CN109302224B - Hybrid beamforming algorithm for massive MIMO - Google Patents
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- 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
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Abstract
The invention belongs to the field of millimeter wave large-scale MIMO systems, and particularly relates to a hybrid beam forming algorithm for large-scale MIMO. This new algorithm aims at jointly optimizing the analog domain beamforming and the digital domain beamforming to maximize the spectral efficiency. The invention is divided into two parts: firstly, simulating a beam forming algorithm; and secondly, after the analog beam shaper is given, the digital beam shaper is obtained according to a water injection method. The algorithm is suitable for different types of analog networks, including continuous adjustable phase shifter networks, finite bit adjustable phase shifter networks, switching networks and the like. Simulation results show that the performance of the algorithm is very close to the optimal performance of all-digital beam forming; and the performance of the hybrid beam forming based on the switch network is close to that of the phase shifter network, thereby being more beneficial to the realization of engineering.
Description
Technical Field
The invention belongs to the field of MIMO communication, and particularly relates to a hybrid beam forming algorithm for large-scale MIMO.
Background
The 5G millimeter wave technology improves the communication bandwidth by hundreds of mega even kilohertz, and installs dozens of even hundreds of antennas at the base station, thereby greatly improving the channel capacity of the cell. However, if a conventional communication receiver is used, the digital domain needs to process hundreds of high-speed code streams in real time, and the difficulty is very great. Researchers put forward that Analog domain Beamforming/ABF is performed before a digital-to-Analog converter (ADC), high-dimensional signals received by M antennas are compressed to N dimensions (N < M), antenna gains of large-scale MIMO are saved through ABF, and meanwhile, signal dimensions are greatly compressed, so that the operation amount of a digital domain and the required number of ADCs are greatly reduced, and hardware cost is obviously reduced. This technique is known as Hybrid Beamforming/HBF.
For the above-mentioned technologies, some research work on Hybrid Beamforming/HBF has been published. The traditional analog domain network is mainly divided into a phase shifter and a switch structure, and how to solve different analog domain network structures (including a switch, a phase shifter with fixed phase, a phase shifter with variable phase and different resolutions, and the like) in one way is still a difficult problem.
Disclosure of Invention
To overcome the disadvantages of the prior art, the present invention aims to provide a hybrid beamforming algorithm for different types of analog networks for massive MIMO. The algorithm is suitable for a phase shifter network, a switch network and a phase shifter and switch composite network in large-scale MIMO, so that the joint optimization of analog domain beam forming and digital domain beam forming is facilitated, and the maximization of the frequency spectrum efficiency is realized.
The invention provides a hybrid beam forming algorithm for large-scale MIMO, which comprises the following specific steps:
first, consider a single-user millimeter wave MIMO system, signal vectorPrecoder via digital basebandAnd analog precoderThen pass throughMtAnd transmitting by using the antenna. The sending antenna is:
x=FRFFBBs (1)
suppose thatWhereinIt is shown that it is desirable to,is dimension NsAnd (4) unit array. After passing through a flat fading channel, we will get the baseband signal:
Y=HFRFFBBs+z (2)
is a matrix of the channels and is,is a covariance matrix ofDue to the fact that the total transmitted power is normalized by the noise powerThe input signal-to-noise ratio is therefore:
the spectral efficiency is:
the purpose of the algorithm provided by the invention is to improve the spectrum efficiency, and the following problems are solved:
wherein the first constraint is related to the input SNR and the set of S in the second constraint depends on the set of RF feedback networks: phase shifter network for infinite resolution S ═ ejφ:φ∈[0,2π]}; for b-bit resolution phase shifter networksFor a switching network S ═ {0,1 }; for phase shifter plus switch network S ═ ejφ:φ∈[0,2π]} {0} orFRFThe constraint of (i, j) ∈ S distinguishes hybrid beamforming from traditional all-digital beamforming.
Secondly, optimizing the analog domain beam forming matrix FRF
Before introducing the optimization method of the analog domain beamforming matrix, we introduce two majorization theories first.
Wherein x [ i ] and y [ i ] are the elements of x and y, respectively, which are the i-th elements.
in the following, we look at the optimization of the analog domain beamforming, assuming Ns=NRFN, for the case where ρ is sufficiently large, satisfies
It is easy to prove that the spectrum efficiency is
We now discuss the two definitions that we have used for the dominance mentioned above.
Theorem 1: function(s)Is the predominant Schur-covex. For each lambdaiIn other words, C (λ) is a non-decreasing function.
Given decomposition of QR into HUsRFQR, definitionConsisting of diagonal elements of R, which we know are HURFIs mainly multiplied by the singular value of, and λ is HURFSquare of the singular value of (a). Therefore, the temperature of the molten metal is controlled,
according to theorem 1, the method
C(λ)≥C(|r|2) (13)
By maximizing the lower bound C (| r! y of C (λ)2) Instead of maximizing C (λ). Next we discuss the structure of the interior of the R diagonal:
theorem 2: concerning HU in QR decompositionRFThe diagonal elements of R of QR,
wherein,
Ui-1represents URFFirst i-1 column, uiRepresents URFColumn i.
