Digital communication receiver using partial knowledge of the channel state information

Abstract

The present invention proposes a demodulator device, a receiver and a demodulation method for M-ary amplitude shift keying systems (MASK) 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 (SCD). 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.

Claims

1. A digital communication receiver for detecting signals transmitted by a digital transmitter through a communication channel, the channel having a channel attenuation |h| and a channel phase shift having a multipath fading effect on the transmitted signals, the receiver comprising a demodulator configured to demodulate signals received by the receiver using channel attenuation coefficients representing the channel attenuation only without any knowledge of the channel phase shift, wherein the demodulator is robust to phase noise, lame phase variations and time-varying I-Q imbalance; the demodulator uses a M-ary amplitude shift keying technique, the transmitted signals being modulated by the transmitter using said same technique before transmission using a modulation order M equal or superior to 2; the detected signals have a symbol Error Rate (SER) intermediate in terms of performance between a coherent detection and a non-coherent detection assuming a same spectral efficiency; the demodulator is less complex than a coherent demodulator, and wherein the SER performance of the detected signals using the demodulator is substantially similar to a SER performance obtained using a coherent demodulator; the channel is a multi-path fading channel; the channel attenuation coefficients are obtained by: inserting pilot symbols d.sub.PSK.sup.{l} within the transmitted signals d.sub.ASK.sup.{l} with a particular time spacing for forming a transmitted frame with data symbols having the following structure d=[d.sub.PSK.sup.{1}, s.sub.ASK.sup.{2}, . . . , d.sub.ASK.sup.{Q}, d.sub.ASK.sup.{Q+1}, d.sub.ASK.sup.{Q+2}, . . . , d.sub.ASK.sup.{2Q}, d.sub.PSK.sup.{2Q+1}, . . . ], where the pilot symbols have a constant modulus |d.sub.PSK.sup.{l}|.sup.2=C.sup.{l}=1 l, where C is a constant, and where Q is a constant set a priori based on configuration criteria; using least-squared estimation to compute such that a channel attenuation coefficient obtained from an lth pilot symbol is in accordance with the following equation: $\begin{array}{c}\hat{}=\frac{{.Math.r_{\mathrm{PSK}}.Math.}^2}{{.Math.d_{\mathrm{PSK}}.Math.}^2}\\ =+h^{*}{d}_{\mathrm{PSK}}^{*}w+{\mathrm{hd}}_{\mathrm{PSK}}{w}^{*}+{.Math.w.Math.}^2\end{array}$ where r.sub.PSK is a received signal that corresponds to a given pilot symbol; forming the following sparse vector using the computed : a=[{circumflex over ()}.sup.{1}], 0.sup.{2}, . . . , 0.sup.{Q}, {circumflex over ()}.sup.{Q+1}, 0.sup.{Q+2}, . . . , 0.sup.{2Q}, {circumflex over ()}.sup.{2Q+1}, . . . ], 2Q+1=L; using interpolation to compute {circumflex over ()}.sup.{i} where=l mod Q1.

2. The digital communication receiver as claimed in claim 1, wherein the demodulation of the signals comprises detecting the transmitted signals by computing {circumflex over (d)}.sub.ASK.sup.{l}=|r.sub.ASK.sup.{l}|.sup.2/{circumflex over ()}.sup.{l}, l mod Q1.

3. The digital communication receiver as claimed in claim 2, wherein the demodulation of the signals further comprises, once {circumflex over (d)}.sub.ASK.sup.{l} is obtained, obtaining channel state information for all data symbols by: compiling .sub.ASK.sup.{l}=r.sub.ASK.sup.{l}/{circumflex over (d)}.sub.ASK.sup.{l}, l mod Q1; using interpolation to find .sub.PSK.sup.{l}, l mod Q1; constructing a vector =[.sup.{1}, .sup.{2}, . . . , .sup.{L}].

4. The digital communication receiver as claimed in claim 3, wherein the demodulation of the signals further comprises detecting an entire received vector comprising the data symbols coherently by:
{circumflex over (d)}=.sup.Hr where r=[r.sup.{1}, r.sup.{2}, . . . , r.sup.{L}], =diag{.sup.{1}, .sup.{2}, . . . .sup.{L}}, and () denotes the Hermitian transpose operation.

5. The digital communication receiver as claimed in claim 4, wherein the configuration criteria based on which Q is set comprises at least one of a channel coherence time, a spectral efficiency, and an interpolation error tolerance.

