed.
- G′, N′ g and m′ g are assigned with a value of 1, the value of N and the value of m, respectively.
- the step 230 shown in FIG. 2 can be further elaborated as follows.
- partitioning of the transmit antennas by the approach depicted in FIG. 3 is based on a sequential search approach.
- the partitioning of the transmit antennas may be accomplished by a general approach. It is accomplished by breaking down the step 230 into the following sub-steps.
- FIG. 4 depicts a hardware setting on which the disclosed method can be implemented.
- a first communication device 410 such as a BS is desired to estimate a massive MIMO channel 440 for communicating with a second communication device 420 such as a UE.
- the first communication device 410 comprises plural radio antennas 412 , a first radio transceiving unit 415 coupled to the radio antennas 412 , and one or more first processors 417 configured to execute a process for estimating the massive MIMO channel when the radio antennas 412 are configured to be transmit antennas and when the second communication device 420 has one antenna 422 configured to be a receive antenna.
- the partitioning of the transmit antennas 412 and the determining of training signals for each antenna group are performed at the one or more first processors 417 of the first communication device 410 because the first communication device 410 usually has more computation resources than the second communication device 420 .
- the transmit antennas are divided into a plurality of antenna groups (e.g. 413 a - c ).
- the one or more first processors 417 instruct the first radio transceiving unit 415 to generate a first set of training signals 441 a for transmitting over the massive MIMO channel 440 via transmit antennas of the first antenna group 413 a .
- the receive antenna 422 captures a combination of such training signals 441 a .
- the combined received signal is then received by a second radio transceiving unit 425 of the second communication device 420 .
- An estimate of the massive MIMO channel 440 associated with the transmit antennas of the first antenna group 413 a may be computed at one or more second processors 427 of the second communication device 420 .
- a digital version of the combined received signal may be sent back to the first communication device 410 via a return channel 450 so that the one or more first processors 417 of the first communication device 410 perform the estimation.
- the transmission of training signals from the first communication device 410 to the second communication device 420 is proceeded for all other antenna groups (such as 413 b and 413 c ) to thereby fully estimate the massive MINO channel 440 .
- DSP digital signal processors
- ASIC application specific integrated circuits
- FPGA field programmable gate arrays
- DSP digital signal processors
- ASIC application specific integrated circuits
- FPGA field programmable gate arrays
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Abstract
Description
- The present invention generally relates to channel estimation for a massive multi-input multi-output (MIMO) communication system. In particular, the present invention relates to such channel estimation with reduced computation requirements.
- Due to various advantages such as a high data-transmission rate, a high beamforming gain and a high spatial resolution, massive MIMO communications have attracted considerable interest for future deployment in mobile communication systems. In a massive MIMO system, a transmitter has a very large number of transmit antennas, e.g., greater than 100. In estimating a massive MIMO channel, the large number of transmit antennas often leads to a high computation requirement and a need for a lot of training resources, e.g., orthogonal time/frequency resource, in channel estimation. It is desirable to reduce these demands in operations in mobile communication systems.
- US20130182594 discloses a reduced-complexity channel-estimation technique by grouping the transmit antennas into groups for training. By reducing the number of antennas for estimation in each group, channel estimation requires less computation. However, spatial correlations are not taken into account to improve accuracy in channel estimation. Reduced-complexity techniques disclosed by US20130272263 and US20140254702 also have an estimation-accuracy issue since channel correlations are not taken into account. U.S. Pat. No. 8,837,621 teaches transmitting pilot reference signals on only a subset of antennas and using spatial interpolation to obtain channel estimates for other antennas. However, high estimation error results when spatial correlations among the antennas are not adequately high.
- There is a need in the art to have a technique for estimating the massive MIMO channel with improved estimation accuracy while maintaining low requirements in computation and in training resources.
