Method and System for Designing a Waveform for Data Communication

Abstract

Embodiments herein disclose a method and system for designing a waveform for data communication. The method includes applying, by a phase rotation applying unit, a constellation specific phase rotation between consecutive data symbols in a data stream to obtain a constellation rotated data stream. Further, the method includes introducing, by a frequency domain pulse shaping filter, an inter symbol interference (ISI) between modulated data symbols of the constellation rotated data stream, such that the ISI develops the waveform of the constellated rotated data stream to be transmitted.

Claims

1-24. (canceled)

25. A method for generating a waveform for data communication, the method comprising: applying, by a transmitter, a constellation specific phase rotation between consecutive data symbols in a data stream to obtain a constellation rotated data stream; obtaining, by the transmitter, a Discrete Fourier transform (DFT) spread signal from the constellation rotated data stream in frequency domain using a DFT, wherein said DFT is at least one of a one-sided DFT and a two-sided DFT; mapping, by the transmitter, the DFT spread signal using one of a localized subcarriers and distributed subcarriers, to produce a mapped spread signal; applying, by the transmitter, a frequency domain pulse shaping filter to the mapped DFT spread signal to obtain a filtered spread signal, wherein the frequency domain pulse shaping filter is a DFT of samples of a time domain pulse shaping filter, wherein said DFT is one of a one-sided DFT and a two-sided DFT; and processing, by the transmitter, the filtered spread signal to generate a waveform.

26. The method as claimed in claim 25, wherein the DFT spread signal is one of DFT of the constellation rotated data stream and periodic extension of the DFT of the constellation rotated data stream in the frequency domain.

27. The method as claimed in claim 25, wherein the size of the DFT of the samples of a time domain pulse shaping filter is less than or equal to the length of DFT spread signal.

28. The method as claimed in claim 25, wherein the size of the DFT of the samples of a time domain pulse shaping filter is equal to the size of the constellation rotated data stream.

29. The method as claimed in claim 25, wherein the samples of a time domain pulse shaping filter includes only causal samples.

30. The method as claimed in claim 25, wherein the samples of a time domain pulse shaping filter includes both causal and non-causal samples.

31. The method as claimed in claim 25, wherein the size of the non-zero values of a time domain pulse shaping filter is two.

32. The method as claimed in claim 25, wherein the size of the non-zero values of the samples of a time domain pulse shaping filter is at least three.

33. The method as claimed in claim 25, wherein the constellation specific phase rotation is 90 degrees and the constellation is BPSK.

34. The method as claimed in claim 25, wherein the method comprises adding at least one of a cyclic prefix and a cyclic suffix to the data stream after performing an Inverse Fourier transform on the filtered spread signal, to obtain a time domain filtered spread signal.

35. A transmitter, wherein the transmitter comprises: a phase rotator operable to apply a constellation specific phase rotation between consecutive data symbols in a data stream to obtain a constellation rotated data stream; a controller operable to obtain a Discrete Fourier transform (DFT) spread signal from the constellation rotated data stream in frequency domain using a DFT, wherein said DFT is at least one of a one-sided DFT and a two-sided DFT, and wherein the controller is operable to map the DFT spread signal, using one of a localized subcarriers and distributed subcarriers, to produce a mapped spread signal; and a frequency domain pulse shaping filter operable to filter the mapped DFT spread signal to obtain a filtered spread signal, wherein the frequency domain pulse shaping filter is a DFT of samples of a time domain pulse shaping filter, and wherein said DFT is one of a one-sided DFT and a two-sided DFT, and wherein the filtered spread signal is processed to generate a waveform.

36. The transmitter as claimed in claim 35, wherein the DFT spread signal is one of DFT of the constellation rotated data stream and periodic extension of the DFT of the constellation rotated data stream in the frequency domain.

37. The transmitter as claimed in claim 35, wherein the size of the DFT of the samples of a time domain pulse shaping filter is less than or equal to the length of DFT spread signal.

38. The transmitter as claimed in claim 35, wherein the size of the DFT of the samples of a time domain pulse shaping filter is equal to the size of the constellation rotated data stream.

39. The transmitter as claimed in claim 35, wherein the samples of a time domain pulse shaping filter includes only causal samples.

