AU2018102034A4

AU2018102034A4 - Power-Efficiency Design Method for Hybrid Automatic Repeat Request Over Time-Correlated Channel

Info

Publication number: AU2018102034A4
Application number: AU2018102034A
Authority: AU
Inventors: Jitong Chen; Hongfei Guo; Shaodan MA; Ting QU; Zheng Shi; Guanghua Yang
Original assignee: Jinan University; University of Jinan
Current assignee: Jinan University
Priority date: 2018-03-19
Filing date: 2018-12-09
Publication date: 2019-01-17
Anticipated expiration: 2026-12-09
Also published as: CN108668350A; CN108668350B

Abstract

The present disclosure discloses a power-efficiency design method for a HARQ over a time-correlated channel, which achieves an optimized design scheme of power allocation and rate selection under a correlation channel. The scheme is applicable to three common HARQ types (Type I, CC and IR) to maximize the power efficiency and ensure communication service quality. The steps include: firstly, decomposing an original problem into three sub-problems using the proximity interruption probability and introducing an auxiliary variable, and closed deriving in turn; determining an upper limit of the power efficiency, balancing spectrum efficiency requirements and self-adaptively selecting a HARQ type; reasonably adjusting the coding scheme and the modulation mode according to the optimal transmission power and the transmission rate to maximize the power efficiency. Compared with the conventional method, the method using the proximity interruption probability can effectively reduce the computational complexity in practical applications and improve performance of the system power efficiency. reasonably selecting a HARQ scheme according to requirements of power and Maximizing power spectrum efficiency: efficiency 1. type-I HARQ 2. HARQ-CC 3. HARQ-IR Obtaining optimal transmit power and optimal transmit rate e ec onof" Selection of adaptive coding scheme adaptive modukationn moeJ Error f(x) Error P(X Send ; Transmitter detection W correction IN cache Modulator X code Co code Ci L- - --- -- -- - L- - HARQ control Correlated Rician h fading channel Feedback channel (ACK/NACK) Gaussian noise ' IN + HARQ control X Error X) Error Receive Demodulator i Receiver -4detection J() correctio cache /balancer code Co code C1 --

Description

Power-Efficiency Design Method for Hybrid Automatic Repeat Request Over Time-Correlated Channel

TECHNICAL FIELD [0001] The present disclosure relates to the field of radio communication technologies, and in particular, to a power-efficiency design method for a hybrid automatic repeat request (HARQ) over a time-correlated channel.

BACKGROUND [0002] In recent years, wireless data traffic and the number of mobile terminals are exploded. Tasks of continuously improving spectrum efficiency and power efficiency of radio communication to meet increasing demands of users become more and more urgent. Adaptive Modulation and Coding (AMC) and HARQ are considered to be two promising technologies. Especially under the condition that a receiver has perfect channel state information, the AMC is a very efficient physical layer technology, which selects a reasonable coding scheme and a modulation mode using available channel state information. However, under the condition that a transmitter only obtains partial or statistical channel state information, the AMC is no longer practical. In this case, multiple transmissions are adopted to improve throughput of a system and reduce an interruption probability. In particular, a hybrid automatic repeat request combined with the link layer and the forward error correction codec of the physical layer are a very effective means, i.e., a hybrid automatic repeat request, as shown in FIG 1. Specifically, in a decoding process, a receiving end firstly performs error detection to detect whether an error bit is included. When the error bit is detected, a decoder immediately performs error correction decoding. Only when the decoding fails, the decoder sends decoding failure information to a sending end, and requests the sending end to resend information. Therefore, the HARQ may effectively improve system performance without requiring perfect channel state information. Generally, HARQ technologies may be classified into three basic types based on codec modes adopted at the receiving end and the sending end, i.e., Type I HARQ, HARQ with chase combining (HARQ-CC), and HARQ with incremental redundancy (HARQ-IR). The Type I HARQ directly discards a decoding-failed codeword. Although the decoding-failed codeword is difficult to recover, the

2018102034 09 Dec 2018 decoding-failed codeword still includes a lot of useful information. As such, such operation obviously results in system performance loss. On the country, buffers equipped with the HARQ-CC and the HARQ-IR store error codewords that are failed to be decoded previously. When new information is received each time, the previously-stored error codewords are decoded combined with currently-received codewords respectively using a chase combination mode and a code combination mode. These two modes may greatly improve receiving performance of the system, and are widely applied in radio communications. However, the improvement of the performance requires good hardware supports.

[0003] However, most of HARQ systems are optimized based on spectrum efficiency, which is not applicable to the purpose of improving power efficiency and green communication in the next generation of mobile communications. In addition to the spectrum efficiency, power efficiency is another important performance metric that is gaining increasing attention in radio communications. This performance metric is especially important in energy-limited networks, especially in Internet of Things (IoT) networks and mobile networks with limited battery capacity. However, this metric is often overlooked in practice, making it is difficult to further improve the system performance. Even if the power efficiency metric is considered, quasi-static fading channels or independent fading channels are assumed in most power design processes. These assumptions are not applicable to communication of a terminal in a mobility environment with a medium or low speed. In this case, fading channels are correlated with each other to some extent, but are not completely correlated. Especially when the HARQ is applied, time correlation between fading channels transmitted multiple times usually has a great negative impact on system performance, resulting in deterioration of the system performance.

SUMMARY [0004] Considering the negative impact of the time correlation of the fading channel on the performance of the HARQ, the present disclosure provides an optimized design of the HARQ combining transmission power allocation and transmission rate selection based on a power efficiency, which uses statistical characteristics of the channel to improve the power efficiency to the maximum extent, and ensure the service quality of mobile users, including constraints of the effective throughput and the interruption probability. In addition, the present disclosure also

2018102034 09 Dec 2018 describes how to properly select a HARQ scheme to weigh requirements of the spectrum efficiency and power efficiency in radio communications.

