Adaptive Coding and Modulation for Satellite Communication Links in the Presenceof Channel Estimation Errors

Vijitha Weerackody

The Johns Hopkins University, Applied Physics Laboratory

11100 Johns Hopkins Road, MD 20723

Email: Vijitha.Weerackody@jhuapl.edu

Abstract—Adaptive coding and modulation (ACM) schemesare very useful in satellite communication systems because theyprovide variable coding rates and modulation levels that can beused under different channel gain conditions. The effectivenessof the ACM scheme depends on the accuracy of the channelestimates. Because channel estimation plays a key role inACM schemes, we present an estimation technique for thechannel SNR. Furthermore, because channel SNR estimates areunreliable, we modify the ACM scheme to incorporate channelestimation errors. It is shown that this scheme significantlyimproves the performance of the ACM scheme.

I. INTRODUCTION

A typical satellite network may consist of multiple termi-

nals of various antenna aperture sizes that are spread over

a large region. In this scenario the link gains from transmit

terminals to receive terminals may vary significantly because

of the varying antenna gains at the satellite and the terminals.

Moreover, rain fading and other propagation conditions may

also vary the link gains. Furthermore, users may require

varying data rates from the satellite links. Adaptive cod-

ing and modulation (ACM) techniques provide spectrally

efficient transmission schemes that are very effective in

supporting these varying data rates under different link gains.

In ACM a set of distinct transmission rates are obtained by

using different combinations of coding rates and modulation

schemes [1]. Under varying link gain conditions, depending

upon the channel signal-to-noise ratio (SNR), a particular

coding rate and modulation scheme from this set is selected

for the transmission link.

The spectral efficiency of a communication link, which

is the data rate normalized with respect to its bandwidth

(bits/s/Hz), is directly proportional to its SNR. In this paper

we will refer to this normalized data rate as the transmission

rate. In ACM the link SNR is quantized to several contiguous

regions so that each quantized SNR region supports a

particular transmission rate. Smaller quantized SNR regions

give more discrete SNR levels and, because transmission

rates are directly proportional to the SNR levels, more trans-

mission rates. When transmission errors are ignored, smaller

SNR quantized regions yield a larger average transmission

rate when considered over all link conditions. However,

implementation and system complexities limit the number of

transmission rates available from a practical ACM scheme.

The estimation accuracy of the SNR values is a key factor

that determines the transmission rates and the performance

of an ACM scheme. Estimation errors may cause the SNR

to be estimated larger or smaller than its actual value. If the

estimated SNR is larger than its actual value, the receiver

and transmitter may decide on a rate that is larger than that

can be supported by the link. This may cause transmission

errors resulting in loss of overall spectral efficiency. On

the other hand, if the estimated SNR is smaller than its

actual value, the selected transmission rate may be too

small for the link. Again, this results in reduced overall

spectral efficiency because the link capacity is under utilized.

Therefore, estimation accuracy of the channel SNR plays a

crucial role in the overall spectral efficiency of the ACM

scheme.

The specific ACM scheme considered in this paper is

described as follows. First, the transmitter and receiver agree

on an ACM scheme that has a finite number of rates. Second,

the maximum-likelihood estimate (MLE) of the SNR is

obtained at the receiver by observing the received signal

over a known number of symbols. Third, the ACM rate

corresponding to this estimated SNR is determined at the

receiver and the transmitter is instructed, via a feedback

channel, to send at this rate. Finally, the transmitter begins

sending data at this ACM rate.

Adaptive power control schemes are used in satellite links

to adapt the transmit power at the ground terminal or the

satellite to compensate for the path attenuation due to rain.

This is a key feature that improves the spectral efficiency

of satellite communication links and has been examined

in detail in the literature and in practice [2], [3]. In this

paper we focus only on ACM schemes and the topic of

combining ACM with adaptive power control is left for

further study. It should be noted that ACM for high-rate

satellite links has been considered in detail in [4], [5]. In

these papers system-level performance analysis is carried out

for a satellite network that incorporates temporal variations

of the rain and inaccurate estimation of the SNR. The issues

addressed in this work is applicable to a network of SOTM

terminals and consider the specific case of designing the

ACM rates to optimize the overall data rate.