40. The transmitter as claimed in claim 35, wherein the samples of a time domain pulse shaping filter includes both causal and non-causal samples.

41. The transmitter as claimed in claim 35, wherein the size of the non-zero values of a time domain pulse shaping filter is two.

42. The transmitter as claimed in claim 35, wherein the size of the non-zero values of the samples of a time domain pulse shaping filter is at least three.

43. The transmitter as claimed in claim 35, wherein the constellation specific phase rotation is 90 degrees and the constellation is BPSK.

44. The transmitter as claimed in claim 35, wherein the transmitter comprises adding at least one of a cyclic prefix and a cyclic suffix to the data stream after performing an Inverse Fourier transform on the filtered spread signal, to obtain a time domain filtered spread signal.

Description

BRIEF DESCRIPTION OF FIGURES

[0015] This invention is illustrated in the accompanying drawings, throughout which like reference letters indicate corresponding parts in the various figures. The embodiments herein will be better understood from the following description with reference to the drawings, in which:

[0016] FIG. 1 is a block diagram of various units present in a transmitter configured for designing a waveform for data communication, according to the embodiments as disclosed herein;

[0017] FIG. 2 is a flow diagram illustrating a method for designing a waveform for data communication, according to the embodiments as disclosed herein;

[0018] FIG. 3a shows the sequence of steps followed in generating a BPSK modulated G-DFT-pre-coded-OFDM signal with linearized Gaussian pulse shaping, according to the embodiments as disclosed herein;

[0019] FIG. 3b shows the steps involved for designing the waveform for QAM systems with arbitrary pulse shaping filter, according to the embodiments as disclosed herein;

[0020] FIG. 4a shows the sequence of steps involved in the design of a frequency domain pulse shaping filter using linearized Gaussian pulse, according to the embodiments as disclosed herein;

[0021] FIG. 4b shows the sequence of steps involved in the design of a frequency domain pulse shaping filter for any time domain pulse, according to the embodiments as disclosed herein;

[0022] FIG. 5 is a block diagram of various units present in a receiver, according to the embodiments as disclosed herein;

[0023] FIG. 6 is a flow diagram illustrating a method for processing a received data stream, according to the embodiments as disclosed herein;

[0024] FIG. 7 shows the sequence of steps involved during signal reception in the GMMSE receiver design, according to the embodiments as disclosed herein;

[0025] FIG. 8 shows the sequence of steps involved during signal reception the single user MMSE receiver design, according to the embodiments as disclosed herein; and

[0026] FIG. 9 shows the sequence of steps during signal reception in the single user WL MMSE receiver design, according to the embodiments as disclosed herein.

DETAILED DESCRIPTION OF INVENTION

[0027] The embodiments herein and the various features and advantageous details thereof are explained more fully with reference to the non-limiting embodiments that are illustrated in the accompanying drawings and detailed in the following description. Descriptions of well-known components and processing techniques are omitted so as to not unnecessarily obscure the embodiments herein. Also, the various embodiments described herein are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments. The term “or” as used herein, refers to a non-exclusive or, unless otherwise indicated. The examples used herein are intended merely to facilitate an understanding of ways in which the embodiments herein can be practiced and to further enable those skilled in the art to practice the embodiments herein. Accordingly, the examples should not be construed as limiting the scope of the embodiments herein.

[0028] The embodiments herein achieve a method and system for designing a waveform for data communication. The method includes applying, by a constellation specific phase rotation applying unit, a constellation specific phase rotation between consecutive data symbols in a data stream to obtain a constellation rotated data stream. Further, the method includes introducing, by a frequency domain pulse shaping filter (FDPSF), an inter symbol interference (ISI) between modulated data symbols of the constellation rotated data stream, such that the ISI develops the waveform of the constellated rotated data stream to be transmitted.

[0029] Unlike conventional systems, the proposed method can design the waveforms with very low peak-to-average-power-ration (PAPR) and small bit error rate (BER) penalty.

[0030] The embodiments herein achieve a method and receiver for processing a received data stream. The received data stream is in a form of waveform designed by a frequency domain pulse shaping filter. The method includes receiving, by a receiving unit, the data stream. The data stream comprises an inter-symbol interference (ISI) between modulated data symbols, of the data stream, introduced by the frequency domain pulse shaping filter. Further, the method includes suppressing, by a vector/matrix-valued filter, the ISI between the modulated data symbols in the data stream. Furthermore, the method includes converting, a converting unit, the received data stream to time domain for detection of a signal after suppressing the ISI.