- An aspect of the present invention is to provide a method for estimating a massive MIMO channel on which a first communication device having plural transmit antennas communicates with a second communication device having a single receive antenna. The massive MIMO channel has a channel covariance matrix that characterizes spatial correlations among the transmit antennas. In the method, the first communication device partitions the transmit antennas into plural antenna groups with each comprising a subset of the transmit antennas such that a pre-determined level of channel-estimation accuracy is attainable. For an individual antenna group, one or more training signals for estimating a group of channels associated with the subset of the transmit antennas belonging to the individual antenna group are determined. In particular, the number of the antenna groups, the subset of the transmit antennas for forming the individual antenna group, and the one or more training signals for the individual antenna group are determined based on the spatial correlations, a maximum allowable total number of training signals and a transmit signal-to-noise ratio (SNR) such that the pre-determined level of channel-estimation accuracy is achievable.
- Preferably, the number of antenna groups is determined by identifying a highest number of antenna groups under a constraint that the pre-determined level of channel-estimation accuracy is achievable. The identified highest number is less than or equal to the maximum allowable total number of training signals.
- In one embodiment, the partitioning of the transmit antennas comprises the following steps. A first step is to computing a first channel-estimation accuracy level achieved in an absence of partitioning the transmit antennas, whereby the pre-determined level of channel-estimation accuracy may be related to the first channel-estimation accuracy level. A second step is as follows. Given a trial number of antenna groups, determine, for each antenna group, a candidate subset of the transmit antennas and a candidate number of the one or more training signals so as to compute a second channel-estimation accuracy level attained by partitioning the transmit antennas into the trial number of antenna groups. In particular, the second channel-estimation accuracy is computed based on the spatial correlations, the transmit SNR, the trial number of antenna groups, and the candidate number of the one or more training signals for each antenna group. In a third step, the second step is repeated for different trial numbers until the second channel-estimation accuracy level achieved for one trial number is better than the pre-determined performance level. The number of antenna groups is determined to be the aforesaid one trial number. The fourth step is to determine, for each antenna group, the subset of the transmit antennas for forming this antenna group to be the candidate subset therefor associated with the aforesaid one trial number.
- The disclosed method is implementable in a base station comprising plural radio antennas, a radio transceiving unit and one or more processors.
- Other aspects of the present invention are disclosed as illustrated by the embodiments hereinafter.
-
FIG. 1 is a flowchart for exemplarily illustrating the method disclosed in the present invention. -
FIG. 2 depicts a flowchart illustrating one general flow of steps for performing the partitioning of the transmit antennas. -
FIG. 3 depicts a flowchart illustrating the steps of partitioning of the transmit antennas according to one embodiment of the present invention. -
FIG. 4 depicts a first communication device sending individual sets of training signals one-by-one to the second communication device according to a partitioning of transmit antennas into plural antenna groups, whereby a massive MIMO channel is estimated. - An aspect of the present invention is to provide a method for estimating a massive MIMO channel. The method is developed based on the following observations.
- Consider a massive MIMO channel on which a first communication device having N transmit antennas communicates with a second communication device having a single receive antenna. Let h be an N×1 complex channel-gain vector of the massive MIMO channel, and R be a channel covariance matrix given by R=E{hhH } where (·)H denotes complex conjugate transpose. It is assumed that R is known to both the first and the second communication devices, and that it remains approximately invariant during a long period. Moreover, h remains invariant during a shorter period within which estimation of h is performed. This period is commonly known as the channel coherence time. It is desired to estimate h by sending one or more training symbols from the N transmit antennas to the second communication device.