Theorem 3: for URFThe column (c) of (a),
From theorems 2 and 3, we can deduce
From there, we can see RiiDependent only on FRFFirst i columns of, and FRFThe last few columns of (c) are irrelevant.
The above observations motivated us to consider an iteration of N steps, where the ith step is the ith diagonal element R used to maximize Rii:
Splitting x into:
and define
The cost function can be rewritten as
For infinite precision phase shifters, xn=ejθThen we can in turn rewrite the cost function:
wherein,
wherein, the angle represents the phase of the complex number, when we are fixedThen, we can optimize x for different set constraints Sn。
Theorem 4: about thetaoptThe solution of (a):
is equivalent to
Wherein,
for a b-bit resolution phase shifter, the integer k is determined by:
and updates θopt
Then, the user can use the device to perform the operation,
for a phase shifter plus switch network, 0 ∈ S, compare g (θ)opt) To the ratio ofxnThe following can be obtained:
in the case of a switching network,
the specific steps of the algorithm 1 to solve the problem (18) are summarized as follows:
(1) inputting: calculating A, B;
(3) When the objective function value is still increased, executing the step (4);
(4) when n is 1 to MtAt the same time, fixBy (28), (29) and (30), x is calculated from the constraints of different Sn;
(5) When the objective function value is not changed, the circulation is exited;
Further, an analog beamforming matrix F is designedRFThe specific steps of algorithm 2 are as follows:
(1) inputting a parameter H;
(3) Taking 1 to N for i, executing the following steps (4) to (8);
(4) calculating A and B according to (20);
(6)FRF(:,i)←x;
(9) Return to FRF。
Thirdly, optimizing the digital beam forming matrix FBB: calculate FRFThen, we solve for F according to the "water filling" method described aboveBB。
First, we fix the analog domain beamforming matrix FRFProblem (5) can be simplified as:
we define
We can substitute equation (7) into equation (6),
Subject to Tr(GGH)≤ρ
wherein,is a semi-unitary matrix representing FRFThe column space of (a). The solution to problem (8) is:
(2)wherein,is a diagonal matrix, gammaiCan be obtained by a water injection power distribution method
(3) Wherein,λithe ith diagonal element of Λ is represented. When in useThen, the lagrange multiplier μ is obtained.
(4) Obtaining a digital domain beam forming matrix F according to a formula (7)BB。
Compared with the prior art, the invention has the beneficial effects that: the algorithm is suitable for different types of analog networks, including continuous adjustable phase shifter networks, finite bit adjustable phase shifter networks, switching networks and the like. Simulation results show that the performance of the algorithm is very close to the optimal performance of all-digital beam forming; and the performance of the hybrid beam forming based on the switch network is close to that of the phase shifter network, thereby being more beneficial to the realization of engineering.
Drawings
Fig. 1 is a hybrid beamforming structure at a transmitting end in a MIMO system.
Fig. 2 shows three implementations of an analog precoder (beamformer): (a) a phase shifter network, (b) a switching network, (c) a phase shifter plus a switching network.
Fig. 3 is a comparison of spectral efficiency for different RF network configurations.
Detailed Description
The technical solution of the present invention will be described in detail with reference to the accompanying drawings and embodiments.
Fig. 1 is a hybrid beamforming structure at a transmitting end in a MIMO system.
Fig. 2 shows three implementations of an analog precoder (beamformer), i.e. three different RF network architectures.
Example 1
The channel model we use is a narrowband millimeter wave cluster channel model:
in which the multipath gain is alphal~CN(0,1),at(θl) And ar(φl) Antenna array responses for the transmitter and receiver, respectively; wherein theta islIs the angle of departure, philIs the angle of arrival. We simulate using a Uniform Linear Array (ULA) whose array response for angle θ is:
The system we actually simulated was a 64 x 16 MIMO system (M)t=64,Mr16), wherein N isRF=NsThe number of multipaths L is 15, 8. The results of fig. 3 demonstrate a comparison of spectral efficiency of our algorithm under the constraints of different RF chains. Comprises a phase shifter network with infinite precision (o-), a phase shifter with 1bit resolution (o-), and a phase shifter with 2bit resolutionA switching network (-), a phase shifter plus a switching network (-). The result shows that the performance of the phase shifter plus switch structure is slightly better than that of a phase shifter structure with infinite precision; and 2bit resolution shifters (e.g., S { ± 1 ± j }) have less than 1dB difference in performance compared to infinite precision shifter networks; the switching network performance is also excellent with less than 4dB difference in performance compared to an infinite precision phase shifter network. For ease of comparison, we also simulated a greedy antenna selection algorithm[1](dotted line in fig. 3); the antenna selection method (only one antenna per RF chain) does not perform as well as the switching network.