[0031] The proposed method can mitigate the ISI and self-interference caused by the FDPSF. The proposed method implements conventional and widely linear frequency domain multi-user user equalization techniques to mitigate the ISI and self-interference introduced by the FDPSF.

[0032] Unlike conventional systems, the proposed frequency domain multi-user user equalizer performs both ISI and self-interference mitigation jointly with low-implementation complexity. The proposed GMMSE type of receiver exploits the redundancy in the frequency domain signal structure introduced by the FDPSG and therefore leads to very efficient multi-user frequency domain equalizer.

[0033] Referring now to the drawings and more particularly to FIGS. 1 through 9, where similar reference characters denote corresponding features consistently throughout the figure, there are shown preferred embodiments.

[0034] FIG. 1 is a block diagram of various units present in a transmitter 100 configured for designing a waveform for data communication, according to the embodiments as disclosed herein. The transmitter 100 includes a phase rotation applying unit 102, a frequency domain pulse shaping filter 104, a computing unit 106, a repeating unit 108, a sampling unit 110, a digital to analog converter 112, and a window applying unit 114. The phase rotation applying unit 102 is configured to apply a constellation specific phase rotation between consecutive data symbols in a data stream to obtain a constellation rotated data stream. The frequency domain pulse shaping filter 104 is configured to introduce an inter symbol interference (ISI) between modulated data symbols of the constellation rotated data stream, such that the ISI develops the waveform of the constellated rotated data stream to be transmitted. The frequency domain pulse shaping filter 104 is configured to shape a spectrum of a spread signal, when the sampling factor is one or more than one.

[0035] The computing unit 106 is configured to compute the multi-point Discrete Fourier Transform (DFT) of the constellation rotated data stream. After computing the multi-point DFT of the constellation rotated data stream, the repeating unit 108 is configured to repeat the constellation rotated data stream in a frequency domain to obtain a spread signal.

[0036] In an embodiment, the sampling unit 110 is configured to sample a linearized Gaussian pulse using an over-sampling factor. In an embodiment, the over-sampling factor is one. In another embodiment, the over-sampling factor is greater than one. After sampling the linearized Gaussian pulse, the computing unit 106 is configured to compute a multi-point two-sided DFT of the sampled linearized Gaussian pulse to obtain the frequency domain pulse shaping filter.

[0037] In an embodiment, the data stream is mapped to a localized subcarrier after introducing the ISI between the data symbols of the data stream. In another embodiment, the data stream is mapped to a distributed sub-carrier.

[0038] The computing unit 106 is configured to add a cyclic prefix, a cyclic suffix or combination of both to the data stream after performing an inverse discrete Fourier transform (IDFT) on the data stream. In another embodiment, the computing unit 106 is configured to add the cyclic prefix, the cyclic suffix or combination of both to the data stream after performing an Inverse Fast Fourier Transform (IFFT) on the data stream. After adding the cyclic prefix, the cyclic suffix or combination of both to the data stream, the digital to analog converter 112 is configured to convert the data stream from the digital signal to the analog signal.

[0039] After adding the cyclic prefix or the cyclic suffix or combination of cyclic prefix and the cyclic suffix to the data stream, the window applying unit 114 is configured to apply the window function on the data stream.

[0040] The proposed transmitter 100 utilizes a time domain signal representation that is distinct from the DFT-precoded-OFDM. The proposed transmitter 100 utilizes the DFT-precoded-OFDM techniques that allow certain amount of self-interference among the users through orthogonal/non-orthogonal subcarrier mapping. The proposed transmitter 100 allows the users to have unequal bandwidth, while prior-art GFDM does not permit this scenario.

[0041] Unlike conventional system, the transmitter 100 can implement FDPS techniques that introduce a controlled amount of ISI between modulation data symbols for reducing the PAPR. In the special case of binary modulation, the transmitter 100 can apply constellation rotation of 90-degrees between consecutive data symbols of the user followed by DFT precoding, user specific frequency domain spreading, and frequency domain subcarrier level pulse shaping filtering.

