AU2018102035A4 - Methods for maximizing goodput of harq-ir over correlated rician fading channels - Google Patents

Abstract

Embodiments of the present application provide a method for maximizing goodput of Hybrid Automatic Repeat request-Incremental Redundancy (HARQ-IR) over correlated Rician fading channels, which implements a solution for optimizing the transmit power and transmit rate when the LOS and time correlation exists. The basic idea of the solution is to limit the maximal average total transmit power while maximizing the goodput utilizing the asymptotic analysis result. The steps include: firstly, deducing an asymptotic outage probability according to statistic characteristics of channel status information, constructing an optimization problem of goodput maximization according to the power limit, decomposing the optimization problem into two sub-optimization problems, i.e. power allocation and rate selection, utilizing the asymptotic analysis result; finally, selecting a reasonable transmission solution according to the optimal power and optimal rate. Compared with the Rician fading scenario, the Rician fading with the LOS is benefit for the improvement of the system performance. While, compared with the traditional methods, the usage of asymptotic outage probability in optimization not only reduces the computation complexity, but also does not cause damage to the system performance. Maximizing HARQ-IR goodput according to statistical characteristic of the CSI in the Maximizing T = R(1 - p ) correlated Rician fading channels Obtaining optimal transmit power and optimal transmit rate r ec ione f"" '"I Selection of adaptive coding scheme adaptive i modulation mole Transitt ) Error J (X) Error 1P(X) Senda4 X" Trnmitrdetection ,o correction cache Modulator code Co code C1 HARQ control Correlated Rician h fading channel Feedback channel (ACK/NACK) Gaussian noise HARQ control X Error (X) Error Receiv Demodulator Receiver detection correction cachee /balancer code Co code C1 I hi

Description

METHODS FOR MAXIMIZING GOODPUT OF HARQ-IR OVER

CORRELATED RICIAN FADING CHANNELS

TECHNICAL FIELD [0001] The present application relates to a field of wireless communication technologies, and more particularly, to a method for maximizing goodput of Hybrid Automatic Repeat request-incremental Redundancy (HARQ-IR) over correlated Rician fading channels.

BACKGROUND [0002] As an effective technique to enhance communications reliability,

HARQ has been widely used in almost all wireless communication systems. Recently, various HARQ schemes operating over Rician fading channels have received increasing research interests typically in light-shadow fading environments (e.g., shopping complex, satellite/airplane-to-ground communications) because of the presence of strong dominant Line-Of-Sight (LOS) component. It should be mentioned herein that Rician fading channels degenerate to Rayleigh fading channels when LOS component vanishes, and HARQ schemes over either correlated or independent Rayleigh fading channels have been vastly investigated. It was shown that ignoring the effect of LOS path would significantly overestimate the system performance and therefore yield misleading design guideline on system performances and optimization design. Therefore, it is considerably necessary to study the performance of HARQ over Rician fading channels that is indispensable for the optimal design of HARQ systems. Pimentel for example studied the error-detecting probability of Type I

2018102035 09 Dec 2018

HARQ over Rician fading channels by using finite-state channel model, based on which the effects of various system parameters upon goodput performance were examined. It is well known from information theoretical aspect that the performance of Type I HARQ is equivalent to that of selection combining in diversity combining due to the same form of signal-to-noise ratio (SNR). Since the existing literature has performed research on selection combining of Rician fading channels, thus these analytical results are also applicable to Type-I HARQ over correlated Rician fading channels.

[0003] However, Rician fading channels are seldom considered into shaping the performance of HARQ schemes with Chase Combining (CC) and Incremental Redundancy (ER) due to the intractability of tackling the sum and the product of multiple shifted random variables, respectively. At present, it is difficult and full of challenges to process the mathematical approach. Nevertheless, since HARQ-CC is essentially the application of Maximal Ratio Combining (MRC), the foregoing research result is also applicable to the analysis of HARQ-CC. Unfortunately, no readily available method can be employed for the analysis of HARQ-IR over Rician fading channels. The outage probability and goodput of HARQ-IR were derived by assuming quasi-static Rician fading channels, in which all HARQ rounds undergo a constant channel realization. This assumption simplifies the analysis of HARQ-IR owing to dealing with only a single random variable, but is certainly inapplicable to that of HARQ-IR over generalized Rician fading channels. To overcome this shortcoming, the present application focuses on the analysis and optimal design of the

2018102035 09 Dec 2018

HARQ-IR over arbitrarily correlated Rician fading channels, which incorporate the impacts of both LOS component and channel time correlation. According to statistical characteristics of status information of correlated Rician fading channels, the present application designs a scheme for optimizing and selecting goodput-maximized power and rate of the HARQ-IR.