- A known technique for estimating h is given by L. Choi et al., “Downlink training techniques for FDD massive MIMO systems: open-loop and closed-loop training with memory,” IEEE Journal of Selected Topics in Signal Processing, vol. 8, no. 5, pp. 802-814, October 2014, the disclosure of which is incorporated by reference herein. First, perform an eigen-decomposition on R to give
-
R=QAQH (1) - where A is a diagonal matrix having eigenvalues of R as diagonal elements, and Q is a matrix containing eigenvectors of R. Consider that m training signals are used to estimate h where m<N. The optimal training signals, represented as an N×m matrix S, are given by
-
S=√{square root over (γ)}Q(1:m) (2) - where y is a transmit signal-to-noise ratio (SNR) and Q(1:m) is an N×m matrix composed of m eigen-vectors corresponding to the m largest eigenvalues of R. The signal received at the second communication device, denoted as an m×1 matrix y, is given by
-
y=S H h+n (3) - where n is an m×1 noise vector. Estimation based on the minimum mean-square error (MMSE) approach yields an estimate of h, denoted as ĥ, given by
-
ĥ=RS(I m +S H RS)−1 y (4) - in which Im is an m×m identity matrix. The estimated channel covariance matrix, {circumflex over (R)}=E(ĥĥH), is
-
{circumflex over (R)}=RS(I m +S H RS)−1 S H R (5) - The mean-square error (MSE) of estimation, η, is given by
-
η=N −1 E(∥h−ĥ∥ 2)=1−μ/N (6) - where
-
- in which λi is the i th largest eigenvalue of R. It is apparent that ĥ obtained by (4) requires an eigen-decomposition operation of (1) and then a computation operation of a matrix inverse in (4). The complexity of each of these two operations is of the order N3. It follows that the overall complexity of performing channel estimation is O(N3), thereby leading to huge computation requirements for a massive MIMO system in which N can be as high as or even greater than 100.
- The inventors have made the following observations that form the basis in developing the present invention. If the N transmit antennas are partitioned into G groups of adjacent antennas, and if the correlation between any two antenna groups is neglected, the estimation of the massive MIMO channel can be done by independently carrying out channel estimation for each antenna group. The overall complexity in performing estimation of the massive MIMO channel is only O(N3/G3) roughly. If the number of antenna groups for dividing the N transmit antennas is large, a significant reduction in computation requirement results. It is therefore desirable to have G as large as possible. However, a higher value of G leads to an increased estimation error due to neglecting the mutual correlation among the G antenna groups. The inventors have observed that due to a large number of transmit antennas, the antenna spacing among the transmit antennas of a massive MIMO system is much shorter than the antenna spacing for a mobile communication system using a low number of transmit antennas, e.g., 8 as is commonly used in a present-day Long Term Evolution (LTE) system. Insufficient antenna spacing and limited scattering during radio propagation both lead to a relatively high spatial correlation. A high spatial correlation results in the largest eigenvalue more dominant than other eigenvalues as compared to the case of low spatial correlation, leading to more accurate channel estimate under the same value of m. This observation is usable as follows in the design of antenna grouping. With a pre-determined value of tolerable loss in performance, e.g., a 5% increase in the MSE, the largest value of G is determined and selected under a given m value such that the resultant performance loss is within this tolerable loss. This approach is adopted in the present invention.
- Let Ng be the number of adjacent antennas in the g th antenna group, and mg be the number of training signals used in channel estimation for this antenna group, where 1≦g≦G and Ng≧mg. The constraints
-
- are required to be satisfied. The signal from the Ng transmit antennas of the g th antenna group arrives at the second communication device. The received signal, denoted as an mg×1 matrix yg, is given by
-
y g =S g H h g +n g (10) - where hg is the Ng×1 complex-channel gain vector of the Ng transmit antennas, ng is an mg×1 noise matrix, and Sg is an Ng×mg matrix representing the training signals for the g th antenna group, given as follows. Obtain a channel covariance submatrix Rg=E{hghg H} extracted from R and then get
-
Rg=QgAgQg H (11) - where Ag is a diagonal matrix having eigenvalues of Rg as diagonal elements, and Qg is a matrix containing eigenvectors of Rg. Then Sg is given by
-
S g =√{square root over (γ)}Q g(1:m g) (12) - where Qg(1:mg) is formed by mg eigen-vectors corresponding to the mg largest eigenvalues of Rg. An estimate of hg from yg is computed by
-
{circumflex over (h)}g =R g S g(I mg +S g H R g S g)−1 y g (13 ) - where ĥg is the estimate of hg. An estimate of h obtained from ĥg, 1≦g≦G, is denoted by {tilde over (h)} and is given by
-
- The MSE of {tilde over (h)}, denoted as ηG, is obtained as
-
ηG =N −1 E(∥h−{tilde over (h)}∥ 2)=1−{tilde over (μ)}/N (15) - where {tilde over (μ)}=tr({tilde over (R)}) in which {tilde over (R)}=E({tilde over (h)}{tilde over (h)}H). Hence, {tilde over (R)}=diag({circumflex over (R)}1, {circumflex over (R)}2, . . . , {circumflex over (R)}G) where {circumflex over (R)}g=E(ĥgĥg H), and
-
- in which λg,i is the i th largest eigenvalue of Rg.