6. The digital communication receiver as claimed in claim 5, wherein the pilot symbols are modulated by the transmitter using phase shift keying (PSK).

7. A computer-implemented demodulation method comprising: receiving from a digital communication receiver signals transmitted by a digital transmitter through a communication channel, the channel having a channel attenuation |h| and a channel phase shift having a multipath fading effect on the transmitted signals; and demodulating the signals received by the receiver using only channel attenuation coefficients representing the channel attenuation without any knowledge of the channel phase shift for detecting the transmitted signals, wherein the demodulation method is robust to phase noise, large phase variations and time-varying I-Q imbalance; the demodulation method uses a M-ary amplitude shift keying technique, the transmitted signals being modulated by the transmitter using said same technique before transmission using a modulation order M equal or superior to 2; the detected signals have a symbol Error Rate (BER) intermediate in terms of performance between a coherent detection and a differentially coherent detection assuming a same spectral efficiency; the demodulation method is less complex than a coherent demodulation, and wherein the SER performance of the detected signals using the demodulation method is substantially similar to a SER performance obtained using a coherent demodulation; the channel is a multi-path fading channel; the channel attenuation coefficients are obtained by: inserting pilot symbols d.sub.PSK.sup.{l} within the transmitted signals d.sub.ASK.sup.{l} with a particular time spacing for forming a transmitted frame with data symbols having the following structure d=[d.sub.PSK.sup.{1}, s.sub.ASK.sup.{2}, . . . , d.sub.ASK.sup.{Q}, d.sub.ASK.sup.{Q+1}, d.sub.ASK.sup.{Q+2}, . . . , d.sub.ASK.sup.{2Q}, d.sub.PSK.sup.{2Q+1}, . . . ], where the pilot symbols have a constant modulus |d.sub.PSK.sup.{l}|.sup.2=C.sup.{l}=1 l, where C is a constant, and where Q is a constant set a priori based on configuration criteria; using least-squared estimation to compute such that a channel attenuation coefficient obtained from an lth pilot symbol is in accordance with the following equation: $\begin{array}{c}\hat{}=\frac{{.Math.r_{\mathrm{PSK}}.Math.}^2}{{.Math.d_{\mathrm{PSK}}.Math.}^2}\\ =+h^{*}{d}_{\mathrm{PSK}}^{*}w+{\mathrm{hd}}_{\mathrm{PSK}}{w}^{*}+{.Math.w.Math.}^2\end{array}$ where r.sub.PSK is a received signal that corresponds to a given pilot symbol; forming the following sparse vector using the computed : a=[{circumflex over ()}.sup.{1}], 0.sup.{2}, . . . , 0.sup.{Q}, {circumflex over ()}.sup.{Q+1}, 0.sup.{Q+2}, . . . , 0.sup.{2Q}, {circumflex over ()}.sup.{2Q+1}, . . . ], 2Q+1=L; using interpolation to compute {circumflex over ()}.sup.{i} where=l mod Q1.

8. The demodulation method as claimed in claim 7, wherein the demodulation of the signals comprises detecting the transmitted signals by computing {circumflex over (d)}.sub.ASK.sup.{l}=|r.sub.ASK.sup.{l}|.sup.2/{circumflex over ()}.sup.{l}, l mod Q1.

9. The demodulation method as claimed in claim 8, wherein the demodulation of the signals further comprises, once {circumflex over (d)}.sub.ASK.sup.{l} is obtained, obtaining channel state information for all data symbols by: compiling .sub.ASK.sup.{l}=r.sub.ASK.sup.{l}/{circumflex over (d)}.sub.ASK.sup.{l}, l mod Q1; using interpolation to find .sub.PSK.sup.{l}, l mod Q=1; constructing a vector =[.sup.{1}, .sup.{2}, . . . , .sup.{L}].

10. The demodulation method as claimed in claim 9, wherein the demodulation of the signals further comprises detecting an entire received vector comprising the data symbols coherently by:
{circumflex over (d)}=.sup.Hr where r=[r.sup.{1}, r.sup.{2}, . . . , r.sup.{L}], =diag{.sup.{1}, .sup.{2}, . . . .sup.{L}}, and () denotes the Hermitian transpose operation.