[0042] The following operation and function explains the design and functioning of transmitter 100 for designing the waveform in detail:

[0043] In an embodiment, the transmitter 100 can be configured to design the waveform for a single user case. The transmitter sends a block of M i.i.d real/complex valued modulation alphabets with zero-mean and variance σ.sup.2. Let a.sub.t(1) denote the modulation data. Here, the transmitter 100 can apply a constellation specific phase rotation θ(1) to obtain: x.sub.t(l)=e.sup.jθ(l)a.sub.t(l). The DFT precoding of the data stream x.sub.t(l) is accomplished using a M-point DFT as

[00001]$\begin{array}{cc}x\left(k\right)=\underset{l=0}{\overset{M-1}{.Math.}}{x}_t\left(l\right)e^{\frac{-j2\pi \mathrm{lk}}{M}}k=0,\mathrm{.Math.},M-1& \left(1\right)\end{array}$

where l, k denote the discrete time and subcarrier indices, respectively, and x(M+k)=x(k) . . . . Alternative to (1), a two sided DFT can be taken as:

[00002]$x\left(k\right)=\underset{l=\frac{-M}{2}}{\overset{\frac{M}{2}-1}{.Math.}}{e}^{j{\theta }_t\left(l\right)}{x}_{i,t}\left(l\right)e^{\frac{-j2\pi \mathrm{lk}}{M}}\frac{-M}{2}\le k\le \frac{M}{2}-1$

[0044] Consider a L fold periodic extension of x(k) where

[00003]$\tilde{x}\left(m\right)=x\left(\left(\left(m+\frac{LM}{2}\right)\mathrm{mod}M\right)+1\right).$

Here, the elements of the vector {tilde over (x)}(m) take the range

[00004]$m=-\frac{\mathrm{LM}}{2},\mathrm{.Math.},\frac{\mathrm{LM}}{2}-1$

and ML=N, N being total number of used subcarriers. In time domain,

[00005]${\tilde{x}}_t\left(n\right)=x_t\left(\frac{n}{L}\right)$

for n=pL where p=0, 1, . . . , M−1 and {tilde over (x)}.sub.1(n)=0 elsewhere and

[00006]$n=-\frac{N}{2},\mathrm{.Math.},\frac{N}{2}-1.$

Here

[0045] [00007]$x_t\left(l\right)={\tilde{x}}_t\left(lL-\frac{N}{2}\right)$

for l=0, . . . , M−1. Let

[00008]$\begin{array}{cc}\tilde{x}\left(m\right)=\underset{n=\frac{-N}{2}}{\overset{\frac{N}{2}}{.Math.}}{\tilde{x}}_t\left(m\right)e^{\frac{-2\pi \mathrm{mn}}{N}}m=\frac{-N}{2},,,\frac{N}{2}-1& \left(2\right)\\ =\underset{l=0}{\overset{M-1}{.Math.}}{x}_t\left(l\right)e^{\frac{-j2\pi \left(\mathrm{lL}-\frac{N}{2}\right)m}{N}}& \left(3\right)\\ e^{j\pi m}\underset{l=0}{\overset{M-1}{.Math.}}{x}_t\left(l\right)e\frac{-j2\pi \mathrm{lLm}}{N}& \left(4\right)\end{array}$

[0046] The DFT operation in (1) can also be implemented as a two-sided DFT with 1 in the range

[00009]$\left[\frac{-M}{2},\mathrm{.Math.},\frac{M}{2}-1\right]\left[\left(-M\right)/2\mathrm{.Math.}M/2-1\right].$

Alternatively, swap the left and right halves of x(k) with zero frequency component in the middle. Now consider a frequency domain pulse shaping filter:

[00010]$\begin{array}{cc}q\left(m\right)=\underset{n=-\frac{N}{2}}{\overset{\frac{N}{2}-1}{.Math.}}{q}_t\left(n\right)e\frac{-j2\pi nm}{N},m=-\frac{N}{2},\mathrm{.Math.},\frac{N}{2}-1& \left(5\right)\end{array}$

Where q.sub.t(n) are the samples of the time domain pulse shaping filter. Please note that, q(m) may take zero values for certain subcarriers. Alternatively, all N subcarriers need not be modulated with data. In some cases, some subcarriers at band edges may be nulled out. Applying the pulse shape to the transmitted data x.sup.˜(m), the proposed method has: x.sub.q(m)=q(m){tilde over (x)}(m).The time domain baseband signal s(t) is obtained using an inverse discrete time Fourier transform (IDFT).