[0005] The object of the present disclosure can be achieved by adopting the following technical solutions:

[0006] When the HARQ is implemented, since the time correlation of the fading channel has a very serious negative impact on the performance of the system, such as an increase in the interruption probability and a decrease in the power efficiency, it is necessary to make full use of the statistical characteristics of the channel to alleviate the negative impact. In particular, in order to improve the power efficiency and ensure that the communication service quality includes the constraints of the effective throughput and the interruption probability, the present disclosure proposes an optimized design scheme for maximizing the power efficiency considering the power allocation and rate selection. There are three basic types of HARQ, namely Type I HARQ, HARQ-CC, and HARQ-IR. In order to select these three HARQ schemes more reasonably and effectively, the present disclosure respectively discusses the maximization of the power efficiency of the three HARQ types, and derives corresponding optimal transmission power and transmission rate through the proximity analysis result of the interruption probability. FIG. 1 is a schematic diagram illustrating a power efficiency design of the present disclosure. The technical solution implementation steps are shown in FIG. 2, including four steps, each of which is described as follows:

[0007] SI. Mathematical modeling of the optimization problem [0008] in an optimized design of transmission power allocation and transmission rate selection of the HARQ over a correlation channel based on a power efficiency, requirements of user service quality should be ensured when maximizing the power efficiency , wherein the user service quality comprises two constraints: requirements of a maximum threshold of a target interruption probability and a minimum value of an effective throughput, respectively expressed as P°^ut’^L ~ ^ε and ; when the two constraints are determined, a problem of maximizing the power efficiency of a HARQ system is constructed as:

2018102034 09 Dec 2018 max 77,

Ρ,,-Λ.Κ subject to ρ^<ε

T_g>T₀

7) > 0, \<1<L R>0, [0009] wherein

11- / l [0010] '^L indicates the power efficiency and / ^Z=1 , [0011] L indicates the maximum number of transmissions of the HARQ, [0012] indicates a transmission power of the I transmission and 1 - - A [0013] R indicates a transmission rate of the HARQ, [0014] ^Paut’¹ indicates a probability of decoding failure of a received signal after the transmission, or is referred to as an interruption probability and 1 - - L [0015] ^g indicates an effective throughput of the HARQ system, [0016] ^ε indicates the maximum threshold of the interruption probability,

T [0017] ⁰ indicates the minimum constraint of the effective throughput;

[0018] S2. Proximity solution for the optimization problem [0019] simplifying the deriving of the optimization problem using a proximity analysis result of the interruption probability in three different HARQ schemes, namely:

a π a \ 1=1 [0020] wherein

r(Z + l) ’

Type I-HARQ

HARQ-CC

HARQ-IR

ΚΜΓ ntx

^σ'^: is an additive white noise power of the transmission, P is a coefficient correlated to the

2018102034 09 Dec 2018 fading channel; then a target interruption probability ^a which is an auxiliary variable is proposed, and the optimization problem is rewritten into:

P(l-a) max —^-=—Pi,-P_L,R,a P subject to p_{mt L} = a

0<α<ε

P(l-a)>T₀ ^>0, \<1<L

R>0, — Σ Pout,l-\^l [0021] wherein P is the total average transmission power and ¹⁼¹ , a target problem is decomposed into three sub-problems comprising reasonably allocation of a transmission power, optimization selection of the target interruption probability, and self-adaptive adjustment of a transmission rate, comprising:

[0022] S201. in the allocation of the transmission power, when the transmission rate R and the target interruption probability ^a are determined, the problem of maximizing the power efficiency is degenerated as:

min P

Pu-Pl subject to p_{mt L} - a ^>0, 1</<Z.

[0023] using the proximity result of the interruption probability, an optimal solution of the power is expressed as a closed expression of the transmission rate R and the target interruption probability ^a, i.e.,

x2'·

M±

A-2 >

P_z ² ,1</<Z-1

2018102034 09 Dec 2018 [0024]

S202. substituting the optimal solution of the power , and 1 into the optimization problem, when the transmission rate R is determined, the optimization problem is degenerated into the optimization problem of the target interruption probability ^a, i.e., max

subject to

0<α<ε

Λ(1-α)£Τ, [0025] wherein ^J ' ' is a function of the target interruption probability and

⁷ v 7 \ 7 , _an optimal solution corresponding to the optimization problem of the target interruption probability is:

[0026]

S203. substituting the optimal target interruption probability ^a into the optimization problem, a final optimization problem is simplified as:

R subject R > T_o [0027] wherein is a function of the maximum number of transmissions and / ' ', for each of the three different types of the HARQ, a numerical solution of the optimal transmission rate R corresponding to the optimization problem is calculated by one-dimensional search, a closed solution of the optimal transmission rate R corresponding to the optimization problem is:

7?* = min|-^—(0) >

[0028] for Type I HARQ, 1^1_Δ J;

R* = min <

[0029] forHARQ-CC,

2018102034 09 Dec 2018 [0030] for HARQ-IR, a proximity expression of the optimal transmission rate is

R* =min

Y’¹ (0) >

J

[0031]	wherein
[0032]	indicates = ^)R(R-T₀)2^-_CT₀(2^-1),
[0033]	indicates an inverse function of
[0034]	Φ (θ) indicates the zero point of
[0035]	_A . ,. Δ = minis,2^_i) ^Δ indicates ^{1 J},
[0036]	(«) indicates = (Λ-Τ„)(2 1η(2)Λ+2*-1)-2^¹ (2«-1)Λ
[0037]	Y (θ) indicates the zero point of
[0038]	-w=(-T.r“(2-iK
[0039]	S3. Selection of the HARQ type
[0040]	according to the closed expression of the transmission power and the transmission

rate derived in step S2, determining an upper limit of the power efficiency, and self-adaptively selecting a HARQ type according to requirements of the spectrum efficiency in an actual system, comprising:

[0041] p

substituting ¹ \<1<L, a , and R j_nto the target function to obtain optimal power efficiencies using the three different types of the HARQ, respectively:

^lo _R*_c _ ιΊ [0042] for Type I HARQ, the optimal power efficiency 1 ;

* __ l_2^-i * [0043] for HARQ-CC, the optimal power efficiency ^^{cc,i Kl} ;

[0044] for HARQ-IR, the optimal power efficiency satisfies

2¹ 1 in-Z * ^x ^KL-\ 7/S.Z — 7/7),1 — ^KL ^ΊΐΆ,ί .