2013 IEEE Military Communications Conference

978-0-7695-5124-1/13 $31.00 © 2013 IEEE

DOI 10.1109/MILCOM.2013.112

622

Combined approaches for ACM and power allocation for

wireless systems have been studied in detail in the literature

[6], [7]. Typically, in a wireless system the transmit power

is varied over all channel conditions and the desired ACM

scheme is obtained by constraining the average power to a

fixed value. On the other hand, in the satellite communica-

tion link problem considered here, maximum power that is

allocated to the terminal is used at all times. This power is

not a variable and is limited by regulatory limits on effective

isotropically radiated power (EIRP) [8] or by the terminal’s

power amplifier stages. Note that in the presence of uplink

power control the transmit power from the terminal changes;

however, the power increase from the terminal compensates

for the fades in the uplink so that, ideally, the power seen

at the satellite is approximately a constant.

II. ESTIMATING THE SIGNAL-TO-NOISE RATIO OF THE

RECEIVED SIGNAL

The topic of estimating the SNR of the received data

symbols has been examined in detail in the literature [9],

[10], [11], [12]. In [9] the MLE of the SNR is obtained

and in [10] this work was extended to include the Cramer-

Rao lower bound for the variance of the SNR estimator. In

this section we will review the MLE for the SNR and its

probability density function (pdf) for the problem considered

in this paper.

At the receiver, the radio frequency signal (RF) is first

downconverted to the baseband and then filtered and sam-

pled by a matched-filter to give the discrete-time signal

required for digital processing. Consider the baseband equiv-

alent form of the received signal just before the matched-

filter

r(t) =∑n

a(n)h(t− nTs) + ω(t) (1)

where a(n) is the complex-valued data symbol whose real

and imaginary components are assumed to be zero mean,

independent and identically distributed (i.i.d.) random vari-

ables, h(t) is a real-valued pulse shaping filter and belongs

to the class of square-root Nyquist pulse shapes, Ts is the

data symbol interval and ω(t) is a zero-mean, circularly-

symmetric, complex-valued additive white Gaussian noise

process (AWGN) with power spectral density N0. The

discrete-time signal is obtained by filtering r(t) using its

matched-filter, h(−t), and sampling at the correct sampling

instant at rate 1/Ts. The sampled output of the matched-filter

is given as

y(k) =√Sx(k) + ω(k) (2)

where S is the signal power, x(k) is the normalized sig-

nal component so that E{|x2(k)|} = 1, and ω(k) is

the noise component. Note that ω(k) is a complex-valued

Gaussian noise process with mean zero and variance N =N0

∫∞−∞ h2(τ)dτ so that the SNR of the signal is S

N .

A. Maximum-Likelihood Estimator for the SNR

The MLE for the SNR has been derived and investigated

in detail in the literature [9], [10]. In this subsection we will

review this estimator in the context of the ACM scheme

considered in this paper. Let us consider a block of K sam-

ples at the output of the matched-filter, y(k). The estimation

problem is stated as follows: obtain the MLE for the SNR of

the sequence {y(k)}, k = 0, 1, 2, . . . , (K − 1), for a given

symbol sequence, {x(k)}, k = 0, 1, 2, . . . , (K − 1). Note

that it is assumed that the receiver knows x(k), which can

be accomplished by inserting a training sequence in the data

stream or using a decision-directed technique [12].

Using the results in [9], [10] the MLE of the SNR is

expressed as

ρML =

1

(∑K−1

k=0 |x(k)|2)2

(∑K−1k=0 (Re{y(k)x∗(k)})

)2

1K

∑K−1k=0 |y(k)|2 − 1

K∑K−1

k=0 |x(k)|2(∑K−1

k=0 (Re{y(k)x∗(k)}))2 .

(3)

Intuitively, because E{ω(k)} = 0, the numerator gives the

estimated signal power and is obtained by correlating y(k)with x∗(k). The denominator is the noise power obtained

by subtracting the estimated signal power from the total

estimated received power.