Reference to the literature
[1]Y.Jiang and M.K.Varanasi,“The RF-chain limited MIMO system-Part I:optimum diversity-multiplexing tradeoff,”IEEE Transactions on Wireless Communications,vol.8,no.10,pp.5238–5247,2009。
Claims (3)
1. A hybrid beamforming algorithm for massive MIMO characterized in that the hybrid beamforming will contain N of informationsDimensional signal vectorFirst passes through a digital baseband precoder, denoted asThen the obtained NRFDimension signal FBBs is through NRFThe RF chain is converted to RF signals and then passed through an analog precoder in the RF domain, denoted asFinally obtaining MtDimension signal x ═ FRFFBBs is through MtTransmitting by each antenna;
the analog precoder consists of different devices, including: a phase shifter network, a switching network and a phase shifter plus switching network; corresponding to different analog precoder forming devices, FRFThe set S to which the element (S) belongs is different: for an infinite resolution phase shifter network, S ═ ejφ:φ∈[0,2π]}; for a b-bit resolution phase shifter network, for a switching network, S ═ {0,1 }; for a phase shifter plus switch network, S ═ ejφ:φ∈[0,2π]} {0} orAiming at different types of simulated precoders, calculating the optimal coefficient of each element of the simulated precoders, thereby obtaining a matrix FRF;
The method comprises the following specific steps:
first step, consider a single-user millimeter wave MIMO system, signal vectorPrecoder via digital basebandAnd analog precoderThen through MtTransmitting by each antenna, wherein the sending signals are as follows:
x=FRFFBBs (1)
suppose thatWhereinIt is shown that it is desirable to,is dimension NsThe unit array of (1); after passing through a narrow-band block fading channel, obtaining a baseband signal:
y=HFRFFBBs+z (2)
h is a matrix of the channel and H is,z is a covariance matrix ofThe total transmission power is white noise due to noise power normalizationAnd the input signal-to-noise ratio is represented by ρ;
the spectral efficiency is:
the frequency spectrum efficiency is improved under the condition of limited input signal-to-noise ratio, and the purpose is to solve the following problems:
secondly, optimizing the analog domain beam forming matrix FRF: mixing HURFQR decomposition to obtain HURFIn the case of QR, where,URFis a semi-unitary matrix representing FRFA column space of (a); the basic idea is to optimize the analog beamforming matrix FRFTo maximize the diagonal elements of R; it uses iterative method to maximize QR decomposition HU in iterative ith stepRFI-th diagonal element R of R in QRii:
Thirdly, optimizing the digital beam forming matrix FBB: given analog domain beamforming matrix FRFProblem (5) to
The method utilizes a water injection power distribution method; wherein:
in the second step, the first step is carried out,
in respect of QRHU in decompositionRFThe diagonal elements of R of QR,
wherein,
Ui-1represents URFFirst i-1 column, uiRepresents URFThe ith column;
for URFThe column (c) of (a),
deducing according to the formulas (15) and (16)
2. The hybrid beamforming algorithm according to claim 1, wherein in the third step, the water-filling power allocation method specifically includes the following steps:
the formula (7) is substituted into the formula (6),
Subject to Tr(GGH)≤ρ
② orderWherein,gamma is a diagonal matrix, gammaiThe power is obtained by a water injection power distribution method;
(iii) wherein,λithe ith diagonal element of Λ is represented whenThen, obtaining a Lagrange multiplier mu;
fourthly, obtaining a digital domain beam forming matrix F according to a formula (7)BB。
3. The hybrid beamforming algorithm of claim 1, wherein in the second step, an iteration of N steps is considered first, wherein the ith step is the ith diagonal element R used to maximize Rii:
Splitting x into:
and define
The cost function is rewritten as
(one) for infinite precision phase shifters, xn=ejθThen the cost function is rewritten:
wherein,
wherein the angle represents the phase of the complex number, when fixedTime of day, limit for different setsS to optimize xn;
About thetaoptThe solution of (a):
is equivalent to
Wherein:
(ii) for a b-bit resolution phase shifter, the integer k is determined by:
and updates θopt
Then, the user can use the device to perform the operation,
(III) for the phase shifter plus switch network, 0 ∈ S, compare g (theta)opt) To the ratio ofThus, xnThe following can be obtained:
(IV) for the switching network,
further, algorithm 1 for solving the problem (18) for infinite precision phase shifter networks, b-bit resolution phase shifters, and for phase shifter plus switching networks and switching networks is as follows:
firstly, inputting: A. b, provided by algorithm 2 below;
Thirdly, when the objective function value is still increased, executing the fourth step;
when n is from 1 to MtAt the same time, fixCalculating x according to the constraints of different S through formulas (28), (29) and (30)n;
Quitting circulation when the objective function value is not changed;
Further, an analog beamforming matrix FRFAlgorithm 2 as follows:
inputting a parameter H;
③ from 1 to N for iRFExecuting the following steps of ((r) - (r));
fourthly, calculating A and B according to a formula (20);
⑥FRF(:,i)←x;
Ninthly returns to FRF。
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CN113472404B (en) * | 2021-07-13 | 2022-02-11 | 西安科技大学 | Method and device for optimizing digital domain beam forming based on condition generation countermeasure network |
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