- Based on the foregoing observations, the present invention is elaborated as follows.
- The present invention provides a method for estimating a massive MIMO channel on which a first communication device having plural transmit antennas communicates with a second communication device having a single receive antenna. In a mobile communication system, the first communication device is usually a base station (BS) while the second communication device may be a user equipment (UE) such as a mobile phone or a tablet having wireless-communication capability. However, the first or the second communication device used herein is not limited only to a BS or a UE. The massive MIMO channel has a channel covariance matrix that characterizes spatial correlations among the transmit antennas.
-
FIG. 1 is a flowchart exemplarily illustrating a flow of steps used in the method as generalized from the embodiment described above. - The method comprises a
step 120 of partitioning, by the first communication device, the transmit antennas into plural antenna groups each comprising a subset of the transmit antennas such that a pre-determined level of channel-estimation accuracy is attainable. In one option used above, the pre-determined level of channel-estimation is set with a value of αμ. Then the first communication device determines, for an individual antenna group, one or more training signals for estimating a group of channels associated with the subset of the transmit antennas belonging to the individual antenna group in astep 130. In thesteps - Preferably, the number of antenna groups is determined by identifying a highest number of antenna groups under a constraint that the pre-determined level of channel-estimation accuracy is achievable. The identified highest number is less than or equal to the maximum allowable total number of training signals.
- The method further comprises a
step 140 that the first communication device transmits the one or more training signals of the individual antenna group to the second communication device, so that complex-channel gains for the subset of the transmit antennas belonging to the individual antenna group are estimable after the one or more training signals are received at the second communication device. Preferably, these complex-channel gains are estimated by a MMSE estimator. After combining estimation results for all antenna groups in a step 150, complex-channel gains for all the transmit antennas are obtained, thereby obtaining full channel estimation. - Before performing the
step 120 of partitioning the transmit antenna, it is possible that the first or the second communication device estimates the channel covariance matrix in astep 110. In the art, various existing techniques are available to an ordinary skilled person for estimating the channel covariance matrix in a mobile communication system. -
FIG. 2 depicts a flowchart illustrating a flow of steps, as follows, for performing the partitioning of the transmit antennas according to one embodiment of the present invention. Dynamic design of training signals is resulted. -
-
Step 210. A first channel-estimation accuracy level achieved in an absence of partitioning the transmit antennas is determined. The pre-determined level of channel-estimation accuracy can be then calculated from the first channel-estimation accuracy level. As one example, the first channel-estimation accuracy level may be chosen as μ, and the pre-determined level may be computed by βμ where β is a number less than unity. In another example, one may use the MSE η as the first channel-estimation accuracy level. -
Step 220. Compute a second channel-estimation accuracy level for each possible partitioning. Given a trial number of antenna groups, determine, for each antenna group, a candidate subset of the transmit antennas and a candidate number of the one or more training signals, so as to compute the second channel-estimation accuracy level attained by partitioning the transmit antennas into the trial number of antenna groups. In particular, the second channel-estimation accuracy is computed based on the spatial correlations, the transmit SNR, the trial number of antenna groups, and the candidate number of the one or more training signals for each antenna group. In one example, the candidate number of the one or more training signals and the second channel-estimation accuracy level correspond to mg and {tilde over (μ)}, respectively. In one practical implementation of thestep 220, the numbers of transmit antennas among all the antenna groups are selected to be approximately the same, the candidate subset of each antenna group has the transmit antennas selected to be adjacent and physically close to each others, and the candidate number of the one or more signals of each antenna group is selected such that a ratio of the number of transmit antennas to the candidate number of the one or more signals for one antenna group is approximately the same to that of another antenna group. -
Step 230. Select the one partitioning that has the highest number of antenna groups and whose second channel-estimation accuracy level is within the pre-determined level of channel-estimation accuracy.