III. ADAPTIVE CODING AND MODULATION RATES IN

THE ABSENCE OF SIGNAL-TO-NOISE RATIO ESTIMATION

ERRORS

As stated in Section I the SNR level of a satellite

communication link could experience large variations. The

transmission rate (bits/s/Hz) supported by a communication

link is directly proportional to the link SNR. Moreover, for

a spectrally efficient communication link its transmission

rate should be matched, as far as possible, to this varying

SNR level. A practical communication system may support

only a finite set of coding and modulation levels and each

one of these levels gives rise to a single transmission rate.

In the ACM scheme considered here the receiver estimates

the SNR of the link and requests the sender to transmit at

a predetermined rate that is appropriate for this estimated

SNR. In this section let us consider the ideal case when the

SNR is estimated without any errors; estimation errors in

the SNR are considered later in Section IV.

Denote by {r1, r2, . . . , rL}, rl > rl−1, the L transmission

rates (bits/s/Hz) corresponding to L distinct coding and

modulation levels. The link SNR, ρ, is quantized to (L+1)levels {ρ1, ρ2, . . . , ρL+1}, ρl > ρl−1 and ρl > 0, and

assume that ρL+1 = ∞. Denote by r the transmission rate

of the link. Then r is determined by the quantization region

of ρ as follows

r = rl, ρl ≤ ρ < ρl+1, l = 1, 2, . . . , L. (4)

623

Note that r1 is the minimum rate and when the link SNR

is below ρ1 there are no transmissions, that is r = 0. For

a practical communication link, depending upon the coding

and modulation scheme, there exists a relationship between

the transmission rate, r, and the corresponding SNR, ρ. Let

us assume that this relationship can be expressed in the

general form r = p(ρ), where p(·) is a non-decreasing

function. For a capacity-achieving coding scheme this is

r = log2(1+ρ), and for a practical coding scheme this may

be modified to r = log2(1 + ρpρ), where ρp < 1 is a factor

that accounts for non-ideal conditions and inefficiencies in

the coding scheme. Observe that ρp is in general a function

of r. Using the above notation for r, the quantized values

of the transmission rates, rl in (4), can be expressed as

rl = p(ρl). When the statistics of the SNR are known, the

values of the SNR quantization levels ρl that maximizes the

average transmission rate can be determined. Design of these

quantization levels is discussed in the next section.

IV. ADAPTIVE CODING AND MODULATION IN THE

PRESENCE OF SIGNAL-TO-NOISE RATIO ESTIMATION

ERRORS

ρl+1ρl

ρl

ρl+1

ρ̂

ρ

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Figure 1. Two-dimensional map showing potential values of ρ̂ and ρ.

In practice the SNR is estimated with some error and, as

discussed in Section II-A, the MLE for the SNR depends on

the number of data symbols as well as the actual value of the

SNR. This estimation error could have a significant impact

on the overall transmission rate of the link. For example,

suppose the estimated SNR, ρ̂, is quantized as in (4) so that

the transmission rate is rl = p(ρl) when ρl ≤ ρ̂ < ρl+1.

Figure 1 shows a map of the actual received SNR, ρ, and its

estimated value ρ̂. Suppose the estimated value of the SNR

is quantized so that it is in the range [ρl, ρl+1). For this ρ̂value, in the absence of estimation errors, (ρ̂, ρ) should be

located on the Line AB shown in this figure. However, in the

presence of estimation errors (ρ̂, ρ) may be anywhere on this

figure such that ρ̂ ∈ [ρl, ρl+1). Suppose (ρ̂, ρ) ∈ R1. Then

the rate determined by the receiver is p(ρl); unfortunately,

the link cannot support this rate because ρ < ρl so the

effective transmission rate is zero. On the other hand, when

(ρ̂, ρ) ∈ (R2+R3), because ρ > ρl, the link can successfully

send data at rate p(ρl). Note that in Region R3 the SNR is

underestimated because ρ̂ < ρ. The link is underutilized in

this case because it can support a rate larger than p(ρl).Because the SNR is estimated at the receiver, it is nec-

essary to determine the statistics of the MLE of the SNR.

The pdf of the MLE of the SNR is derived in [9] and in

the next subsections this pdf is used to determine the ACM

rates and the corresponding SNR quantization ranges.