SUMMARY [0004] An objective of the present application is to overcome the above disadvantages in the prior art, and provides a method for maximizing goodput of Hybrid Automatic Repeat request-incremental Redundancy (HARQ-IR) over correlated Rician fading channels.

[0005] The objective of the present application may be achieved via the following technical solution:

[0006] Since the performance of the HARQ depends on the performance metric of the outage probability, the outage probability of the HARQ-IR over correlated Rician fading channels is firstly calculated, which is an indispensable step in the design of HARQ-IR system optimization. In order to obtain simple closed-form outage probability, the expression of the outage probability in the high SNR regime may be asymptotically analyzed, and the analysis should consider the impact of the LOS and time correlation on the outage probability. Based on the constructed goodput maximization problem and the obtained simple closed-form outage probability, the optimal transmit power and transmit rate are decomposed. At last, modulation and

2018102035 09 Dec 2018 coding solution may be reasonably selected using the optimal transmit power and optimal transmit rate. The design diagram of the goodput maximization is shown in figure 1, the implementation steps of the technical solution is shown in figure 2, including three steps, each of the step is described as follows:

[0007] SI, deducing an asymptotic outage probability according to statistic characteristics of channel status information, including:

[0008] SI01, constructing a HARQ signal transmission model according to a

HARQ-IR mechanism, firstly encoding each original information message to a long codeword, equally partitioning each long codeword into & sub-codewords, wherein K denotes the maximum allowable number of transmissions, all symbols of & -th sub-codeword xk experience same channel realization in transmission when a block fading condition is satisfied, a signal ^k received in the -th HARQ round is

Ik = ^hk^k + , h n wherein, ^k denotes a channel impulse response, ^k denotes a complex Additive White Gaussian Noise (AWGN) vector with zero mean and covariance matrix 4,

i.e. n, ~ CN (0,N ₀I).

[0009] SI02, constructing a correlated Rician fading channel model, denotes a correlated Rician fading channel response vector, |_ ^K follows a multi-variate circularly-symmetric normal distribution whose expectation vector and covariance matrix are x (^ζ,ΐ’···’^ζ,χ) and C^=E((h*-h£^)(hr-h£(J!:) ) = E(hxhx ) , wherein ^hz,x stands for

Line-Of-Sight (LOS) components;

2018102035 09 Dec 2018 [0010] SI03, calculating an asymptotic outage probability, as the SNR tends to

P_k —---> oo

N v infinity, i.e., ⁰ , an asymptotic outage probability expression after K times of transmission is expressed as:

wherein,

denotes signal transmit power of -th transmission, £ is a preset signal transmit rate, g_K(R) = (-1/ + 2^(-1/

4=0 (J? In 2)^¹ (XT-Ar-l)!

[0011] S2, constructing an optimization problem of goodput maximization and decomposing the optimization problem;

[0012] wherein in a solution for maximizing goodput of the HARQ-IR over correlated Rician fading channels, a performance metric for evaluating the goodput of a single HARQ transmission is effective goodput ⁸ ' Pout,K), _meanwhile, in order to ensure that the energy efficiency is not too low, maximal average transmit power is limited while maximizing the goodput, the goodput is maximized via optimizing the transmit power and transmit rate and the optimization problem is constructed as:

max	Ροια,κ} K
S.t.	^iPkPout,k-l — PT k=l R>0

2018102035 09 Dec 2018 [0013] ^Pout’^k denotes a system outage probability after times of p

transmission, ^r denotes the maximal threshold of an average transmit power, the goodput maximization is sequentially decomposed into optimal power allocation and optimal rate selection, a decomposing step includes:

[0014] S201, performing optimal power allocation, wherein for any given p ,,, p transmit rate R, optimization of transmit powers i’”’> κ j_s re-expressed a problem of minimized limit:

“I? Pout,K

K ^s-t- ^jPkPout,k-\ — ^Pt k=\

Pv—,P_K>Q , [0015] putting the asymptotic outage probability expression obtained in step

SI into the above optimization problem, the optimal transmit power is expressed as:

* P 2^K~^l

P* _ ¹ 2*-l

I'Yk-l [0016] S202, performing optimal rate selection, wherein after the optimized transmit power is determined, the optimal transmit power is expressed as a transmit rate function, the optimal transmit power is put in an original optimization problem, the optimization problem is finally converted into the selection of the optimal rate:

T_g

Sk-A^R})

R>Q max

R

s.t.

[0017]

Wherein

2018102035 09 Dec 2018

transmit rate is decomposed with one dimensional finite search;

the optimal [0018] S203, performing optimal rate approximated close-form decomposition, wherein computation complexity of the optimal transmit rate is reduced with bounds [0019] τ τ (r]

S2031, replacing the goodput ⁸ with upper/lower bound ^a ' ', when ^a — L denotes the bounds of the goodput, ^a —R denotes the upper bound of the goodput, that is , ζ_α=\ [0020] wherein, f-T

KJ f i Y KJ ,K-k-l , a — L

K-k (ln(2))² , a-U [0021]

S2032, with the bounds of the goodput, relaxing the original optimization problem as:

max

R

s.t.

T_a{R} = R-(_a{R(2^R

R>Q

-of ,X-1 [0022]

S2033, configuring the optimal transmit rate corresponding to the bounds of the goodput as a zero point of ^a , i.e., Ψ^a (θ) , wherein ^Ι(2^ί'-1 + Ιιι(2)Λ2^ί') [0023]

S3, reasonably selecting an actual transmission solution;

[0024] wherein a coding and decoding solution and an adaptive selection

2018102035 09 Dec 2018 modulation technology are reasonably selected according to the optimal transmit power expression and optimal transmit rate expression.

[0025]

Further, the bounds of the effective goodput derived at step S203 is

7?ln(2)^ g_k(R) 7?ln(2) obtained via an inequality & k [0026]

Further, a relationship between the optimal goodput corresponding to

T (R*} < T* < T (R*) the bounds in step S203 and a real optimal goodput is ^{L L s u u} .

_Δ dT(R\ ^_Ο(Λ) = ’

Further, a function dR j_{n s}t_ep S203 is a monotone [0027] decreasing function, a zero point of the function uniquely exists and is obtained by performing rapid value calculation using a bisection method.

[0028]

Further, in high SNR regime, the optimal goodput obtained at step S2 follows a scaling law of

	i	( p
0	log2	rT KJJ
	k

and a slope is 2 2 [0029]

Further, in step S2, the LOS components have positive impacts on the obtained optimal goodput, while time correlation has negative impacts on the obtained optimal goodput.

[0030]

Compared with the prior art, embodiments of the present application have following advantages and effects:

[0031] 1. Taking the outage probability as the basic performance metric, embodiments of the present disclosure try to perform asymptotic analysis on the outage probability in high SNR regime. The closed-form of the asymptotic outage probability not only quantifies the impact of the LOS and time correlation, but also optimizes the design of the system due to its simple expression, which is benefit for

2018102035 09 Dec 2018 the present application to implement maximization of the effective goodput. Where, the effective goodput is an important metric for measuring the average goodput of the HARQ.

[0032] 2. Via limiting the maximal average transmit power, the optimal transmit power and transmit rate are selected to maximize the system goodput. Using the decomposing theorem, the goodput maximization problem is converted to the single variable optimization problem, which may reduce the computation complexity.

[0033] 3. Further, meaning insights may be obtained from the optimized result, such as the scaling law of the optimal goodput with regard to the SNR, negative impact of the time correlation on the optimal goodput and a result that the system performance of the HARQ-IR may benefit from the LOS. These direct conclusions may have profound guiding significance for the design of the HARQ-IR system.