11. The demodulation method as claimed in claim 10, wherein the configuration criteria based on which Q is set comprises at least one of a channel coherence time, a spectral efficiency, and an interpolation error tolerance.

12. The demodulation method as claimed in claim 11, wherein the pilot symbols are modulated by the transmitter using phase shift keying (PSK).

13. A demodulator device for detecting signals transmitted by a digital transmitter to a digital receiver through a communication channel, the channel having a channel attenuation |h| and a channel phase shift having a multipath fading effect on the transmitted signals, the demodulator device being configured to communicate with the digital receiver for demodulating signals received by the receiver using channel attenuation coefficients representing the channel attenuation only without any knowledge of the channel phase shift, wherein the demodulation is robust to phase noise, large phase variations and time-varying I-Q imbalance; the demodulator device uses a M-ary amplitude shift keying technique, the transmitted signals being modulated by the transmitter using said same technique before transmission using a modulation order M superior to 2; the detected signals have a Bit Error Rate (BER) intermediate in terms of performance between a coherent detection and a differentially coherent detection assuming a same spectral efficiency; the demodulator device is less complex than a coherent demodulator, and wherein the BER performance of the detected signals using the demodulator is substantially similar to a BER performance obtained using a coherent demodulator; the channel is a multi-path fading channel; the channel attenuation coefficients are obtained by: inserting pilot symbols d.sub.PSK.sup.{l} within the transmitted signals d.sub.ASK.sup.{l} with a particular time spacing for forming a transmitted frame with data symbols having the following structure d=[d.sub.PSK.sup.{1}, s.sub.ASK.sup.{2}, . . . , d.sub.ASK.sup.{Q}, d.sub.ASK.sup.{Q+1}, d.sub.ASK.sup.{Q+2}, . . . , d.sub.ASK.sup.{2Q}, d.sub.PSK.sup.{2Q+1}, . . . ], where the pilot symbols have a constant modulus |d.sub.PSK.sup.{l}|.sup.2=C.sup.{l}=1 l, where C is a constant, and where Q is a constant set a priori based on configuration criteria; using least-squared estimation to compute such that a channel attenuation coefficient obtained from an lth pilot symbol is in accordance with the following equation: $\begin{array}{c}\hat{}=\frac{{.Math.r_{\mathrm{PSK}}.Math.}^2}{{.Math.d_{\mathrm{PSK}}.Math.}^2}\\ =+h^{*}{d}_{\mathrm{PSK}}^{*}w+{\mathrm{hd}}_{\mathrm{PSK}}{w}^{*}+{.Math.w.Math.}^2\end{array}$ where r.sub.PSK is a received signal that corresponds to a given pilot symbol; forming the following sparse vector using the computed : a=[{circumflex over ()}.sup.{1}], 0.sup.{2}, . . . , 0.sup.{Q}, {circumflex over ()}.sup.{Q+1}, 0.sup.{Q+2}, . . . , 0.sup.{2Q}, {circumflex over ()}.sup.{2Q+1}, . . . ], 2Q+1=L; using interpolation to compute {circumflex over ()}.sup.{i} where=l mod Q1.

14. The demodulator device as claimed in claim 13, wherein the demodulation of the signals comprises detecting the transmitted signals by computing {circumflex over (d)}.sub.ASK.sup.{l}=|r.sub.ASK.sup.{l}|.sup.2/{circumflex over ()}.sup.{l}, l mod Q1.

15. The demodulator device as claimed in claim 14, wherein the demodulation of the signals further comprises, once {circumflex over (d)}.sub.ASK.sup.{l} is obtained, obtaining channel state information for all data symbols by: compiling .sub.ASK.sup.{l}=r.sub.ASK.sup.{l}/{circumflex over (d)}.sub.ASK.sup.{l}, l mod Q1; using interpolation to find .sub.PSK.sup.{l}, l mod Q1; constructing a vector =[.sup.{1}, .sup.{2}, . . . , .sup.{L}].

16. The demodulator device as claimed in claim 15, wherein the demodulation of the signals further comprises detecting an entire received vector comprising the data symbols coherently by:
{circumflex over (d)}=.sup.Hr where r=[r.sup.{1}, r.sup.{2}, . . . , r.sup.{L}], =diag{.sup.{1}, .sup.{2}, . . . .sup.{L}}, and () denotes the Hermitian transpose operation.

