Patent Application: US-201514816576-A

Abstract:
the present invention proposes a demodulator device , a receiver and a demodulation method for m - ary amplitude shift keying systems that requires partial knowledge of the csi , namely , the channel attenuation coefficient . therefore , the new demodulator , receiver and demodulation method do not require the knowledge of the channel phase shift . consequently , no complicated channel estimation techniques are required , and the system will be very robust to the system impairments such as phase noise , i - q imbalance , etc . in this sense , the new technique is denoted as semi - coherent demodulation . to reduce the complexity of the new scd , a suboptimal demodulator is derived which has much lower complexity than the optimal while providing almost the same error probability .

Description:
in mask modulation , the baseband representation of the transmitted signal is given where m is the modulation order , the amplitudes a i ε for coherent detection , while for ncd a i ≧ 0 . without loss of generality , the amplitudes are selected such that a i + 1 & gt ; a i . moreover , the amplitude spacing is usually assumed to be uniform where a i + 1 − a i = δ . since the average symbol power is normalized to unity , then 1 / mσ i = 0 m − 1 a i 2 = 1 . the transmitted amplitudes can be described by , a i = i × δ , iε { 0 , 1 , . . . , m − 1 }, ( 2 ) assuming that the information symbols are transmitted over a rayleigh frequency - flat fading channel , the received signal can be expressed as ν = ha i + w , iε { 0 , 1 , . . . , m − 1 } ( 4 ) where the channel fading coefficient h is a complex normal random variable h ˜ cn ( 0 , 2σ h 2 ) and w ˜ cn ( 0 , 2σ w 2 ) denotes the additive white gaussian noise ( awgn ). to perform ncd , the energy of the received signal should be computed , η =| ν | 2 =| h | 2 | a i 2 |+( h * a i * w + ha i w *)+| w | 2 . ( 5 ) where (. )* denotes the complex conjugate . the received signal energy η is the decision variable that will be fed to the maximum likelihood detector ( mld ). the conditional probability distribution function ( pdf ) of η can be expressed as p ⁡ ( η | e i ) = 1 2 ⁢ ( σ w 2 + σ h 2 ⁢ e i ) ⁢ exp ⁡ ( - 1 2 ⁢ η σ w 2 + σ h 2 ⁢ e i ) , ( 6 ) where e i = a i 2 . the pdf in ( 6 ) for m = 4 is shown in fig1 where it is clear that the only amplitude that can be identified easily is the a 0 = 0 case . for all other symbols , the probability of error is very high . consequently , ncd of mask can provide reliable symbol error rate ( ser ) only for the m = 2 case , which leads to low spectral efficiency . based on the pdf given in ( 6 ), the mld can be expressed as [ 5 ], it is worth noting that the mld of ncd of mask requires accurate knowledge of σ w 2 and σ h 2 . the ser using mld can be expressed as [ 5 ], p s = 1 - 1 m + 1 m ⁢ ∑ i = 1 m - 1 ⁢ exp ⁡ [ - ln ⁡ ( γ i + 1 + 1 γ i + 1 ) 1 - γ i + 1 γ i + 1 + 1 ] - exp ⁡ [ - ln ⁡ ( γ i + 1 + 1 γ i + 1 ) γ i + 1 + 1 γ i + 1 - 1 ] ( 8 ) the ser of the ncd - mask for m = 2 using optimal mld is presented in fig3 . as it can be noted from the figure , the ser is decreasing as a function of snr , which implies that the ncd of mask where m = 2 can provide reliable ser at high snr values . as it can be noted from the figure , the performance degradation of the ncd as compared to the cd is equivalent to 10 db . unlike the m = 2 case , the m = 4 ser depicted in fig4 shows that ncd is prohibitively high to be incorporated in any practical application . as it can be seen from the figure , the ncd suffers from an error floor at ser ˜ 0 . 3 . the ser for the cd in rayleigh fading channels is reported in [ 6 ]. to eliminate the impact of the multiplicative fading we introduce the new scd , which can be obtained by equalizing the received symbols energy using only the magnitude of the channel coefficients . the equalized envelop ζ can be expressed as as depicted in ( 9 ), the multiplicative effect of multipath fading has been converted into an additive disturbance . the process of computing | h | 2 for practical systems will be presented in the following sections . the conditional pdf of the decision variable ζ is given by p ⁡ ( ζ | e i ) = ( ψ i + σ w 4 ) ⁢ σ h 2 [ ( ζ - e i ) 2 ⁢ σ h 4 + 2 ⁢ ψ i + σ w 4 ] 3 / 2 ( 10 ) where 104 i =( ζ + e i ) σ w 2 σ h 2 . as it can be noted from fig2 that considers the m = 4 case , the conditional pdfs are well separated and the tails of both pdfs decay rapidly as a function of ζ which implies