[0045] wherein

2018102034 09 Dec 2018 [0046] [0047] [0048] [0049] [0050] η

^L indicates

k

,-1

S4. Reasonably selection of the coding scheme and modulation mode based on the HARQ type and according to the optimal transmission power and the transmission rate, selecting a reasonable channel coding scheme (Turbo code, convolutional code, etc.) and a modulation mode (PSK, QAM, etc.) to maximize the power efficiency of the actual communication system, and ensure communication service quality.

[0051] [0052]

The present disclosure has the following advantages and effects over the prior art:

complexity. The theoretical analysis result in the closed form is derived by means of the proximity interruption probability and the form is simple. The numerical analysis shows that under the strict interruption constraint or high SNR condition, the proposed solution is consistent with the simulation result, and the strict interruption probability constraint is also in line with practical application requirements. As such, the proposed design scheme is effective, which can greatly reduce the computational complexity and improve the power efficiency.

[0053] 2. The theoretical result in the design scheme disclosed in the present disclosure provides a very meaningful guidance and reference value for practical applications. The theoretical analysis result of the upper limit of the power efficiency can determine which HARQ type is adopted for transmission. The optimal solution of the power and rate guides how to match the coding scheme and the modulation mode.

BRIEF DESCRIPTION OF THE DRAWINGS [0054]

FIG. 1 is a schematic diagram illustrating a power efficiency design of the present disclosure;

[0055]

FIG. 2 is a flow chart illustrating a joint power allocation and rate selection algorithm in the present disclosure;

2018102034 09 Dec 2018 [0056] FIG. 3 is a schematic diagram illustrating verification of a theoretical analysis result of the present disclosure;

[0057] FIG. 4 is a schematic diagram illustrating comparison of power efficiency of three common HARQ types according to the present disclosure;

[0058] FIG. 5 is a graph of performance for optimal power efficiency and corresponding spectrum efficiency.

DETAILED DESCRIPTION [0059] Hereinafter, technical solutions in embodiments of the present disclosure will be clearly and completely described with reference to the accompanying drawings. It is obvious that the described embodiments are a part of the embodiments of the present disclosure, and not all embodiments. All other embodiments obtained by a person skilled in the art based on the embodiments of the present disclosure without creative efforts belong to the protection scope of the present disclosure.

[0060] Embodiments [0061] The embodiment describes application of the HARQ in a peer-to-pear radio communication system. According to the HARQ protocol, multiple codewords including information of bit may be successfully received by a receiving end through continuously retransmission. It should be noted that in Type I HARQ and HARQ-CC, a same codeword is transmitted during each retransmission process, whereas in HARQ-IR, each retransmission process transmits codewords including different redundant information. For these three different types of HARQ, a signal received at the receiving end may be expressed as:

y_l I =1,2,···,£, [0062] [0063] x TVx in which the length of a transmitted signal ¹ is ^s, and each symbol in ¹ obeys E(x^Tx I = N a complex Gaussian distribution in which the mean is 0 and the variance is 1, i.e., ' ¹⁵

P 7Z ¹ represents a transmission power during the ¹ transmission; ¹ represents complex Gaussian white noise of zero mean and unit variance; L indicates the maximum number of allowed transmissions;

h1 ¹ indicates a Rayleigh fading channel coefficient for the ¹ transmission. A

2018102034 09 Dec 2018 signal received by a terminal moved with a low speed or a high speed may experience a correlated fading channel. To simulate time correlation of a channel, a widely-used Rayleigh time-correlated fading channel is used here:

h_l=a_lUl-p^h_l+p^l-^lh₀\, 1 = 1,2,L, ¹ / (2) [0064] in which P and ^σ* respectively represent a time-correlated coefficient and A h h · * * h variance of ” ; ^{05 15 L} obey a circular symmetric complex Gaussian distribution of which a mean is zero and a variance is one, i.e., (θΌ Thj_s channel model is general and versatile. A quasi-static fading channel (i.e., a completely-correlated fading channel, in which hi h₂ h_{z an}j _a f_ast p_acQ_ng _ch_annei 0 _e, _an independent fading channel, in which hph₂, ,h_{L are} i_nj_ep_enj_ent _with each other) are two special cases of the channel model, which correspond to two special cases in which P~^ and P~^, respectively. The present disclosure configures a fixed length for codewords transmitted each time, i.e., ^s. As such, an initial transmission rate of the HARQ is

[0065] It is assumed that perfect instantaneous channel state information is available at the receiver, but only statistical characteristics of channel state information are available at a

P •••P transmitter. In order to improve communication performance, transmission powers ^{15 L} and transmission rate R may be optimally designed making full use of the statistical characteristics of the channel state information at the transmitter. The present disclosure focuses on the design of the power efficiency of the HARQ. The design goal is to maximize the power efficiency by jointly optimizing the transmission power and rate under quality of service (QoS) constraints. Since all system performance indicators may be expressed as a function of the interruption probability, a definition and a calculation method of the interruption probability are introduced as follows. [0066] For the HARQ scheme, when the receiving end does not correctly decode information after L transmissions, it is determined that the transmission for the information fails,

i.e., an interruption event. Different HARQ types have different calculating methods and results

2018102034 09 Dec 2018 for the interruption probability. According to Shannon theorem, calculation expressions of interruption probabilities of three different types of HARQ are shown as follows:

Pout,L

(3) [0067] However, in general, the expression of the interruption probability is extremely complicated and difficult to handle. Especially in the case of a correlation fading channel, the interruption probability is either expressed as a special function with high computational complexity or expressed as infinite series. It is difficult to flexibly apply such complicated expressions of the interruption probability to the optimization design of the system. Therefore, the present disclosure utilizes a proximity analysis result of the interruption probability, i.e., an approximate expression of the interruption probability under the condition of a high signal to noise ratio. The proximity interruption probability expression is simple in form and has low computational complexity, and is especially suitable for the optimization design of the system. In the case of high SNR, proximity expressions of interruption probabilities of three different types of HARQ may be expressed as:

[0068] k A-=l J (4) in which when ° =1, otherwise indicates asymptotically equal, where depends on different types of HARQ, namely: ^(2^-1)', Typel-HARQ ί_Δ(2^Λ-1)^λ

---3_, HARQ-CC cc

T(Z ₊ 1) ’ _iigL(R), HARQ-IR (5)

2018102034 09 Dec 2018 [0069]

If 7? > 0, then , otherwise θ. In formula (5), ^( ) indicates a Gamma .(ifrp))'¹

Π·- ^σ>^! , m which ⁽(^L·^ function, indicates influence of a fading channel and especially indicates influence of channel correlation and f L Λ*-*) l(L,p)= 1+ΣΛτϊΠ) [0070] ^} (6) in which ^(°’^p)=l, then ^⁼¹. In (5), if 7? > 0 and - θ , configuring (2-1/=θ,then

4,2,-,2 .1,-,1,0 ra+ioo 2^ J = 1 -------r ds

2ri^ia~™ 5(5-1) =(-i)^£ ₊2-£(-ir^(7?hl2r\ is expressed as:

2^r )

[0071] (7)

It can be seen from the unified expression (4) that the result not only provides a clear physical connotation but also provides the possibility of maximizing the power efficiency of the present invention. Compared to a conventional method in which an accurate expression of the interruption probability is used for poor search, the system optimization design based on this method using (4) may greatly reduce the computational complexity.

[0072]

A performance metric that measures power efficiency is power efficiency, of which a strict definition is the amount of information transmitted by per unit of energy. In a HARQ system, assuming that the maximum number of transmissions is L, according to the update process theory, the power efficiency may be expressed as the ratio of the average number of correctly-received bits ^E = ZtiTWi = _{? namely}.

to the average consumed energy

Λ_;Λ(ι-α4_; ^τ.

^L ε NJ* P

N,P (8)

2018102034 09 Dec 2018 p=y^z p _P in which ^~“^{=γ out,}‘~' ¹ is the total average transmission power and [0073]

T = 7? (1 — ό ) T ⁸ \ ^out<^L) g j_{s o}ft;_en referred to as effective throughput, which is an important performance metric to measure HARQ throughput. In the condition of high SNR, the effective throughput is asymptotically equivalent to the spectrum efficiency. The spectrum efficiency refers to the average number of bits successfully transmitted each time, of which a definition is given later.

[0074] In order to make full use of the statistical characteristics of the channel, the present disclosure optimizes the transmission power ¹⁵ ’ ^L and the transmission rate R of information taking maximizing the power efficiency as a goal. Considering the widely-existing time-correlated fading channels and requirements of QoS in actual communication services, the present invention proposes a very practical joint power and rate optimization strategy for the three different types of HARQ based on these two aspects. Two QoS constraints that are of particular interest in the present invention are interrupt probability and effective throughput constraints, i.e., ^°“^ίΛ “^£ and . Given these constraints, the transmission power and the transmission rate are optimized by maximizing the power efficiency,

i.e.:

max η,

Pl-Pl,* subject to p_mt<L<s

T_g>T₀

P, >0, \<1<L ^R~^Q’ (9)

T [0075] in which ^ε and ⁰ represent the maximum allowable interruption probability and the minimum required effective throughput, respectively. If the exact expression of the interruption probability is used for optimization, the complexity of calculating an optimal solution is very large, and it is almost impossible to derive a closed solution of the optimal solution. Therefore, a proximity result of the interruption probability is used, i.e., expression (4). However, since expression (9) is a fraction optimization problem and the expression of the power efficiency is also very complicated, it is still a great challenge to derive a closed solution of expression (9).

2018102034 09 Dec 2018 (X⁼P

To solve this problem, an auxiliary variable (target interruption probability) is proposed.

As such, the original optimization problem may be expressed as:

7?(l-a) max ——^L

Pi,-P_L,R,a P subject to p_0Ut>L=a

0<α<ε

Λ(1-α)£Τ,

P_t>0, \<1<L R>0, (10) [0076] As can be seen from expression (10), maximizing an optimization goal requires

P ··· P solving three sets of variables, i.e., the transmission power ¹⁵ ’ ^L, the target interruption probability ^a, and the transmission rate R. Through iterative optimization, the optimization problem (10) may be further equivalently decomposed into three sub-problems: optimal power allocation, optimal interruption probability selection, and self-adaptive adjustment of the transmission rate.

[0077] A. Optimal power allocation [0078] The optimization problem (10) may be degenerated as follows under the given transmission rate R and the target interruption probability ^a :

min P

Pi,-Pl subject to p_0UtL - a > 0, 1</<Z. Qj) [0079] Substituting the proximity expression (4) of the interruption probability into (10), an optimal transmission power may be derived using the Karush-Kuhn-Tucker (KKT) condition. The optimal transmission power may be represented as a function of the transmission rate R and the target interruption probability ^a, shown as below:

k (12)

2018102034 09 Dec 2018 £=/+1 \ |0080] simplified to:

[0081]

Therefore, a corresponding minimum average total transmission power P may be __t (2^£-lW²¹·^

2^l~²

U 31-2^ (14)

Obviously, as can be seen from (12), (13), and (14), reduction of the target p* interruption probability ^a may result in an increase in the transmission power ¹ , thus

D* resulting in an increase in the minimum average total transmission power . In addition, when >fc £ approaches infinity, the minimum average total transmission power P is unrelated to the target interruption probability ^a.