17. The demodulator device as claimed in claim 16, wherein the configuration criteria based on which Q is set comprises at least one of a channel coherence time, a spectral efficiency, and an interpolation error tolerance.

18. The demodulator device as claimed in claim 17, wherein the pilot symbols are modulated by the transmitter using phase shift keying (PSK).

Description

DRAWINGS

(1) The invention will now be described with reference to the accompanying drawings, which illustrate a preferred embodiment of the present invention without restricting the scope of the invention's concept, and in which:

(2) FIG. 1 illustrates the PDF of a conventional NCD decision variables for M=4 and SNR=30 dB;

(3) FIG. 2 illustrates the PDF of SCD decision variables for M=4 and SNR=30 dB;

(4) FIG. 3 illustrates SER of CD, NCD and SCD using MLD, M=2;

(5) FIG. 4 illustrates SER of CD, NCD and SCD using MLD, M=4;

(6) FIG. 5 illustrates SER of CD, SCD and NCD using MLD and MDD, M=2;

(7) FIG. 6 illustrates SER of SCD for various vehicle speeds with imperfect channel estimates, M=2;

(8) FIG. 7 illustrates SER of CD and SCD using different .sub.PN.sup.2 values;

(9) FIG. 8 illustrates proposed blind CSI estimation using amplitude-coherent detection using a simple frame structure, where each frame is composed of two symbols, one ASK and PSK;

(10) FIG. 9 shows the SER using the proposed blind channel estimation algorithm compared to QPSK modulation under different scenarios.

DETAILED DESCRIPTION OF THE INVENTION

(11) MASK Modulation

(12) In MASK modulation, the baseband representation of the transmitted signal is given by
d=A.sub.i, i{0,1, . . . , M1}(1)
where M is the modulation order, the amplitudes A.sub.i R for coherent detection, while for NCD A.sub.i0. Without loss of generality, the amplitudes are selected such that A.sub.i+1>A.sub.i. Moreover, the amplitude spacing is usually assumed to be uniform where A.sub.i+1A.sub.i=. Since the average symbol power is normalized to unity, then

(13) $\frac{1}{M}\underset{i=0}{\overset{M-1}{.Math.}}{A}_i^2=1.$
The transmitted amplitudes can be described by,

(14) $\begin{array}{cc}{A}_i=i,i\left\{0,1,\mathrm{.Math.},M-1\right\},\mathrm{where}& \left(2\right)\\ =\sqrt{\frac{6}{\left(2M-1\right)\left(M-1\right)}}.& \left(3\right)\end{array}$

(15) Conventional NC MASK Detection

(16) Assuming that the information symbols are transmitted over a Rayleigh frequency-flat fading channel, the received signal can be expressed as
v=hA.sub.i+w, i{0,1, . . . ,M1}(4)

(17) where the channel fading coefficient h is a complex normal random variable h(0, 2.sub.H.sup.2) and w(0, 2.sub.w.sup.2) denotes the additive white Gaussian noise (AWGN). To perform NCD, the energy of the received signal should be computed,

(18) $\begin{array}{cc}\begin{array}{c}={.Math.v.Math.}^2\\ ={.Math.h.Math.}^2.Math.A_i^2.Math.+\left(h^{*}{A}_i^{*}w+h{A}_i{w}^{*}\right)+{.Math.w.Math.}^2.\end{array}& \left(5\right)\end{array}$
where ()* denotes the complex conjugate. The received signal energy is the decision variable that will be fed to the maximum likelihood detector (MLD). The conditional probability distribution function (PDF) of can be expressed as

(19) 0$\begin{array}{cc}P\left(|E_i\right)=\frac{1}{2\left({}_w^2+{}_h^2{E}_i\right)}\exp \left(-\frac{1}{2}\frac{}{{}_w^2+{}_h^2{E}_i}\right),& \left(6\right)\end{array}$
where E.sub.i=A.sub.i.sup.2. The PDF in (6) for M=4 is shown in FIG. 1 where it is clear that the only amplitude that can be identified easily is the A.sub.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.