BRIEF DESCRIPTION OF THE DRAWINGS [0034] Figure 1 is a schematic of a system in accordance with various embodiments of the present application;

[0035] Figure 2 is a flow chart illustrating an algorithm of goodput maximization in accordance with various embodiments of the present application;

[0036] Figure 3 is a verification schematic of asymptotic outage probability in accordance with various embodiments of the present application; and [0037] Figure 4 is a diagram illustrating performance comparison between goodput maximization algorithm and uniform power allocation algorithm in

2018102035 09 Dec 2018 accordance with various embodiments of the present application.

DETAILED DESCRIPTION [0038] Embodiments of the present application will be described in detail hereinafter with reference to accompanying drawings and embodiments to make the objective, technical solutions and merits therein clearer. Apparently, the described embodiments are part of, rather than all of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art of the present application without creative work should be covered by the protection scope of the present invention.

[0039] Embodiment [0040] In embodiments of the present application, the application of the

HARQ-IR over correlated Rician fading channels is taken into consideration. According to the HARQ-IR mechanism, each original information message is first encoded to a long codeword and then equally partitioned into K sub-codewords, where K denotes the maximum allowable number of transmissions. The K sub-codewords will be delivered one by one until the destination succeeds in decoding the message. It is worth mentioning that code combining technique is employed at the destination for signal reception. Specifically, the erroneously received sub-codewords are combined with the currently received sub-codeword for joint decoding. Based on the success or the failure of the reception, a binary positive/negative acknowledgement message (ACK or NACK) will be fed back to inform the source.

2018102035 09 Dec 2018

Define xk as the k-th sub-codeword. We assume a block fading channel which means that all the symbols of xk experience the same channel realization in the k-th transmission. Accordingly, the signal received in the kth HARQ round is written as y_k = ^h _k*_k + «λ (i) [0041] where ⁿ* denotes a complex Additive White Gaussian Noise (AWGN) vector with zero mean and covariance matrix i.e. ⁿ* ~ (θ>Ν₀Ι) I h

represents an identity matrix; ^k denotes the channel impulse response in the kth transmission. Unlike prior literature, both time correlation and LOS links are considered to accurately examine the performance of HARQ-IR when in light-shadow fading and slow-to-medium mobility environment, and they would apparently affect the performance as well as the optimal design of HARQ-IR. To this end, the h =(h. hl correlated Rician distribution is herein adopted to model ^{K v} t’”' ^k) . More |_ specially, ^K follows a multi-variate circularly-symmetric normal distribution whose expectation vector and covariance matrix are (^ί,ΐ’···’^ί,κ) _and ^Cx ^E((^hv ^h/.,J0U ^h/.,J ) E(hxhx ). _wherein Κλ stands for the

LOS components, (*)^H stands for scattering components, symbol and dct(·) _reSp_ecti_vely denote operations of conjugate transpose and determinant. To reflect the strength of the LOS components relative to the scattering h_L,_k I² /-2

E h_k components, the Rician factor of the k-th channel coefficient is joint Probability Density Function (PDF) of ^K is given by:

2018102035 09 Dec 2018

Α_χ(^)^— κ j .ίΓ< ex^p{ (hA« h_£A:) C_K (h^ det(C^) ^{v J} ₍₂₎ [0042] From (1), the received SNR in the kth HARQ round is obtained as ₇ =aM ‘ ^N» (3) [0043] where Pk is the transmit power in the kth HARQ round.

[0044] 1. Asymptotic outage probability [0045] Outage probability is known as the most essential metric to evaluate the performance of HARQ systems. By applying information-theoretic capacity achieving channel coding to HARQ-IR, an outage will be declared if the accumulated / = ?* log (1 + 7 ) mutual information ^K 2 k j_s b_ei_ow q_)e transmit rate R. More precisely, the outage probability of HARQ-IR after K HARQ rounds is given by P„« = ^Pr(L</?) = Ρτ[Π(1 + η)<2''

k. W ) (4) [0046] Its analysis consequently turns to determine the distribution of the product of multiple shifted SNRs. However, the time correlation among fading channels leads to correlated SNRs, which makes the derivation of P^u!<^K challenging because of the involvement of multi-fold integral. More specifically, putting (3) into (4) gives rise to (5)

Where, d^d^h,} ,.M{h_K}d3{h_K} _md [0047] ^{L J} respectively denote the real and imaginary parts of complex number ^z. In a large number of existing literature, either time-correlated Rayleigh or Nakagami-m

2018102035 09 Dec 2018 fading channels are assumed for the outage analysis of HARQ-IR, the channel model in (2) accounts for the impacts of LOS link as well as time correlation, thus further impeding the mathematical derivation of . It is virtually impossible to obtain an exact expression for P°^ut’^K via the integral in (5). Instead, in embodiments of the present application, asymptotic outage analysis is conducted in the sequel to offer a compact and insightful expression for outage probability in high SNR regime.