[00011]$\begin{array}{cc}s\left(t\right)=\underset{m=-\frac{N}{2}}{\overset{\frac{N}{2}-1}{.Math.}}q\left(m\right)\tilde{x}\left(m\right)e^{j2\pi m\Delta f\left(t-T_{CP}\right)},t\in \left[0,T+bT\right]& \left(6\right)\end{array}$

where T is the useful portion of OFDMA symbol, T.sub.CP is the duration of the cyclic prefix (CP) and Δf=1/T is the subcarrier spacing. Note that b=1 when the system uses CP only and b=2 when the system uses cyclic prefix as well as cyclic suffix. Using (4) and (5), the analog signal can be rewritten as

[00012]$\begin{array}{cc}s\left(t\right)=\frac{1}{N}\underset{m=-\frac{N}{2}}{\overset{\frac{N}{2}-1}{.Math.}}{e}^{j\pi m}q\left(m\right)\tilde{x}\left(m\right)e^{j2\pi m\Delta f\left(t-T_{\mathrm{CP}}\right)},& \mathrm{ }\left(7\right)\\ t\in \left[0,T+\mathrm{bT}\right]& \\ =\frac{1}{N}\underset{l=0}{\overset{M-1}{.Math.}}{x}_t\left(l\right)\underset{m=\frac{=\mathrm{LM}}{2}}{\overset{\frac{\mathrm{LM}}{2}-1}{.Math.}}q\left(m\right)e^{j2\pi m\left(\frac{1}{T}\left(t-T_{\mathrm{CP}}\right)-\frac{\mathrm{lL}}{N}+\frac{1}{2}\right)}& \left(8\right)\\ =\frac{1}{N}\underset{l=0}{\overset{M-1}{.Math.}}{e}^{j\theta \left(l\right)}{a}_t\left(l\right)q_p\left(t-T_{\mathrm{CP}}-\frac{\mathrm{lT}}{M}+\frac{T}{2}\right)& \left(9\right)\end{array}$

where

[00013]$q_p\left(t\right)={.Math.}_{m=-\frac{N}{2}}^{\frac{N}{2}-1}q\left(m\right)e^{j2\pi m\frac{t}{T}}$

and t∈[0,T+bT] is the time domain pulse shaping function and x.sub.t(l)=e.sup.jθ(l)a.sub.t(l).Note that q.sub.p(t)=q.sub.p(t+rT), r being an integer. The transmitter 100 sends successive data blocks serially where each data block is limited to duration of T+bT.sub.CP seconds. Here, the time domain signal has a form similar to conventional SC-FDMA with q(t) being the pulse shaping function.

[0047] In another embodiment, let us consider the multiple access scenarios. In this scenario, the number of users shares the available bandwidth simultaneously. Therefore, the both non-orthogonal and orthogonal user allocations may be considered, where the users may employ distinct pulse shapes with different bandwidth requirements. Assuming there are a total of u users, let us denote the data of the i.sup.th user with x.sub.i(k) where

[00014]$\begin{array}{cc}{x}_i\left(k\right)=\underset{l=0}{\overset{M_i-1}{.Math.}}{e}^{j{\theta }_i\left(l\right)}{x}_{i,t}\left(l\right)e^{\frac{-j2\pi \mathrm{lk}}{M_i}},k=0,\mathrm{.Math.},M_i-1& \left(10\right)\end{array}$

where Mi is the data length of the i.sup.th user, θ.sub.i(l) being the constellation rotation employed by the i.sup.th user data x.sub.i,t. Note that the DFT operation in (10) can be implemented using a two sided DFT as

[00015]$x_i\left(k\right)=\underset{l=\frac{-M_i}{2}}{\overset{\frac{M_i}{2}-1}{.Math.}}{e}^{j{\theta }_t\left(l\right)}{x}_{i,t}\left(l\right)e^{\frac{-j2\pi \mathrm{lk}}{M_i}}\frac{-M_i}{2}\le k\le \frac{M_i}{2}-1$