A. Optimized Adaptive Coding and Modulation Rates

Let us consider designing the SNR quantization levels

and the corresponding transmission rates to maximize the

average transmission rate. Note that in this paper we consider

only the MLE given by (3). The receiver observes the

signal y(k) shown in (2) and carries out the following

steps: estimates the received SNR, ρ̂; quantizes this to one

of (L + 1) levels, {ρ1, ρ2, . . . , ρL+1}; and determines the

appropriate rate rl as shown below. The objective here is to

determine the quantization levels of ρ̂ and the corresponding

rates rl so that the average rate, ra,e, is maximized. The rate

corresponding to the lth estimated SNR quantization region

is given as

r = rl = p(ρl), ρl ≤ ρ̂ < ρl+1, l = 1, 2, . . . , L. (5)

Note that, as in Section III, r1 is the minimum rate and data

are not sent when ρ̂ < ρ1. Also, ρl+1 = ∞. Observe that

the rate rl is selected when ρ̂ is such that ρl ≤ ρ̂ < ρl+1

and this rate can be supported by the link only when ρ ≥ ρl.It follows that data can be sent successfully when (ρ̂, ρ) are

in Regions (R2 + R3) in Figure 1. Therefore, the average

rate in the presence of estimation errors in the SNR is now

expressed as

ra,e =L∑

l=1

rl Pr{ρl ≤ ρ̂ < ρl+1, ρ ≥ ρl}. (6)

For a given distribution of ρ and the quantization scheme

in (5), the optimum values of ρl can be determined by max-

imizing the above expression with respect to the variables

ρl. Because ra,e in (6) is a two-dimensional integral it is

difficult to obtain closed form expressions for the optimum

values of ρl. However, an iterative scheme similar to that

given in the next subsection can be used here. Note that

in this problem the set of ACM rates, {rl}, are dependent

on the a priori distribution of ρ. The distribution of ρcould be different for different terminal configurations and

propagation conditions. Therefore, in a practical application

there could be several distributions for ρ. In such cases this

method requires multiple sets of ACM rates with each set

corresponding to a single distribution of ρ. This is a key

shortcoming in this optimization problem because it may be

624

necessary to generate multiple sets of ACM rates. Typically,

in a practical application only a single set of ACM rates is

available. What is attractive is to devise an optimum SNR

quantization scheme for this given set of ACM rates. This

scheme is addressed in the next subsection.

B. Quantization of SNR Levels for a Fixed ACM Rate Set

Let us consider the case when the transmission rates are

fixed and given as {r1, r2, . . . , rL}. The problem considered

here is that of determining the quantization scheme for the

estimated SNR that gives rise to these transmission rates.

As noted at the beginning of this section, when the SNR

is overestimated the effective rate could be reduced to zero

because of transmission failures. In order to increase the

success of transmissions, let us consider incorporating a

margin, ζl(≥ 1), to the estimated SNR value so that the

new SNR quantization regions are such that

r = rl = p(ρl) if ζlρl ≤ ρ̂ < ζl+1ρl+1, l = 1, 2, . . . , L(7)

where ζl increases the lower limit of the lth SNR quantiza-

tion level from ρl to ζlρl to account for estimation errors.

Let us compare this quantization scheme to the previous

one shown in (5). Suppose the actual SNR level is such

that ρl < ρ < ρl+1 and the estimated SNR is such that

ζlρl ≤ ρl+1 < ρ̂ < ζl+1ρl+1. Then, according to the

quantization scheme in (7), the transmission rate chosen

is rl = p(ρl) so a transmission failure will not occur. On

the other hand, according to the scheme in (5) transmission

rate for these values of ρ̂ is p(ρl+1), which results in a

transmission failure.

Consider the problem of determining the estimated SNR

quantization levels for a given set of transmission rates,

{r1, r2, . . . , rL}. The variables here are the values ζl, l =1, 2, . . . , L, which can be determined by maximizing the

average rate ra,e. The average transmission rate given in

(6) can be modified and expressed as

ra,e =

L∑l=1

rl

∫ ∞

ρ=ρl

∫ ζl+1ρl+1

ρ̂=ζlρl

fρ̂,ρ(ρ̂, ρ) dρ̂ dρ (8)

where fρ̂,ρ(ρ̂, ρ) is the joint pdf of ρ̂ and ρ. The optimization

problem in this section is expressed as

argmaxζ2,...,ζL

ra,e (9)

where ζ1 and ζL+1 are set to unity.