(20) Based on the PDF given in (6), the MLD can be expressed as [5],

(21) $\begin{array}{cc}\widehat{A_i}=\arg \underset{A_i}{\min }\frac{}{\left({}_w^2+{}_h^2{E}_i\right)}+\ln \left({}_w^2+{}_h^2{E}_i\right),i=\left[0,1,\mathrm{.Math.},M-1\right].& \left(7\right)\end{array}$

(22) It is worth noting that the MLD of NCD of MASK requires accurate knowledge of .sub.w.sup.2 and .sub.h.sup.2. The SER using MLD can be expressed as [5],

(23) $\begin{array}{cc}{P}_S=1-\frac{1}{M}+\frac{1}{M}\underset{i=1}{\overset{M-1}{.Math.}}\exp \left[-\frac{\ln \left(\frac{{}_{i+1}+1}{{}_i+1}\right)}{1-\frac{{}_i+1}{{}_{i+1}+1}}\right]-\exp \left[-\frac{\ln \left(\frac{{}_{i+1}+1}{{}_i+1}\right)}{\frac{{}_{i+1}+1}{{}_i+1}-1}\right]\mathrm{where}{}_i=\frac{{}_h^2}{{}_w^2}{E}_i.& \left(8\right)\end{array}$

(24) The SER of the NCD-MASK for M=2 using optimal MLD is presented in FIG. 3. 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 FIG. 4 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].

(25) The New Semi-Coherent Demodulator

(26) 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 can be expressed as

(27) $\begin{array}{cc}\begin{array}{c}=\frac{}{{.Math.h.Math.}^2}\\ =\frac{{.Math.v.Math.}^2}{{.Math.h.Math.}^2}\\ =.Math.A_i^2.Math.+\frac{1}{{.Math.h.Math.}^2}\left[\left(h^{*}{A}_i^{*}w+{\mathrm{hA}}_i{w}^{*}\right)+{.Math.w.Math.}^2\right].\end{array}& \left(9\right)\end{array}$

(28) As depicted in (9), the multiplicative effect of multipath fading has been converted into an additive disturbance. The process of computing |h|.sup.2 for practical systems will be presented in the following sections.

(29) The conditional PDF of the decision variable is given by

(30) $\begin{array}{cc}P\left(|E_i\right)=\frac{\left({}_i+{}_w^4\right){}_h^2}{{\left[{\left(-E_i\right)}^2{}_h^4+2{}_i+{}_w^4\right]}^{3/2}}& \left(10\right)\end{array}$
where .sub.i=(+E.sub.i).sub.w.sup.2.sub.h.sup.2. As it can be noted from FIG. 2 that considers the M=4 case, the conditional PDFs are well separated and the tails of both PDFs decay rapidly as a function of , 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.

(31) The SER of the SCD using MLD is presented in FIGS. 3 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>2, which implies that it can provide higher spectral efficiency as compared to NCD. Furthermore, it can be noted from FIG. 3 that the SER degradation of SCD as compared to CD is about 5.5 dB at SER of 10.sup.3, and it is about 11 dB when M=4.

(32) Based on the PDF given in (10), it can be shown that the optimum detector has high complexity, and it requires the knowledge of .sub.w.sup.2 and .sub.h.sup.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

(33) $\begin{array}{cc}\widehat{A_i}=\arg \underset{E_i}{\min }{\left[-E_i\right]}^2,i=\left[0,1,\mathrm{.Math.},M-1\right],& \left(11\right)\end{array}$

(34) which corresponds to the minimum distance detector (MDD). The SER based on MDD can be expressed as

(35) $\begin{array}{cc}{P}_S=1-\frac{1}{M}+\frac{1}{M}\left[\underset{i=1}{\overset{M-1}{.Math.}}{}_i-\underset{i=2}{\overset{M}{.Math.}}{}_i\right],\mathrm{where}{}_i\stackrel{}{=}\frac{1-{}^2\left[i-0.5\right]}{2\sqrt{{\left({}^2\left[i-0.5\right]\right)}^2+2{}^2\left[2i^2-3i+1.5\right]+1}}{}_i\stackrel{}{=}\frac{1+{}^2\left[i-0.5\right]}{2\sqrt{{\left({}^2\left[i-1.5\right]\right)}^2+2{}^2\left[2i^2-5i+3.5\right]+1}}.\mathrm{where}=\frac{{}_H^2}{{}_w^2}\stackrel{\_}{E},\mathrm{and}\stackrel{\_}{E}=\frac{1}{M}\underset{i=0}{\overset{M-1}{.Math.}}{E}_i& \left(12\right)\end{array}$
is the average power per symbol which is normalized to unity for all systems.

(36) The SER for M=2 is shown in FIG. 5 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.