that the ser will be much lower than that of the conventional non - coherent detectors . moreover , it can be noted that the peak values of the pdf is inversely proportional to the transmitted amplitude , which is uncommon in most conventional systems . the ser of the scd using mld is presented in fig3 and 4 for m = 2 and 4 , respectively . as it can be noted from both figures , the ser of the scd significantly outperforms ncd . moreover , scd managed to provide reliable ser for m & gt ; 2 , which implies that it can provide higher spectral efficiency as compared to ncd . furthermore , it can be noted from fig3 that the ser degradation of scd as compared to cd is about 5 . 5 db at ser of 10 − 3 , and it is about 11 db when m = 4 . based on the pdf given in ( 10 ), it can be shown that the optimum detector has high complexity , and it requires the knowledge of σ w 2 and σ h 2 . consequently , suboptimal solutions should be considered . towards this goal , it is straightforward to show that in high snr scenarios , an efficient suboptimal detector for scd can be expressed as â i = argmin e i [ ζ − e i ] 2 , i =[ 0 , 1 , . . . , m − 1 ], ( 11 ) which corresponds to the minimum distance detector ( mdd ). the ser based on p s = 1 - 1 m + 1 m ⁡ [ ∑ i = 1 m - 1 ⁢ λ i - ∑ i = 2 m ⁢ χ i ] , ( 12 ) λ i ⁢ = δ ⁢ 1 - δ 2 ⁡ [ i - 0 . 5 ] ⁢ γ 2 ⁢ ( δ 2 ⁡ [ i - 0 . 5 ] ⁢ γ ) 2 + 2 ⁢ δ 2 ⁡ [ 2 ⁢ ⁢ i 2 - 3 ⁢ ⁢ i + 1 . 5 ] ⁢ γ + 1 χ i ⁢ = δ ⁢ 1 + δ 2 ⁡ [ i - 0 . 5 ] ⁢ γ 2 ⁢ ( δ 2 ⁡ [ i - 1 . 5 ] ⁢ γ ) 2 + 2 ⁢ δ 2 ⁡ [ 2 ⁢ ⁢ i 2 - 5 ⁢ ⁢ i + 3 . 5 ] ⁢ γ + 1 . γ = σ h 2 σ w 2 ⁢ e _ , and ē = 1 / mσ i = 0 m − 1 e i is the average power per symbol which is normalized to unity for all systems . the ser for m = 2 is shown in fig5 using mld and mdd . because the mld and mdd have equal ser for the cd , only one curve is presented . as it can be noted from the figure , the ser degradation of scd as a result of using mdd is negligible while it is substantial for the ncd case . consequently , the mdd for scd offers near - optimal ser with low complexity . as it can be noted from ( 9 ), the partial csi required for the scd is the channel attenuation coefficient | h | 2 . the most straightforward approach to obtain | h | 2 is to insert pilot symbols within the information symbols with a particular time spacing . the spacing between the pilot symbols can be optimized based on the channel variations in the time domain . for quasi static and slowly varying channels , the number of pilots is insignificant and hence , the spectral efficiency degradation becomes negligible . the main requirement for the pilot symbols is to have a constant modulus , | s | 2 = p , where p is a constant . therefore , the energy of the received signal when a pilot symbol s is transmitted can be expressed as , η p =| ν p | 2 =| h | 2 | s | 2 +( h * s * w = hsw * )+| w | 2 . ( 13 ) the estimated value of | h | 2 ≐ α can be obtain by computing { circumflex over ( α )}= η p /| s | 2 . the channel variations over time can be described using jake &# 39 ; s model [ 7 ]. assuming that the channel is rayleigh fading with l h independent multipath components , the time correlation between the channel coefficients can be expressed as , e [ h n h m ]= β l j 0 ( 2π f d t s ( n − m )), ( 14 ) where t s is the symbol period , β l is the normalized power of the lth multipath component where σ l = 0 l h β l = 1 , j 0 (.) is the bessel function of the first kind and zero order and f d is the maximum doppler shift . therefore , the time variation over few consecutive symbols is small . in broadband communications , the ratio of number of pilot symbols to the information symbols is one of the main factors that determine the system spectral efficiency . typically , the pilot spacing in the time domain is about 4 symbols [ 8 ]-[ 13 ]. in the previous parts , the ser performance was obtained under ideal channel conditions and perfect channel estimation . therefore , this section presents the ser in the presence of mobility , channel estimation errors , and phase noise . the ser of the scd in the presence of mobility is presented in fig6 using m = 2 . the channel is assumed to be rayleigh frequency - nonselective with time correlation that follows the jake &# 39 ; s model . the bit rate is set to 2 mbps and the carrier frequency is 2 . 