Next, because it is difficult to obtain an analytical solution

to (9), in this subsection we consider an iterative solution

that maximizes the average rate ra,e. This iterative technique

is carried out in two loops as shown in Table I. Here, the

levels ρl, l = 1, 2, . . . , L, such that rl = p(ρl), are fixed

because rl are given. Consider the maximization stage when

the loop indices are k and l. The quantization levels for ρ̂at this stage are:

{ρ1, ζ

k2 ρ2, ζ

k3 ρ3, . . . , ζ

kLρL, ρL+1

}, where

Table IITERATIVE SCHEME TO DETERMINE ζkl THAT MAXIMIZES ra,e IN (9).

Initialvalues: ζ12 , ζ

13 , . . . , ζ

1L; ζk1 = 1, ζkL+1 = 1

k loop: for k = 1, 2, . . . , kmax

l loop: for l = 2, 3, . . . , L

ηkl (ζ̄) = p(ρl−1)∫∞ρ=ρl−1

∫ ζ̄ρlρ̂=ζk

l−1ρl−1

fρ̂,ρ(ρ̂, ρ) dρ̂dρ

+p(ρl)∫∞ρ=ρl

∫ ζkl+1ρl+1

ρ̂=ζ̄ρlfρ̂,ρ(ρ̂, ρ) dρ̂dρ

ζkl = argmaxζ̄ {ηkl (ζ̄)}; ζkl ≤ ζ̄ ≤ ζkl+1ρl+1

ρl

rka,e,l =∑L

l=1 p(ρl)∫∞ρ=ρl

∫ ζkl+1ρl+1

ρ̂=ζklρl

fρ̂,ρ(ρ̂, ρ) dρ̂ dρ

endζk+1l = ζkl

end

the last level is ρL+1 = ∞, and the corresponding value

of ra,e is denoted by rka,e,l. Note that the role of ζkl is to

ρ̂ρρl+1ρl ζ l

kρl ζ l+1k ρl+1

ζρl = ?

Figure 2. Updating ζkl at the (k, l)th step of the iterative process shownin Table I.

increase the lth SNR quantization level to account for the

estimation errors. Therefore, let us consider updating ζkl at

the (k, l)th step of the iteration so that it is in the range

ζkl ρl ∈[ζkl ρl, ζ

kl+1ρl+1

], when all ζkl′ , l

′ �= l, are fixed. This

range of values for the next update is shown in Figure 2.

It follows from (8) that ζkl contributes to only two integrals

in the L−term summation of rka,e,l. Considering only these

two terms of rka,e,l, the average rate because of only ζkl can

be expressed as

ηkl (ζ̄) = rl−1

∫ ∞

ρ=ρl−1

∫ ζ̄ρl

ρ̂=ζkl−1ρl−1

fρ̂,ρ(ρ̂, ρ) +

rl

∫ ∞

ρ=ρl

∫ ζkl+1ρl+1

ρ̂=ζ̄ρl

fρ̂,ρ(ρ̂, ρ)

where ζ̄ is a variable in the range given below. The optimum

value of ζ̄ at the (k, l)th iteration is then used to update ζkland is expressed as

ζkl = argmaxζ̄

(ηkl (ζ̄)

); ζkl ≤ ζ̄ ≤ ζkl+1ρl+1

ρl, l = 2, 3, . . . , L.

As shown below this iterative scheme converges to a max-

imum value of the average rate function in (8). Because

optimum ζkl is determined by maximizing its contribution to

625

rka,e,l, it follows that rka,e,l+1 ≥ rka,e,l. Also, it follows that

rka,e,2 ≥ rk−1a,e,L. Therefore, it can be seen that this iterative

process converges to a maximum value of ra,e. In the next

subsection we employ this iterative scheme to a specific

scenarios and demonstrate the improvement in the average

rate that is achieved using this scheme.