[0082] [0083]

B. Optimal interruption probability selection

Substituting the optimal transmission power expressions (12) and (13) into the optimization problem (10), the original problem may be simplified to an optimization problem of the transmission rate R and the target interruption probability ^a, shown as below: R (1 - cr) p*

0<(Z <£

R(l-a)>T₀

7? > 0 max subject to [0084] (15)

According to formula (14), a target function of the power efficiency in the above optimization problem may be expressed as:

—=—- = —---(1-α α^ζ -¹---P* 2^f-i J--------., > , >. VW If

Π , (16) [0085]

Obviously, the target interruption probability only exists in in (16). When the transmission rate is determined, the optimization problem (15) of the target interruption probability may be simplified to:

2018102034 09 Dec 2018 max f (a) subject to 0 < a < £

7?(l-a)>T₀ [0086] The feasibility and optimal solution for problem (17) may be obtained by the following theorem 1.

[0087]

7? < T

Theorem 1: when ^{_ 0}, there is no feasible solution to the optimization problem

7? > T (17). When °, an optimal target interruption probability is maximum value ) of the corresponding target function is:

f τ Ά ¹o ν i-aJJ

I ίζ(Λ-Τ,)-ζ RT <z*=min^ ε,Ι—-, 2~^L

R (18) >

- , and a [0088] ^{C = _}L-in which 2 -1,

A = min(f,2^£) , v(t) . . „ . .

^{1 J}, and ^v ' is a unit step function, i.e.:

'0 t<0 t>0 (19) [0089]

C. Self-adaptive adjustment of the transmission rate.

[0090] *

When the optimal target interruption probability ^a is determined, and it can be

7? > T seen from Theorem 1 that the feasible solution exists only when ⁰, the power optimization problem in (15) may be simplified to:

R max T]_L = ψ/(α*^>) , n# subject R > T_o (20) [0091]

By substituting (18) into (20), the optimal transmission rate & is numerically derived by one-dimensional search. However, such method lacks clear physical connotation. The present disclosure aims to derive a closed solution of the optimal transmission rate so as to simplify the computational complexity and provide a clear physical meaning. It can be seen from expression (5) that the calculation of in the target function depends on which type of HARQ

2018102034 09 Dec 2018 is used. As such, optimal selections of the optimal rate are different for different types of HARQ. Therefore, hereinafter the optimal rate adjustment and the maximum power efficiency of each type of HARQ are discussed in detail.

[0092] [0093]

C.l Type I HARQ

1) The optimal transmission rate: substituting (5) into (20), the power efficiency of

Type I HARQ may be expressed as:

f(a\R [0094] in which ^L ( ζ n|fy k ' [0095] [0096] (21)

1-2~^l hr = Π l-2“^£ (22) substituting (18) into (21) to obtain: ί τ Y

1__L·

T Ry ⁰ 2*-l τ Ά ¹0 i-aJJ z -i y k-ixj (23)

T R> °

It can be seen from (23) that when 1^_ A , the first term on the right side of the equation is zero, so that the power efficiency degenerates into

R

2^R . At this time, ^^r’^L becomes a decrement function of the transmission rate R. In addition, it may be .R > T proved that the power efficiency ^I>L is a continuous function in the interval ⁰.

7? > T

Considering the constraints ⁰ that must be satisfied in (20), it may be concluded that the transmission rate R corresponding to the maximum power efficiency must be within the interval ίτ₀Λ

Y ^1_Δ-Ι. In the interval Y r

To⁰ 1-Δ

T ί o

-, the second term on the right side of equation (23) is zero, so that the power efficiency may be simplified to:

2018102034 09 Dec 2018 [0097]

Therefore, the optimal selection of the transmission rate in (20) may be equivalent to the following minimization problem:

Φ(Λ) = (2«-1)(1-A]

T subject to T_n < R < —— ⁰ 1-Δ min

R [0098] (25)

In the optimization problem (25), the optimal transmission rate at which the power efficiency is maximized may be given by the following theorem 2.

[0099]

Theorem 2: under the condition of guaranteeing the interruption possibility of the

Type IHARQ and the QoS constraints of the effective throughput,

R* =min-i [00100] in which indicates an inverse function of „(R) ₌ ln(2)R(R-T₀)2^_CT₀(2^-l) _Assuchj ^(0) _{is zero point of} ^_ύο,

When ^ε > 2 \ the optimal transmission rate is simplified to (θ).

[00101] It should be noted that since is an incremental function of R in range (Τ_ο»°°) , _th_{e zero} p_O{_nt Φ (θ) _may b_e easily calculated by dichotomy.

[00102] 2) The optimal power efficiency: substituting the optimal transmission rate (26) into (24), the optimal power efficiency of Type I HARQ may be expressed as:

t k - a τ ^⁰) ⁹ 2^fi*-l ~^{Ψ L 0} R*^c(2^r*-1) ( f (27) g

[00103] It may be proved that ^L is a decrement function of a time-correlated coefficient

P. In other words, the time correlation of the fading channel has a negative impact on the optimal power efficiency. As such, the power efficiency of HARQ over the time-correlated fading channel

2018102034 09 Dec 2018 is less than that over the fast fading channel. It may be expected that when considering the QoS constraints, the maximum power efficiency of Type I HARQ is less than (^) [00104] To discuss the optimal power efficiency in detail, monotonicity of the maximum number of transmissions L is analyzed firstly. From the original problem of maximizing the power efficiency in (9), following characteristics may be found:

[00105] Characteristic 1: The optimal power efficiency of all three HARQ schemes is a non-decrement function of the maximum number of transmissions L . At the same time, the η_Γ < lim η, = η_Ύ power efficiency satisfies [00106] For Type I HARQ schemes, the obtained power efficiency is maximum when

L —» oo, which is expressed as . The expression is given by the following theorem 3.