4 ghz . the pilot symbols are inserted periodically with a separation of 4 data symbols . the channel attenuation at the non - pilot symbols is obtained using linear interpolation . as it can be noted from the figure , the ser degradation is less than 3 db for a vehicle speed ( v ) of 120 km / h and it is about 2 db when v = 60 km / h . although such degradation is generally acceptable at such high speeds , the ser can still be improved using more accurate interpolation techniques . the ser of scd and cd in the presence of phase noise ( pn ) is presented in fig7 the received signal in the presence of pn can be expressed as ν = he jφ a i + w , iε { 0 , 1 , . . . m − 1 } where φ is a function of the phase noise power , and it is typically modeled as a random jitter φ ˜ n ( 0 , σ pn 2 ) [ 14 ], where σ pn 2 is measured in rad 2 . as it can be noted from the figure , the ser of scd is independent of the pn , which is expected because the ser depends only on the magnitude of the channel response . on the contrary , cd is sensitive to pn particularly at high values of σ pn 2 . it is worth noting that pn can be caused by the transmitter and receiver frequency jitter , timing and frequency synchronization , and channel estimation error , therefore , large pn values might be experienced in particular system and channel conditions [ 14 ]. the new receiver for digital communication systems proposed is based on a novel demodulation technique that requires only partial knowledge of the channel state information , which simplifies the channel estimation process . the error rate performance of the new receiver is substantially lower than that of the conventional non - coherent demodulators . the proposed system enables high spectral efficiency implementation of digital communication systems by exploiting the pilots for joint data transmission and channel estimation . in this section , we propose a low complexity blind channel estimation technique using acd . as it can be noted from aforementioned discussion , the partial csi required for the acd is the channel attenuation coefficient α . the most straightforward approach to obtain α is to insert pilot symbols within the information symbols , and then use least - squared estimation to compute α . the main requirement for the pilot symbols is to have a known amplitudes at the detector side . therefore , without loss of generality , we assume that the pilot symbols d psk { l } satisfy | d psk { l } | 2 = c { l } = 1 ∀ l . since mpsk has constant modulus , we assume that all pilot symbols are mpsk modulated . if the pilot and data symbol during the lth signaling interval are denoted by d psk { l } and d ask { l } , respectively , then the transmitted frame has generally the following structure , d =[ d psk { 1 } , s ask { 2 } , . . . , d ask { q } , d ask { q + 1 } , d ask { q + 2 } , . . . , d ask { 2q } , d psk { 2q + 1 } , . . . ]. ( 15 ) the value of q depends on the channel coherence time , spectral efficiency , interpolation error tolerance , etc . using least square estimation , the channel attenuation factor obtained from the lth pilot symbol can be expressed as , α ^ = ⁢  r psk  2  d psk  2 = ⁢ α + h * ⁢ d psk * ⁢ w + h ⁢ ⁢ d psk ⁢ w * +  w  2 ( 16 ) where r psk is the received signal that corresponds to a given pilot symbol . similar to conventional coherent systems , the channel estimates can be used to form the following sparse vector a =[{ circumflex over ( α )} { 1 } ], 0 { 2 } , . . . , 0 { q } , { circumflex over ( α )} { q + 1 } , 0 { q + 2 } , . . . , 0 { 2q } , { circumflex over ( α )} { 2q + 1 } , . . . ], 2q + 1 = l . ( 17 ) then , interpolation can used to compute { circumflex over ( α )} { i } where = l mod q ≠ 1 . finally , the data symbols can be detected by computing { circumflex over ( d )} ask { l } =| r ask { l } | 2 /{ circumflex over ( α )} { l } , l mod q ≠ 1 . as it can be noted from the aforementioned discussion , the pilot symbols design and channel estimation approach used are generally similar to those used in coherent detection . however , it is interesting to note that once { circumflex over ( d )} ask { l } is obtained , then the full csi can be obtained for all data symbols where ĥ ask { l } = r ask { l } /{ circumflex over ( d )} ask { l } , l mod q ≠ 1 . then , interpolation can be used to find ĥ psk { l } , l mod q = 1 , which allows constructing the vector ĥ =[ ĥ { 1 } , ĥ { 2 } , . . . , ĥ { l } ]. consequently , the entire received vector can be detected coherently where r =[ r { 1 } , r { 2 } , . . . , r { l } ], ĥ = diag { ĥ { 1 } , ĥ { 2 } , . . . , ĥ { l } }, and (.) denotes the hermitian transpose operation . therefore , if the pilot symbols