C. Example: Adaptive Coding and Modulation in the Pres-ence of Rain Fading

Let us apply the ACM scheme with the iterative approach

discussed in the preceding subsection to an example scenario

in the presence of rain fading in the uplink. We do not

consider uplink power control to overcome fading in this

example. It can be shown that the SNR at the receiver, ρ,

can be expressed in the terms of its clear-sky value, ρcs,

as ρ = Auρcs. The rain attenuation factors in the uplink,

Au, are generated according to Rec. ITU-R P.618-10 [13].

For these simulations the transmit terminal was located in

Kumasi, Ghana, and the satellite was stationed at 60◦ E.

The overall link parameters were set such that ρcs = 4dB. The specific error correction coding rates, modulation

schemes and spread spectrum factors that are used are shown

in Table II. Denote the forward error correction (FEC) code

rate by rFEC; modulation level, which is the number of coded

bits per modulated symbol, by mmod; and the waveform

spread factor by sspread. Then the spectral efficiency shown

in this table is given by(

rFEC×mmod

1.2×sspread

)bits/s/Hz, where the

factor 1.2 accounts for pulse shaping filters. As discussed

in Section III, let us assume that the ACM scheme is such

that the rate is given by r = p(ρ) = log2(1 + ρpρ), where

the factor ρp = 0.5 accounts for the deviation from the

ideal Shannon capacity limit. This expression is then used

to compute the SNR quantization ranges, (ρl, ρl+1), l =1, 2, . . . , L, that support the transmission rates shown in the

second column of Table II. Note that these SNR quantization

ranges correspond to the case when there are no errors in

the SNR estimation process.

Table IITHE ACM SCHEME, TRANSMISSION RATES AND THE SNR

QUANTIZATION RANGE USED IN THE SIMULATIONS.

ACM Scheme Transmission SNR QuantizationRate, bits/s/Hz Range, dB

3/4, 8PSK, 1 1.875 [7.26, ∞)3/4, 4PSK, 1 1.25 [4.39, 7.26)2/3, 4PSK, 1 1.109 [3.63, 4.39)1/2, 4PSK, 1 0.834 [1.93, 3.63)1/2, BPSK, 1 0.417 [ -1.75, 1.93)1/2, BPSK, 2 0.209 [-5.07, -1.75)1/2, BPSK, 3 0.139 [ -6.95, -5.09)1/2, BPSK, 4 0.104 [ -8.25, -6.95)1/2, BPSK, 5 0.083 [-9.25, -8.25)1/2, BPSK, 6 0.069 [-10.06, -9.25)1/2, BPSK, 7 0.059 [-10.75, -10.06)1/2, BPSK, 9 0.047 [-11.82, -10.75)1/2, BPSK, 13 0.032 [-13.44, -11.82)1/2, BPSK, 16 0.026 [-14.39, -13.44)

Figure 3 shows the improvement in the average trans-

mission rate obtained using the iterative scheme presented

in Section IV-B and shown in Table I. These figures show

the initial SNR quantization regions obtained using the rates

given in Table II and the modified SNR quantization regions

and the corresponding rates for values of K = 10, 20, 50

and 250. Note that K is the number of complex-valued

symbols used in the estimation of the SNR at the receiver.

From these figures it can be seen that for smaller values

of K, especially for K = 10 or 20, the modified SNR

quantization values are very large for the larger ACM rates.

For example, let us consider K = 20 and the rate equal to

0.834 bits/s/Hz. The initial SNR quantization range for this

rate is (1.93, 3.63) dB. The iterative scheme increases this

SNR range to (1.93, 5.93) dB. Similarly, for larger ACM

rates the corresponding modified SNR quantization values

are significantly larger than their initial values. Table III

shows the final average rates obtained using this iterative

approach. As can be seen this iterative scheme improves the

average rate significantly, especially when K is small. It can

be seen that the average rate improves by 79% and 37% for

K = 20 and 50, respectively. Also, for comparison purposes,

this figure shows the rate obtained when the ACM rates and

the SNR quantization levels are continuous. The average

rate for this case is 1.01 bits/s/Hz, which is substantially

more than the average rate obtained using a finite-level ACM

scheme.