[0048]

P, —---> oo

N

As the SNR tends to infinity, i.e., ⁰ , the domain of integration in (5) ⁰ denotes ^{1 k 1} .Here, we have

Λ, (h) Λ_α. (θ) = K . . ^{k k} π det(C_x) k=l [0049]

Where the notation refers to “asymptotically equal to”.

Accordingly, (5) can be rewritten as

a- „ ¢/11 = n β₍₁₊Α|_Λ*|² _)<2* K Pasy_out.K k=i ^Λ θ (7) [0050]

Where pasy_out;K is the asymptotic outage probability under high

SNR. With the definitions of hK and dhK, the asymptotic outage probability pasy_out;K can be expressed as

Π(1+>ΗΜ)Ν(3{Μ)²)<2«

4=1 ^1N θ (8) [0051] Applying polar coordinates to (8), i.e., ^rk ^cos @k _anJ (3) then can be derived as:

(9)

2018102035 09 Dec 2018 [0052] /•2/r

-J,· άθ_γ···άθ_κ /'_Kdi\ · · dr_K

By making the change of variable as (9) can be simplified as t =^r^{2 k} N_o ^k and ^€ II· , v * * _ J

Sk(_R) (10) [0053]

Where, can be expressed as = (-])-₊2-Σ(-1)^Λ7?1η2)^ h (K-k-l)\ ₍₁₁₎

Where is an increasing and convex function of R . Plugging

10054]

[0055] where A, B and C clearly signify the influences of time correlation and

LOS paths, transmit rate, and transmit powers, respectively,

f.A' det(CJ and ¹ by convention. The simple expression of asymptotic outage probability not only uncovers insightful results but also facilitates the optimal design of HARQ-IR system over correlated Rician fading channels. The correctness of the asymptotic outage probability is verified via figure 3. [0056] 2. Goodput maximization-based asymptotic outage probability

2018102035 09 Dec 2018 [0057] Another widely concerned performance metric in evaluating the goodput of HARQ schemes is goodput, which is defined as the product of transmit

T — — η ) rate and successful probability, i.e., ^{8 V} Ρομ,κ) As proved that the effective goodput is equivalent to the average goodput of HARQ in asymptotic sense, namely high SNR or low outage. Hence, it is meaningful to take the effective goodput maximization as the objective function for optimal design of HARQ-IR. More specifically, here we aim to achieve the maximization of the effective goodput d P P through joint optimization of the transmit rate A and powers >’ ’ . Meanwhile, in order to ensure that the energy efficiency is not too low, the average total transmit

V Pp _ <P power for each message delivery is usually limited, such as * out,k-i τ

P Ό = 1

Where, ^T refers to the allowable average total transmit power, -° is

T defined according to usual practice. Therefore, the maximization of ⁸ is therefore formulated as max

s.t.

κ ^^^kPout,k-\ —^T k=\

R>0.

(13) [0058]

In order to obtain the close-form solution and simply the computation complexity, the asymptotic outage probability is hereafter applied to derive the optimal solution.

[0059]

2. A. Problem decomposition [0060]

To enable the optimization, the special and compact form of

2018102035 09 Dec 2018 η

I'asy^out^ _moti_vates us to decompose (13) into two sub-problems, i.e., optimal power allocation and optimal rate selection, as illustrated below.

[0061] Optimal power allocation: For any given transmit rate R, the transmit powers P 1,...,PK can be optimized first as a function of the rate. It is clear from (13) that the powers are involved in the objective function through the outage probability.

Then given a transmit rate R, the optimization problem in (13) is equivalent to mtn

P out,K

s.t.