(37) Partial CSI Estimation

(38) As it can be noted from (9), the partial CSI required for the SCD is the channel attenuation coefficient |h|.sup.2. The most straightforward approach to obtain |h|.sup.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|.sup.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,

(39) $\begin{array}{cc}\begin{array}{c}{}_P={.Math.v_P.Math.}^2\\ ={.Math.h.Math.}^2{.Math.s.Math.}^2+\left(h^{*}{s}^{*}w+{\mathrm{hsw}}^{*}\right)+{.Math.w.Math.}^2.\end{array}& \left(13\right)\end{array}$

(40) The estimated value of |h|.sup.2 can be obtain by computing {circumflex over ()}=.sub.P/|s|.sup.2.

(41) The channel variations over time can be described using Jake's model [7]. Assuming that the channel is Rayleigh fading with L.sub.h independent multipath components, the time correlation between the channel coefficients can be expressed as,
E[h.sub.nh.sub.m]=.sub.lJ.sub.0(2f.sub.dT.sub.s(nm)),(14)
where T.sub.s is the symbol period, .sub.l is the normalized power of the lth multipath component where .sub.l=0.sup.L.sup.h.sub.l=1, J.sub.0() is the Bessel function of the first kind and zero order and f.sub.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].

(42) Numerical Results

(43) 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.

(44) The SER of the SCD in the presence of mobility is presented in FIG. 6 using M=2. The channel is assumed to be Rayleigh frequency-nonselective with time correlation that follows the Jake'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.

(45) The SER of SCD and CD in the presence of phase noise (PN) is presented in FIG. 7 The received signal in the presence of PN can be expressed as
v=he.sup.jA.sub.i+w, i{0,1, . . . , M1}
where is a function of the phase noise power, and it is typically modeled as a random jitter N(0, .sub.PN.sup.2) [14], where .sub.PN.sup.2 is measured in rad.sup.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 .sub.PN.sup.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].

(46) 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.

(47) Blind CSI Estimation Using Amplitude-Coherent Detection

(48) 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 . The most straightforward approach to obtain is to insert pilot symbols within the information symbols, and then use least-squared estimation to compute . 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.sub.PSK.sup.{l} satisfy |d.sub.DSK.sup.{l}|.sup.2=C.sup.{l}=1 l. Since MPSK has constant modulus, we assume that all pilot symbols are MPSK modulated.

(49) If the pilot and data symbol during the lth signaling interval are denoted by d.sub.PSK.sup.{l} and d.sub.ASK.sup.{l}, respectively, then the transmitted frame has generally the following structure,
d=[d.sub.PSK.sup.{1}, s.sub.ASK.sup.{2}, . . . , d.sub.ASK.sup.{Q}, d.sub.ASK.sup.{Q+1}, d.sub.ASK.sup.{Q+2}, . . . , d.sub.ASK.sup.{2Q}, d.sub.PSK.sup.{2Q+1}, . . . ].(15)

(50) The value of Q depends on the channel coherence time, spectral efficiency, interpolation error tolerance, etc.

(51) Using least square estimation, the channel attenuation factor obtained from the lth pilot symbol can be expressed as,

(52) $\begin{array}{cc}\begin{array}{c}\hat{}=\frac{{.Math.r_{\mathrm{PSK}}.Math.}^2}{{.Math.d_{\mathrm{PSK}}.Math.}^2}\\ =+h^{*}{d}_{\mathrm{PSK}}^{*}w+{\mathrm{hd}}_{\mathrm{PSK}}{w}^{*}+{.Math.w.Math.}^2\end{array}& \left(16\right)\end{array}$
where r.sub.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 ()}.sup.{1}], 0.sup.{2}, . . . , 0.sup.{Q}, {circumflex over ()}.sup.{Q+1}, 0.sup.{Q+2}, . . . , 0.sup.{2Q}, {circumflex over ()}.sup.{2Q+1}, . . . ], 2Q+1=L.(17)

(53) Then, interpolation can used to compute {circumflex over ()}.sup.{i} where=l mod Q1. Finally, the data symbols can be detected by computing {circumflex over (d)}.sub.ASK.sup.{l}=|r.sub.ASK.sup.{l}|.sup.2/{circumflex over ()}.sup.{l}, l mod Q1.