-
- Furthermore, in one embodiment, the partitioning of the transmit antennas is realizable as follows.
- The values of G, Ng and mg are advantageously determined by a search process as illustrated by a flowchart depicted in
FIG. 3 . For the sake of convenience in illustrating the process, the variables G, Ng and mg denote working variables during computation. - In a
first initialization step 310, G is set to G=1 and S is computed by (2). Then β is computed by (7) in asecond initialization step 320. The computed value of μ corresponds to the MSE η under the condition that no antenna grouping is used, and serves as a reference performance indicator for comparison with {tilde over (μ)}, a performance indicator when antenna grouping is present. Alternatively, one may use η as the reference performance indicator for comparison with ηG instead. Since a higher value of {tilde over (μ)} corresponds to a lower MSE of ηG as evidenced in (15), it is desired to find a maximum value of G such that the performance loss is within a tolerable limit. Exemplarily, the maximum value of G is determined under the condition that {tilde over (μ)} is greater than a certain proportion, β, of μ. A pre-determined value of β, which is less than unity, may be selected according to the channel-estimation accuracy that is required. For example, β may be selected to be 0.95 or 0.98. - It is desirable to find a value of G that is as high as possible in order to reduce the resultant computation requirement in channel estimation as much as possible. The search for this highest value of G is performed by a
loop comprising steps step 330. Thestep 340 comprises determining candidate values of Ng and mg for 1≦g≦G such that (8) and (9) are satisfied. As mentioned above, a more accurate channel estimate is obtained in the presence of higher spatial correlation under a given value of mg. It follows that under the same mg value, preferably a higher value of Ng is selected in case the corresponding Rg, which is known from R, indicates high spatial correlation. The performance measure {tilde over (μ)} given by (16) is then computed in thestep 350. After {tilde over (μ)} is computed, a first test condition of {tilde over (μ)}>βμ is tested in thestep 355. If the first test condition is not satisfied, the current trial value of G yields a performance loss that is not deemed to be acceptable. The trial value of G is then decremented by one in thestep 370, and the loop is re-executed for the updated trial value of G unless this updated value is already one. - Denote G′, N′g and m′g as the final values of G, Ng and mg obtained at the end of the search process, respectively. The m′g training signals identified for the g th antenna group are collectively denoted by an N′g×m′g matrix S′g.
- When the first test condition ({tilde over (μ)}>βμ) tested in the
step 355 yields an answer of yes, the current trial value of G satisfies the channel-estimation accuracy requirement whereas the previous one with a G value greater than the current trial value by one does not. It follows that the current trial value of G is the highest possible value that satisfies the channel-estimation accuracy requirement. This current value of G is assigned to G′ in astep 360, together with assigning the trial value of Ng determined in thestep 340 as N′g, and the determined trial value of mg as m′g. In thestep 360, S′g is determined to be Sg computed by (12) under the determined trial value of mg. - In a
step 375, the next trial value of G is tested with a second test condition of G=1. As is mentioned above, the loop is re-executed for this next trial value if the second test condition has an answer of no. If the answer is yes, there is not a possible antenna-grouping arrangement to satisfy the channel-estimation accuracy requirement. In this regard, the values G′, N′g and m′g are identified as those for the no-grouping situation, and astep 380 is executed. In thestep 380, G′, N′g and m′g are assigned with a value of 1, the value of N and the value of m, respectively. - According to the foregoing determination of G′, N′g and m′g, the
step 230 shown inFIG. 2 can be further elaborated as follows. -
- The
step 220 is repeated for different trial numbers arranged in descending order and starting from the maximum allowable total number of training signals, until the second channel-estimation accuracy level achieved for a certain trial number is better than the pre-determined performance level. Then the determined number of antenna groups is the aforesaid certain trial number. - For each antenna group, the subset of the transmit antennas for forming this antenna group is determined to be the candidate subset of the transmit antennas associated with the aforesaid one trial number.