[0062]

According to the KKT condition, the optimal transmit power may be deduced as:

K-\ [0063]

Then, the optimal transmit powers are expressed as the function of R, therefore, putting the optimal transmit power into the asymptotic outage probability, n

and the ^^out’^K is expressed as:

Pout,K = g_k(R) nK-k

V (17) [0064] where % is independent of R and is explicitly given by ^Λ P_T1^K~²

A^1-2 lN₀(2^-l)J

K

K

Π k=\ \2^W (18)

2018102035 09 Dec 2018 [0065] p

As expected, (17) is a decreasing function of ^T , which eventually results in the increase of goodput.

[0066]

2) Optimal rate selection: after determining the optimal transmit powers, the second sub-problem is devoted to the optimal rate selection in order to maximize the goodput ^g . Based on (13) and (17), the optimal rate selection is formulated as max

R

Ar=l V g_kW

s.t.

R>Q.

(19) [0067]

Since (19) is a single-variable optimization problem, there are numerous optimization tools that can be used to solve (19) numerically. But it is impossible to derive the optimal rate in closed-form due to the complex form of the objective function, which hinders us from extracting meaningful insights. Here we resort to effective approximation of the goodput using certain lower or upper bound for problem relaxation so that closed-form solution is enabled. To this end, we utilize the following tight inequalities as

Λ1η(2) ^ g_k(R) ^7?ln(2) k-1 g_k^R) k (20) [0068]

Taking the left side inequality of (20) as an example, it yields a lower bound of the goodput. To be more specific, when 2 < k < K, by applying the g_kW inequality to , the goodput is then lower bounded as (21)

2018102035 09 Dec 2018 [0069]

Where, ^K-k-\ (i V

UJ (ln(2))² and denotes

T the lower bound of the goodput. By replacing ⁸ in (19) with the lower bound , the optimization problem is relaxed as max 7;(Λ) = Λ-<_£(Λ(2^Λ-l)f

s.t. R>0.

[0070] (22)

Taking the first order derivative of with respect to R and then setting it equal to zero give the optimal transmit rate, such that

K_L ~Ψ[. (θ) (23) [0071]

Where

6) denotes the inverse function of Ψ^L [0072]

In other words, (23) means that the optimal rate is the zero point of

ΨIt is worth mentioning that the zero point (θ) uniquely exists because

V'lW is a decreasing function of R .

[0073]

Similarly, with the right side inequality of (20), an upper bound of the optimal ζ_ν=«Π be

7^) = ^-^,(^-1))² goodput can be obtained as \ \ //

K-k _OX-1 1 (1(2)) . Similarly, the corresponding optimal =^(0) ^κ f-T ^k={k, derived as = = (2^s -l + in(2)R2^R) , where rate can where

2018102035 09 Dec 2018

R R [0074] After determining the rates ^L and ^u , the corresponding lower and

T (R*) T (R*) upper bounds of the optimal goodput are given by l\ l) and cA u) , respectively. Clearly, the original two inequalities in (20) imply that the optimal

7* goodput ^g can be bounded as:

TA)₍₂₄₎ [0075] 2. B. Discussions [0076] Even section 2.A has provided an analytical approach to obtain the optimal transmit powers and rate, the expression of the approximated optimal rate, i.e., ^a is still very cumbersome and therefore impedes the extraction of meaningful insights for the optimal goodput. In order to perform subsequent asymptotic analysis, the asymptotic property of ^a in the following lemma may be used.

[0077]

P

Lemma 1: under high allowable total average transmit power τ ,i.e., high SNR, ^a can be asymptotically approximated with a lower bound as ln(2) [0078]

9=—-~

Where ln(2)2 IT₀(·) denotes the upper branch of lambert-W function.

[0079]

With this lemma, asymptotic expressions can be derived for the bounds of the optimal goodput in high SNR regime.

Pt

--T (R*3

Theorem 1: in high SNR regime, i.e., , ^a/ approaches to ^a , which means P°^ut>^K , and “ ' ^a' is asymptotic to [0080] \

(26)

2018102035 09 Dec 2018 [0081] and I = (2-2^)108,

Where, k

ln(2)2» |(ln(<

k _ β n det(C_A )t t=i dctlC.,, )e

1-2^a ₂K-1 V ^ZK

2^i;-l, f ii ^Hr ~^lh detCCJe¹¹^ ^Cfc ““

2^K-'ⁱ ,,-2 (28) (27) dominates the impacts of time correlation and LOS links.