Table IIIAVERAGE RATE FROM THE ITERATIVE SCHEME FOR THE EXAMPLE IN

SECTION IV-C.

Number of symbols, K 10 20 50 100 250Average rate with 0.37 0.39 0.54 0.64 0.74SNR quantization valuesin Table II (bits/s/Hz)Average rate using SNR 0.69 0.70 0.74 0.76 0.79quantization scheme inSection IV-B (bits/s/Hz)

V. CONCLUDING REMARKS

A typical small-aperture satellite communication network

may have diverse channel gains among the large number

of inter-terminal satellite links. ACM techniques are very

useful in such situations because they significantly improve

the overall spectral efficiency. ACM schemes that contain

finer quantization levels for transmission rates increase the

overall spectral efficiency. However, if the channel is not

estimated with sufficient accuracy, because of transmission

errors, the resulting ACM schemes may degrade the overall

spectral efficiency. Therefore, channel estimation is a key

feature for an effective ACM scheme and this issue was

addressed in detail in this paper.

626

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Figure 3. SNR quantization ranges and corresponding transmissionrates for the iterative scheme shown in Table I for the example givenin Section IV-C. Each figure also shows the initial rates, labeled as Non-optimized, given in Table II. Number of symbols in the observation interval,from top to bottom: K = 10; K = 20, K = 50 and K = 250.

REFERENCES

[1] A. Goldsmith, Wireless Communications. Cambridge Univer-sity Press, 2005.

[2] L. J. Ippolito, Satellite Communications Systems Engineer-ing. Atmospheric Effects, Satellite Link Design and SystemPerformance. Wiley, 2008.

[3] A. Dissanayake, “Application of open-loop uplink powercontrol in ka-band satellite links,” Proceedings of the IEEE,vol. 85, pp. 959 –969, jun 1997.

[4] S. Cioni, R. De Gaudenzi, and R. Rinaldo, “Channel esti-mation and physical layer adaptation techniques for satellitenetworks exploiting adaptive coding and modulation,” Inter-national Journal of Satellite Communications and Network-ing, vol. 26, no. 2, pp. 157–188, 2008.

[5] M. Angelone, A. Ginesi, E. Re, and S. Cioni, “Performanceof a combined dynamic rate adaptation and adaptive codingmodulation technique for a DVB-RCS2 system,” in Ad-vanced Satellite Multimedia Systems Conference (ASMS) and12th Signal Processing for Space Communications Workshop(SPSC), 2012 6th, pp. 124–131, 2012.

[6] A. J. Goldsmith and S.-G. Chua, “Variable-rate variable-power mqam for fading channels,” IEEE Transactions onCommunications, 1997.

[7] L. Lin, R. D. Yates and P. Spasojevic, “Adaptive transmissionwith discrete code rates and power levels,” IEEE Transactionson Communications, 2003.

[8] V. Weerackody and L. Gonzalez, “Mobile Small Aper-ture Satellite Terminals for Military Communications,” IEEECommunications Magazine, vol. 45, pp. 70–75, Oct. 2007.

[9] R. M. Gagliardi and C. M. Thomas, “PCM data reliabilitymonitoring through estimation of signal-to-noise ratio,” IEEETransactions on Communications Technology, 1968.

[10] D. R. Pauluzzi and N. C. Beaulieu, “A Comparison ofSNR Estimation Techniques for the AWGN Channel,” IEEETransaction on Communications, vol. 48, pp. 1681–1691,October 2000.

[11] S. Cioni, G. Corazza, and M. Bousquet, “An analyticalcharacterization of maximum likelihood signal-to-noise ratioestimation,” in Wireless Communication Systems, 2005. 2ndInternational Symposium on, pp. 827–830, 2005.

[12] Y. Yang and V. Weerackody, “Estimation of link carrier-to-noise ratio in satellite communication systems,” in IEEEMilitary Communications Conference, 2010 - MILCOM 2010,pp. 1552 –1557, Oct. 31 2010-Nov. 3 2010.

[13] International Telecommunication Union. RecommendationITU-R P.618-10, Propagation data and prediction methodsrequired for the design of Earth-space telecommunicationsystems. 2009.

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