[00107] Theorem 3: under the time-correlated Rayleigh fading channel and under the conditions of the interruption probability and the constraints of the effective throughput, an upper limit of the optimal power efficiency of Type I HARQ may satisfy:

[00108]

4(2⁷°-1) ' > (28) ^ = 111116* in which ζ-χ» exists to the limit. The maximum power efficiency ^{7 =0} is a decrement

T function of a throughput threshold ⁰. In particular, when the average gain of the

Rayleigh fading channel is 1, i.e., ^σ' \ ^< \ and under the condition of satisfying the interruption probability constraints and the effective throughput constraints, the maximum power efficiency of Type I HARQ may satisfy:

θτ.

GO ϋ

T 1 n =--— < lim---fo---= —1— = n^niax

4(2^-1)-^4(2-.-1) 41n(2) _(2?) [00109]

This means that the maximum power efficiency that Type I HARQ may achieve is

41n(2) when considering QoS constraints.

[00110]

C.2 HARQ-CC

2018102034 09 Dec 2018 [00111] 1) Optimal rate: similar to the analysis in C.l, using the obtained optimal p* ... p* _a* transmission power ¹ ’ ’ ^L , the optimal target interruption probability and the definition in (5), the power efficiency of HARQ-CC in (20) may be expressed as:

7cc./=

(30)

Λ- = ΓΊ k² [00112] in which ^L 1 U=i . It should be noted that the only difference between (21) k and (30) is that (30) includes an additional product item ^L , which is unrelated to the transmission rate. As such, the optimal transmission rate R of HARQ-CC may be derived by

Theorem 2, which is the same as the optimal transmission rate of Type I HARQ shown in (26). [00113] 2) Optimal power efficiency: Similarly, the optimal power efficiency of HARQ-CC may be expressed as:

WcC.L ^{= K}L ² 7/.Z, ζβΐ)

A* > 1 [00114] Because of ^L , it is easy to see that the optimal power efficiency of HARQ-CC * * is greater than that of Type I HARQ, i.e., ^^{CC L} . Furthermore, according to characteristic 1 and theorem 3, it is easy to obtain the following conclusion about the optimal power efficiency of the HARQ-CC.

[00115] Theorem 4: under the time-correlated Rayleigh fading channel and under the conditions of the interruption probability and the constraints of the effective throughput, an upper limit of the optimal power efficiency of HARQ-CC may satisfy:

* _< * = ^X^To

Hcc,l - <cc,^

V > rm [00116] in which particular, when the average gain of the

Rayleigh fading channel is 1, i.e., ^σ' ^σ' <| ~ , and under the condition of satisfying the interruption probability constraints and the effective throughput constraints, the maximum power efficiency of HARQ-CC may satisfy:

a □ο ^Δ max iCCpD (33) * _{= <} , ___________ ________ ^cc” 4(2⁷°-1) 4(2⁷⁰ -1) 41n(2)

2018102034 09 Dec 2018 [00117] In other words, the maximum power efficiency of HARQ-CC is ^ln(2) _wh_en considering QoS constraints, which is greater than the power efficiency of Type I HARQ.

[00118] [00119]

HARQ-IR is:

C.3 HARQ-IR

1) Optimal rate: Substituting (5) into (20) to obtain the power efficiency of

V_!R,L = ψθ₁ ~

Π /(a)⁷* a⁴ _k=^g_k__x(R\ (34)

Substituting (18) into (34) to obtain:

[λ· TJ J;jj '1? 1¾) [00120] ^^To ^(Ι-Δ)Δ¹

1-2^-ί +

(_L

Π(Μ*)) ν' J (35) —c

T R>— , and ^{,s/ l}' When 1^_Δ , the first term on the right side of equation (35) is equal to 0, and the power efficiency is degraded ^(1-Δ)Α

I-2’^l [00121] in which . When into

11(^ W) l·¹ ) [00122]

It may be proved that is a monotonically incremental function of .

T

Therefore, when ^IR,L is a decrement function of . Combining the continuity of

T p— ^x0 ~ R > T ^rR-^L on the point of _an(j the constraint ⁰ in the problem (20), it may be concluded that the optimal rate at which the maximum power efficiency of HARQ-IR is achieved

2018102034 09 Dec 2018 r_T i must be located within the interval of k ^{1 Δ} efficiency may be simplified to:

_ ^z^T0

7m,z ^— . / ^AW (36)

T_o < R < -2®_

-. Therefore, when 1^_ Δ , the power

100123] Therefore, the optimal selection of the transmission rate in (20) becomes an optimization problem as follows:

Α(Λ) min

R subject [00124] to T_Si<R<⁷°

1-Δ (37)

Because the form of is complicated, it is very difficult to derive a closed expression for the optimal transmission rate. However, by analyzing a following characteristic of the function an approximate closed expression of the optimal transmission rate may be derived.

[00125]

Characteristic 2: Function may satisfy:

2^-1 2^_l-2^-'· 2^_1 2^_l _£Λ(Λ)ί(Ιη(2))Ί^ ₍₃₈₎ [00126] inwhich [00127]

Using a boundary expression in characteristic 2 and the median theorem, may be expressed as:

[00128]

Obviously, satisfy:

<ζ<^

2^-1 ~ (40) min

R

Substituting (39) into the optimization problem (37) to obtain: gt(R) subject to T_a<R<^1-Δ (41) [00129]

2018102034 09 Dec 2018 [00130] Using the proof similar to Theorem 2, the optimal solution of (41) may be obtained using the KKT condition, which is explained by the following theorem.