T f R* 1 This theorem not only reveals the slope of ^a\ ^a ‘

N the transmit SNR ⁰ , but also exhibits the effects of time correlation and LOS path [0082] with respect to on the goodput, as concluded in the following two remarks.

[0083]

Applying the squeeze theorem to (24) , it follows that lim p_r —--->cc %

< lim %

¹⁰§2 [0084]

Substituting (26) into (29), the slope of the goodput with respect to the

SNR is:

lim---^PT >oo ₁ l°g₂ = 2-2^l_*\ (30)

2018102035 09 Dec 2018 [0085] Accordingly, the scaling law with regard to the optimal goodput is found in the following remark 1.

[0086] Remark 1: in high SNR regime, the optimal goodput follows a scaling law of

		( p Yl
0	log2	N ko ) J
	I

, and the slope is

2-2

1-K

O(-) stands for the big O motation. Clearly as the maximum number of transmissions & increases to infinity, the slope grows from 1 to 2.

[0087] Moreover, the second term I on the right hand side of (26) dominates the impacts of time correlation and LOS links. Clearly, the impacts of correlation matrix CK and LOS channel coefficients h^K on the optimal goodput are heavily coupled, which complicates the analysis. This obliges us to investigate these two impacts separately. Hence, in the following remark, the impact of time correlation is studied by assuming no LOS links, and the impact of LOS links is then discussed in the absence of channel correlation. Finally, the following remark may be obtained.

[0088] Remark 2: Time correlation has a detrimental impact on the optimal goodput, while the optimal goodput can benefit from LOS paths.

[0089] At last, in order to highlight the superior performance of the proposed optimization strategy, the comparison with average power allocation strategy is adopted here, that is, it is assumed that each transmit power is constant. It can be clearly seen from figure 4 that there is apparent distance of goodput of the strategy in SNR, which shows the superior performance of the strategy, that is, the strategy may effectively utilize the statistic characteristics of the channel status information to improve the goodput of the system.

2018102035 09 Dec 2018 [0090] To sum up, the theoretical and numerical analysis results show that in the condition of strict outage constraint and high SNR, the solution provided embodiments of the present disclosure is consistent with the simulation result. Where, the strict outage probability constraint satisfies the requirements in practice. Therefore, this solution is an effective approach to improve power efficiency. The theorem result of the maximum power efficiency in this embodiment also provides very meaningful application instruct and reference value to the actual system design.

[0091] The foregoing is only preferred examples of the present disclosure, which is not used for limiting the protection scope of the present disclosure. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present disclosure, should be covered by the protection scope of the present disclosure.

Claims (6)

1. What is claimed is:

   1. A method for maximizing goodput of Hybrid Automatic Repeat request-incremental Redundancy (HARQ-IR) over correlated Rician fading channels, comprising following steps:

   SI, deducing an asymptotic outage probability according to statistic characteristics of channel status information, including:

   5101, constructing a HARQ signal transmission model according to a HARQ-IR mechanism, firstly encoding each original information message to a long codeword, equally partitioning each long codeword into & sub-codewords, wherein K denotes the maximum allowable number of transmissions, all symbols of & -th sub-codeword xk experience same channel realization in transmission when a block fading condition is satisfied, a signal ^k received in the -th HARQ round is y_k = ^h _k*_k + , h n wherein, ^k denotes a channel impulse response, ^k denotes a complex Additive White Gaussian Noise (AWGN) vector with zero mean and covariance matrix ^.i.e. -h ~CN (0,N₀I).

   h = (h h }

   5102, constructing a correlated Rician fading channel model, ^K v u— |_ denotes a correlated Rician fading channel response vector, ^K follows a multivariate circularly-symmetric normal distribution whose expectation vector and covariance matrix are ^_LtK -(h_Ll,...,h_LK) and

   C*=E((h_x-h_£^)(h*-h_£3r) ) = E(iuiu ) , _wherein ^hz,x _{stands for} Line-Of-Sight (LOS) components;

   2018102035 09 Dec 2018

   SI03, calculating an asymptotic outage probability, as the SNR tends to infinity,

   P_k

   -----> 00

   i.e., No , an asymptotic outage probability expression after K times of transmission is expressed as:

   wherein, ?^k denotes signal transmit power of -th transmission, R is a preset signal transmit rate, gz(R) =(-1)*+2*Σ(-1)* k=0 (7? In 2)^¹ (ΑΓ-Λτ-Ι)!