are regular mpsk data - bearing symbols , then the data can be recovered and utilized . in this sense , the data and pilot symbols exchange their roles recursively to estimate the csi and detect the data with low complexity and no power or spectrum penalties . fig8 shows the proposed technique using a simple frame structure , where each frame is composed of two symbols , one ask and psk . the interpolation is not required in such scenarios because h { l } ≈ h { l + 1 } . because both d psk and d ask symbols are bearing data , none of them should be referred to as pilot symbol . moreover , the ratio between the number of psk and ask symbols is channel and system dependent . however , psk ser is typically lower than acd . therefore , the number of psk symbols can be increased to provide lower ser as long as the separation between ask symbols is small enough to provide accurate channel estimation . it is important to note that using a 0 = 0 for channel estimation with acd should be avoided since the channel coefficient is undefined in such scenarios . a simple solution to resolve this matter is to use a m =( m + 1 )× δ , mε { 0 , . . . , m − 1 }. for an average power 1 / mσ m = 1 m e m = 1 and equally spaced constellation points , the amplitude separation can be defined as s m + 1 − s m ≐ δ , where δ = 6 ( m + 1 ) ⁢ ( 2 ⁢ ⁢ m + 1 ) . it is worth noting that the ser when a 0 & gt ; 0 is higher than the case where a 0 = 0 due to the loss of power efficiency . such limitation can be avoided by setting a 0 = 0 , however , csi over the entire frame has to be recovered from nonuniformly spaced samples [ 15 ]. fig9 shows the ser using the proposed blind channel estimation algorithm compared to qpsk modulation under different scenarios . the results are obtained for n = 1 and m = 4 regardless of the modulation type . the transmitted frames for qpsk modulation with pilot estimation are composed of 5 symbols with qpsk modulation , 4 data symbols and one pilot , and all symbols have equal power . the proposed hybrid frame comprises of 5 symbols as well , 4 qpsk modulated and one with 4 - ask modulation . the channel is assumed to be quasi - static rayleigh fading where the channel parameters remain fixed over one frame period , while they changes randomly at different frame periods . as it can be noted from the figure , the pure acd with perfect channel estimation exhibits the highest ser . such performance is obtained because mask is less power efficient than qpsk even under imperfect channel estimation conditions . however , the ser of the hybrid frame using the proposed channel estimation exhibits a 4 db improvement over mask with acd at ser = 10 − 3 . the ser of conventional qpsk with pilot based channel estimation leads the proposed system by about 3 . 5 db . however , such ser performance improvement is obtained at the expense of spectral efficiency . moreover , the ser degradation is caused partially by channel estimation errors and the higher ser of the mask symbol used within the frame . nevertheless , the proposed blind channel estimation demonstrated a highly reliable results with 100 % spectral efficiency . moreover , the performance gap could be less under more severe channel models such as the ones with strong phase noise . j . proakis and m . salehi , digital communications , 4th edition , mcgrawhill , 2001 . a . al - dweik and f . xiong , “ frequency - hopped multiple - access communications with noncoherent m - ary ofdm - ask ,”, ieee transactions on communications , vol . 51 , no . 1 , pp . 33 - 36 , january 2003 . d . divsalar and m . simon , “ multiple - symbol differential detection of mpsk ,” ieee transactions on communications , vol . 38 , no . 3 , pp . 300 - 308 , march 1990 . o . ozdemir , r . hamila , and n . al - dhahir , “ exact average ofdm subcarrier sinr analysis under joint transmit — receive i / q imbalance ,” ieee transactions on vehicular technology , vol . 63 , no . 8 , pp . 4125 - 4130 , october 2014 . r . mallik and r . murch , “ noncoherent reception of multi - level ask in rayleigh fading with receive diversity ,” ieee transactions on communications , vol . 62 , no . 1 , pp . 135 - 143 , january 2014 . m . simon and m . alouini , digital communication over fading channels — a unified approach to performance analysis , 1st ed ., wiley , 2000 . w . c . jakes , microwave mobile communications . piscataway , n . j . : ieee press , 1994 . radio broadcasting systems ; 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