[00131] [00132] [00133] zero point

R* = Υ⁴(θ) [00134]

Theorem 5: The optimal solution for the optimization problem (41) is:

R* = min (TIL γ-¹ (o)l

11-Δ ^V Ί (42) . Y(7?) = (/?-T₀)(2*ln(2)R + 2*-l)-2-ⁱ⁺¹(2⁵-l)tf Υ’ΎΟ) . , in which ^{v v v} ’ > ' > , ^{v 7} is the of .When ^£ - 2^z , the optimal transmission rate may be simplified to

It should be noted that since is an incremental function of R , it is easy to

Y'¹ (o) find the zero point ^v ’ [00135] 2) Optimal power efficiency: According to the definition of the power efficiency of HARQ-IR in (36) may be expressed as: y^T₀ (

L

Π

I [00136] [00137] ( τ Y^c

1-A

I

Γ* [00138] [00139] [00140] (43)

Using the following inequality: g_k(R) ^2*-l

St-ι (^) (44)

Substituting inequality (44) into (43) to obtain:

VlR,L * (45) [00141] Obviously, in terms of the power efficiency, HARQ-IR is superior to HARQ-CC.

Moreover, the optimal power efficiency of HARQ-IR is not less than the power efficiency of

HARQ-CC, i.e., ~ .

2018102034 09 Dec 2018 [00142] Substituting the optimal rate R in (42) into (39) and combined with the boundary inequalities of the parameter in equations (36) and (40), it may be proved that the optimal power efficiency of HARQ-IR satisfies an inequality as follows:

[00143] [00144] [00145] (46) in which the expression of is:

2¹ ' (47) * * Combining (46) and the inequality of ^^cc,i, it may be found that the optimal

7«=^T₀(ta(2))-²A i-2 [00146] power efficiency of HARQ-IR satisfies an inequality as follows:

^^LPir,l (48)

When the number of transmissions approaches infinity, i.e., 7 —> °o, following

100147] [00148] max' 2¹k- i-²’¹

N.-1 > 7cC,Z ” — — ^KL inequality is correct:

[00149] max > 7cc>} ₍₄₉₎ in which the definition of ^^cc’°° is in Theorem 4, and . Using (47), [00150] may be simplified to:

2^-1-2~^z l-2'^£ X

2¹ l-2“^£ [00151] (50) [00152] hm^=2 in which the last equation is correct because of ^i_>°° 4 when 7 —> co, _tfr_e inequality ^ε - 2^L is correct. According to Theorem 5, the optimal transmission rate

R Ύ (θ). In other words, ) θ. Therefore, the optimal transmission rate R may be expressed as:

2018102034 09 Dec 2018

2“^Ζ+1(2^Λ* -1)7?*

R* = T- + .------------.--2^R ln(2)7?*+2* -1 (₅₁) [00153] At the same time, it should be noted that the optimal rate R exists in the interval

A=mink,2^_i) limA = 0 lim7? = T₀ . .

of ^{1 _} , ^{1 J}, ^L~*°° , and may be obtained using the clamping theorem. Using this limit and substituting (51) into (50) to obtain:

- . lim ((2^R' -1) 7?*) lim (r* - T- )1-2-¹

471n(2) // °/

J ^T°_T —lim \ ln(2)(2^T° -1) ' 2-^z+1(2**-1)t?*

2~^z \-2“^z

2^Λ’In(2)7?*+2^s’ -1 (52) [00154]

Substituting (32) and (52) into (49) to obtain:

max<

[00155] *

Obviously, both the lower and upper limits of in (53) are decrement functions

T T —> 0 of the threshold ⁰ of the effective throughput. In addition, when ⁰ , the following inequality is correct:

max/ (54) lim . — - —— t„^o2-1 In (2) [00156] Since ^v ', the following inequality is correct:

max /

X >1 [00157] Considering ⁰⁰ and based on the clamping theorem, a following conclusion may be obtained:

2018102034 09 Dec 2018

	T. 41„(2) ₍₅₆₎
[00158]	According to (53), (56) and characteristic 1, the following conclusion about the

optimal power efficiency of HARQ-IR may be obtained.

[00159]

Theorem 6: under the time-correlated Rayleigh fading channel and under the

conditions of the interruption probability and the constraints of the effective throughput, the optimal power efficiency of HARQ-IR may satisfy:

* « κ θ I ΰ

A ₍₅₇₎ [00160] In particular, when the average gain of the Rayleigh fading channel is 1, i.e., ^σ’ ^σΔ 1, ^< 1, and under the condition of satisfying the interruption probability constraints and the effective throughput constraints, the upper limit of the maximum power efficiency of HARQ-IR may be expressed as:

blR.X,

I A K_r ^111(2)(2^-1) 4 In (2) (58) [00161] Comparing the results in Theorem 4 and Theorem 6, it may be concluded that

41n(2)

HARQ-CC and HARQ-IR may achieve the same maximum power efficiency [00162] FIG. 3 verifies the correctness of the theoretical analysis in the present disclosure. In summary, HARQ-IR may achieve the maximum power efficiency, then HARQ-CC, while the power efficiency of Type I HARQ is the lowest, as shown in FIG. 4. However, it should be pointed out that the obtaining of the higher power efficiency is at the expense of spectrum efficiency. Therefore, in practice, the type of HARQ may be reasonably selected considering both of the spectrum efficiency and the power efficiency. In particular, HARQ-CC may achieve best compromise between the power efficiency and the spectrum efficiency among the three types of HARQ, as shown in FIG. 5. In summary, various embodiments of the present disclosure propose a power-efficiency-based design scheme of combining power optimization and rate selection for a HARQ over a time-correlated Rayleigh fading channel, which may improve the power efficiency of the system to the maximum extent, and guarantee the quality of services provided to mobile users.

2018102034 09 Dec 2018 [00163] The foregoing is optional implementation modes of the present disclosure. It should be noted that, for persons having ordinary skill in the art, various improvements and retouches, which are made without departing from the principle of the present disclosure, should be covered by the present disclosure.