   S2, constructing an optimization problem of goodput maximization and decomposing the optimization problem;

   wherein in a solution for maximizing goodput of the HARQ-IR over correlated

   Rician fading channels, a performance metric for evaluating the goodput of a single

   HARQ transmission is effective goodput ⁸ ' Pout,K), _meanwhile, in order to ensure that the energy efficiency is not too low, maximal average transmit power is limited while maximizing the goodput, the goodput is maximized via optimizing the transmit power and transmit rate and the optimization problem is constructed as:

   s.t.

   K ^i^kPout,k-l — ?T k=\ ·Λ>θ

   R>0

   2018102035 09 Dec 2018

   P»ut,k denotes a system outage probability after times of transmission, ?^T denotes the maximal threshold of an average transmit power, the goodput maximization is sequentially decomposed into optimal power allocation and optimal rate selection, a decomposing step includes:

   S201, performing optimal power allocation, wherein for any given transmit rate R, optimization of transmit powers i’’”> κ j_s re-expressed a problem of minimized limit:

   min

   Pl ,-,Pk

   Pout,K

   K ^s-t· k=l putting the asymptotic outage probability expression obtained in step SI into the above optimization problem, the optimal transmit power is expressed as:

   ¹ 2*-l

   S202, performing optimal rate selection, wherein after the optimized transmit power is determined, the optimal transmit power is expressed as a transmit rate function, the optimal transmit power is put in an original optimization problem, the optimization problem is finally converted into the selection of the optimal rate:

   max

   R

   R>0

   s.t.

   2018102035 09 Dec 2018

   1^K wherein , ^Λ P_T2^K1 •U-2* lN₀(2*-1)J κ

   Π

   A-=I f 11^ -1.

   detCC^)?⁶*-^{1 Ct}det(C_A)e^hi* ^c* ^t optimal transmit rate is decomposed with one dimensional finite search;

   , the

   S203, performing optimal rate approximated close-form decomposition, wherein computation complexity of the optimal transmit rate is reduced with bounds τ τ (r\

   S2031, replacing the goodput ^s with upper/lower bound , when ^a — R denotes the bounds of the goodput, — R denotes the upper bound of the
2. 2^-1 goodput, that is ' ⁷ ' ’’ fn:¹ a-L wherein,

   S2032, with the bounds of the goodput, relaxing the original optimization problem as:

   max Γ,(Λ) = Λ-<,(λ(2’s.t. R > 0

   0)

   S2033, configuring the optimal transmit rate corresponding to the bounds of the goodput as a zero point of ) , j _e , _a Ψ_α\ ) ₃ wherein (/,^) = 1-^2^(^(2^-1))² ‘(2 -1 +111(2)752⁸).

   S3, reasonably selecting an actual transmission solution;

   2018102035 09 Dec 2018 wherein a coding and decoding solution and an adaptive selection modulation technology are reasonably selected according to the optimal transmit power expression and optimal transmit rate expression.

   2. The method according to claim 1, wherein the bounds of the effective goodput derived at step S203 is obtained via an

   Wk g_k(R) ^ln(2) inequality k
3. 3. The method according to claim 1, wherein a relationship between the optimal goodput corresponding to the bounds in step S203 and a real optimal goodput is
4. 4. The method according to claim, 1, a function ^a dR in step S203 is a monotone decreasing function, a zero point of the function uniquely exists and is obtained by performing rapid value calculation using a bisection method.
5. 5. The method according to claim 1, wherein in high SNR regime, the optimal

   C2 -r goodput obtained at step S2 follows a scaling law of v \ oJJ and a slope is
6. 6. The method according to claim 1, wherein in step S2, the LOS components have positive impacts on the obtained optimal goodput, while time correlation has negative impacts on the obtained optimal goodput.

   2018102035 09 Dec 2018