(54) 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)}.sub.ASK.sup.{l} is obtained, then the full CSI can be obtained for all data symbols where .sub.ASK.sup.{l}=r.sub.ASK.sup.{l}/{circumflex over (d)}.sub.ASK.sup.{l}, l mod Q1. Then, interpolation can be used to find .sub.PSK.sup.{l}, l mod Q=1, which allows constructing the vector =[.sup.{1}, .sup.{2}, . . . , .sup.{L}]. Consequently, the entire received vector can be detected coherently
{circumflex over (d)}=.sup.Hr(18)
where r=[r.sup.{1}, r.sup.{2}, . . . , r.sup.{L}], =diag{.sup.{1}, .sup.{2}, . . . , .sup.{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. FIG. 8 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.sup.{l}h.sup.{l+1}.

(55) Because both d.sub.PSK and d.sub.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.

(56) It is important to note that using A.sub.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.sub.m=(m+1), m{0, . . . , M1}. For an average power

(57) $\frac{1}{M}\underset{m=1}{\overset{M}{.Math.}}{E}_m=1$
and equally spaced constellation points, the amplitude separation can be defined as s.sub.m+1s.sub.m, where

(58) 0$=\sqrt{\frac{6}{\left(M+1\right)\left(2M+1\right)}}.$
Therefore, P.sub.s can be expressed as

(59) $\begin{array}{cc}{P}_S=1-\frac{1}{M}+\frac{1}{M}\underset{i=1}{\overset{M-1}{.Math.}}{A}_i-B_{i+1}{A}_i\stackrel{}{=}\frac{1-{}^2\left[i+0.5\right]}{2\sqrt{{\left({}^2\left[i+0.5\right]\right)}^2+2{}^2\left[2i^2+i+0.5\right]+1}}{B}_i\stackrel{}{=}\frac{1+{}^2\left[i-0.5\right]}{2\sqrt{{\left({}^2\left[i-0.5\right]\right)}^2+2{}^{2}2i^2-i+0.5]+1}}.& \left(5\right)\end{array}$

(60) It is worth noting that the SER when A.sub.0>0 is higher than the case where A.sub.0=0 due to the loss of power efficiency. Such limitation can be avoided by setting A.sub.0=0, however, CSI over the entire frame has to be recovered from nonuniformly spaced samples [15].

(61) Numerical Results of the Blind Detection Technique

(62) FIG. 9 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.sup.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.

REFERENCES

(63) [1] J. Proakis and M. Salehi, Digital Communications, 4th Edition, McGrawhill, 2001. [2] 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. [3] D. Divsalar and M. Simon, Multiple-symbol differential detection of MPSK, IEEE Transactions on Communications, vol. 38, no. 3, pp. 300-308, March 1990. [4] 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. [5] 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. [6] M. Simon and M. Alouini, Digital Communication over Fading ChannelsA Unified Approach to Performance Analysis, 1st Ed., Wiley, 2000. [7] W. C. Jakes, Microwave Mobile Communications. Piscataway, N.J.: IEEE Press, 1994. [8] Radio broadcasting systems; digital audio broadcasting (DAB) to mobile, portable and fixed receivers, ETS Standard 300 401, 1995. [9] Digital video broadcasting (DVB); framing structure, channel coding and modulation for digital terrestrial television, ETSI Standard EN 300744 v1.6.1, 2008. [10] IEEE Standard for Local and metropolitan area networks Part 16: Air Interface for Broadband Wireless Access Systems Amendment 3: Advanced Air Interface, IEEE Standard 802.16m, 2011. [11] LTE; Evolved Universal Terrestrial Radio Access (E-UTRA) and Evolved Universal Terrestrial Radio Access Network (E-UTRAN); Overall description, 3GPP Standard TS 36.300, 2011. [12] IEEE 802.11p: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications Amendment 6: Wireless Access in Vehicular Environments, Jul. 15, 2010. [13] IEEE Standard for Broadband over Power Line Networks: Medium Access Control and Physical Layer Specifications, IEEE Standard 1901, 2010. [14] R. Krishnan, A. Graell, T. Eriksson and G. Colavolpe, Constellation Optimization in the Presence of Strong Phase Noise, IEEE Transactions on Communications, vol. 61, no. 12, pp. 5056-5066, December 2013. [15] S. Maymon and V. Oppenheim, Sinc interpolation of nonuniform samples, IEEE Trans. Signal Process., vol. 59, no. 10, pp. 4745-4758, October 2011.