Claims

What is claimed is:

1. A power-efficiency design method for a hybrid automatic repeat request (HARQ) over a time-correlated channel, comprising:

SI. in an optimized design of transmission power allocation and transmission rate selection of the HARQ over a correlation channel based on a power efficiency, requirements of user service quality should be ensured when maximizing the power efficiency , wherein the user service quality comprises two constraints: requirements of a maximum threshold of a target interruption z? ε probability and a minimum value of an effective throughput, respectively expressed as ^0Ut’^L

T > T and ^{8 0}; when the two constraints are determined, a problem of maximizing the power efficiency of a HARQ system is constructed as:

max Pi, · Pl-^r Pl subject ^tO PouLL^S M^To P, >0, \<1<L R>0,

wherein

Pl indicates the power efficiency and

L indicates the maximum number of transmissions of the HARQ, p<

indicates a transmission power of the I transmission and 1 P

R indicates a transmission rate of the HARQ, ^Pou1’¹ indicates a probability of decoding failure of a received signal after the transmission, or is referred to as an interruption probability and 1 - P,

2018102034 09 Dec 2018 ^g indicates an effective throughput of the HARQ system, ^ε indicates the maximum threshold of the interruption probability, indicates the minimum constraint of the effective throughput;

S2. simplifying the deriving of the optimization problem using a proximity analysis result of the interruption probability in three different HARQ schemes, namely:

wherein _ffi(2*-l)' , r(i + l) ’ ί'.ϊ. (*)·

Type I-HARQ

HARQ-CC

HARQ-IR ‘ It>.’ f L 2(i-l) \ _L ^{k 1} P ' ^{k }} , ^σ,: is an additive white noise power of the k transmission, P is a coefficient correlated to the fading channel; then a target interruption probability ^a which is an auxiliary variable is proposed, and the optimization problem is rewritten into:

7?(l-a) max ————p,,-Pl,r^ P subject to p_outL = a

Q<a <ε β(ι-«)>τ₀

7]>0, \<1<L R>0,

2018102034 09 Dec 2018 — P Σ Pout,l-\Pl wherein P is the total average transmission power and ¹⁼¹ , a target problem is decomposed into three sub-problems comprising reasonably allocation of a transmission power, optimization selection of the target interruption probability, and self-adaptive adjustment of a transmission rate, comprising:

S201. in the allocation of the transmission power, when the transmission rate R and the target interruption probability ^a are determined, the problem of maximizing the power efficiency is degenerated as:

min P

P^-Pl subject to p_out<L=a

7>>0, 1<1<L.

using the proximity result of the interruption probability, an optimal solution of the power is expressed as a closed expression of the transmission rate R and the target interruption probability ^a, i.e.,

L

T = n t=Z+l x2'·

M±

A-2 >

1 < Z < Z, —1

S202. substituting the optimal solution of the power ¹ , and into the optimization problem, when the transmission rate R is determined, the optimization problem is degenerated into the optimization problem of the target interruption probability ^a, i.e., max f (a) a ^{v 7} subject to 0<α<ε

Λ(1-α)>Τ„

2018102034 09 Dec 2018 wherein f (ct) = (1 — (x) (x^2L_1is a function of the target interruption probability and ^{v 7 v 7} , an optimal solution corresponding to the optimization problem of the target interruption probability is:

*

S203. substituting the optimal target interruption probability ^a into the optimization problem, a final optimization problem is simplified as:

max

Λ subject R > T_o wherein is a function of the maximum number of transmissions and for each of the three different types of the HARQ, a numerical solution of the optimal transmission rate R corresponding to the optimization problem is calculated by one-dimensional search, a closed solution of the optimal transmission rate R corresponding to the optimization problem is:

R* = min <

for Type I HARQ,

1-Δ J .

R* =minforHARQ-CC,

1-Δ J .

J for HARQ-IR, a proximity expression of the optimal transmission rate is wherein

2018102034 09 Dec 2018 indicates = 1»(2)Λ(Λ-T_o)2-^₀ (₂« -1)

Φ indicates an inverse function of (θ) indicates the zero point of a . ,. Δ = πιϊη(£·,2^ζ) ^Δ indicates ^{1 J}, indicates = “^To)(²* ln(2)Z? + 2* -1)-2 ⁱ⁺¹ (2* -1)^

Y (θ) indicates the zero point of indicates k*’ΊV

S3, according to the closed expression of the transmission power and the transmission rate derived in step S2, determining an upper limit of the power efficiency, and self-adaptively selecting a HARQ type according to requirements of the spectrum efficiency in an actual system, comprising:

substituting , « , and into the target function to obtain optimal power efficiencies using the three different types of the HARQ, respectively:

. fr’-T.y

Ίι.t ^^lT|>/[•«M**-1) for Type I HARQ, the optimal power efficiency '';

* __ l_2^_z* for HARQ-CC, the optimal power efficiency ^^{cc,z Kl};
2¹ 'z-i r i—z - *** < * <f l-2^_£ for HARQ-IR, the optimal power efficiency satisfies ^Kla ^^ir>l ~^r^^1R>^L ~ *^L ^^IR>^L ;

wherein

2018102034 09 Dec 2018 n

^L indicates ,-1

S4. based on the HARQ type and according to the optimal transmission power and the transmission rate, selecting a reasonable channel coding scheme (Turbo code, convolutional code, etc.) and a modulation mode (PSK, QAM, etc.) to maximize the power efficiency of the actual communication system, and ensure communication service quality.

2. The method of claim 1, wherein the proximity result of the interruption probability in step S3 is an upper limit of an actual interruption probability, therefore, the derived optimal power efficiency corresponds to a lower limit of actual system performance, wherein the maximum power obtained by Type I HARQ is 4 In 2 bit/joule, and the maximum power obtained by

HARQ-CC and HARQ-IR is 41n2 bit/joule, wherein ^=1-6617
3. The method of claim 1, wherein the type of the HARQ is selected at step S3 considering the power efficiency and a spectrum efficiency performance graph.
4. The method of claim 1, wherein the channel coding scheme in step S4 comprises a turbo code, a convolution code, a LDPC code, and a polarization code, the modulation mode comprises PSK and QAM.

2018102034 09 Dec 2018