- The
- Note that the partitioning of the transmit antennas by the approach depicted in
FIG. 3 is based on a sequential search approach. Alternatively, the partitioning of the transmit antennas may be accomplished by a general approach. It is accomplished by breaking down thestep 230 into the following sub-steps. -
- Repeat the
step 220 for different trial numbers. - A subset of all the trial numbers used in the
step 220 is identified such that each trial number in this subset has the second channel-estimation accuracy level better than the pre-determined performance level. - The number of antenna groups is determined to be the highest trial number in the subset of the trial numbers.
- For each antenna group, the subset of the transmit antennas for forming this antenna group is determined to be the candidate subset the transmit antennas associated with the highest trial number.
- Repeat the
-
FIG. 4 depicts a hardware setting on which the disclosed method can be implemented. Afirst communication device 410 such as a BS is desired to estimate amassive MIMO channel 440 for communicating with asecond communication device 420 such as a UE. Thefirst communication device 410 comprisesplural radio antennas 412, a firstradio transceiving unit 415 coupled to theradio antennas 412, and one or morefirst processors 417 configured to execute a process for estimating the massive MIMO channel when theradio antennas 412 are configured to be transmit antennas and when thesecond communication device 420 has oneantenna 422 configured to be a receive antenna. Preferably but not strictly required, the partitioning of the transmitantennas 412 and the determining of training signals for each antenna group are performed at the one or morefirst processors 417 of thefirst communication device 410 because thefirst communication device 410 usually has more computation resources than thesecond communication device 420. The transmit antennas are divided into a plurality of antenna groups (e.g. 413 a-c). For thefirst antenna group 413 a, the one or morefirst processors 417 instruct the firstradio transceiving unit 415 to generate a first set of training signals 441 a for transmitting over themassive MIMO channel 440 via transmit antennas of thefirst antenna group 413 a. The receiveantenna 422 captures a combination of such training signals 441 a. The combined received signal is then received by a secondradio transceiving unit 425 of thesecond communication device 420. An estimate of themassive MIMO channel 440 associated with the transmit antennas of thefirst antenna group 413 a may be computed at one or moresecond processors 427 of thesecond communication device 420. Alternatively, a digital version of the combined received signal may be sent back to thefirst communication device 410 via areturn channel 450 so that the one or morefirst processors 417 of thefirst communication device 410 perform the estimation. The transmission of training signals from thefirst communication device 410 to thesecond communication device 420 is proceeded for all other antenna groups (such as 413 b and 413 c) to thereby fully estimate themassive MINO channel 440. - The embodiments disclosed herein may be implemented using general purpose or specialized computing devices, computer processors, or electronic circuitries including but not limited to digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA), and other programmable logic devices configured or programmed according to the teachings of the present disclosure.
- The present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiment is therefore to be considered in all respects as illustrative and not restrictive. The scope of the invention is indicated by the appended claims rather than by the foregoing description, and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Claims (19)
S′ g =√{square root over (γ)}Q g(1:m′ g), 1≦g≦G′
{tilde over (h)} g =R′ g S′ g(I m
S′ g =√e,rad γQ g(1;m′ g), 1≦g≦G′
ĥ g =R′ g S′ g(I m
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