Let {tilde over (x)}.sub.i(m) denote the L.sub.i fold periodic extension of x.sub.i(k) where L.sub.iM.sub.i=N and let q.sub.j(l) be the FDPSF associated with this user that is defined as

[00016]$\begin{array}{cc}{q}_i\left(m\right)=\underset{n=-\frac{N}{2}}{\overset{\frac{N}{2}-1}{.Math.}}{q}_{i,t}\left(n\right)e^{\frac{-j2\pi \mathrm{mn}}{N}},\mathrm{for}m=-\frac{{\stackrel{\_}{M}}_i}{2},\mathrm{.Math.},\frac{{\stackrel{\_}{M}}_i}{2}-1& \mathrm{ }\left(11\right)\\ =0\mathrm{elsewhere}& \left(12\right)\end{array}$

where, q.sub.i,n(t) are the corresponding time domain samples. Note that the FDPSF takes non-zero values over M.sub.i subcarriers where M.sub.i-M.sub.i is the excess number of subcarriers employed for the i.sup.th user. In this case, (M.sub.i−M.sub.i)Δf is denoted as the excess bandwidth employed by the i.sup.th user. Further, the users are frequency multiplexed over the given the band of interest as

[00017]$\begin{array}{cc}{s}_i\left(t\right)=\frac{1}{N}\underset{m=-\frac{N}{2}}{\overset{\frac{N}{2}-1}{.Math.}}{q}_i\left(m-m_i\right){\tilde{x}}_i\left(m\right)e^{\mathrm{j2}\pi \Delta f\left(t-T_{CP}\right)},t\in \left[0,T+b{T}_{CP}\right]& \left(13\right)\end{array}$

where m.sub.i is the frequency shift of the i.sup.th user. The proposed method provides a non-orthogonal multicarrier signal, if the values of m.sub.i are set to integer multiples of M.sub.i.

[0048] In an embodiment, the proposed method chooses m.sub.i=

[00018]$\left(i-1\right)M_i-\frac{N-{\stackrel{\_}{M}}_i}{2}\mathrm{for}i=1,2,\mathrm{.Math.},u_i.$

In another embodiment, the values of m.sub.i are chosen based on the subcarrier mapping procedure employed by the transmitter 100.

[0049] The transmitted signal can be represented in an alternative form as

[00019]$\begin{array}{cc}{s}_i\left(t\right)=\frac{1}{N}\underset{l=0}{\overset{M_i-1}{.Math.}}{e}^{j\theta \left(l\right)}{a}_{i,t}\left(l\right)q_{i,p}\left(t-T_{CP}-\frac{lT}{M_i}+\frac{T}{2}\right),t\in \left[0,T+b{T}_{CP}\right]& \left(14\right)\end{array}$

Where

[0050] [00020]$q_{i,p}\left(t\right)={.Math.}_{m=\frac{{-}_N}{2}}^{\frac{N}{2}-1}{q}_i\left(m-m_i\right)e^{j2\pi m\frac{t}{T}}$

is the time domain pulse shaping function employed by the i.sup.th user. Here, q.sub.i,p(t)=q.sub.i,p(t+rT), where r is an integer.

[0051] let

[00021]$\begin{array}{cc}{q}_{i,p}\left(t\right)=\underset{m=\frac{-N}{2}}{\overset{\frac{N}{2}-1}{.Math.}}{q}_i\left(m-m_i\right)e^{j2\pi m\frac{t}{T}}t\in \left[0,T+b{T}_{CP}\right]& \left(15\right)\end{array}$

[0052] Using (11) and substituting m−mi=m1 in (15) to express q.sub.i(t) in alternative form as

[00022]$\begin{array}{cc}{q}_{i,p}\left(t\right)=e^{j2\pi m_i\frac{t}{T}}\underset{m=\frac{-{\stackrel{\_}{M}}_i}{2}}{\overset{\frac{{\stackrel{\_}{M}}_i}{2}-1}{.Math.}}{q}_i\left(m\right)e^{j2\pi m\frac{t}{T}}& \mathrm{ }\left(16\right)\\ =q_{0,i}\left(t\right)e^{-j2\pi m_i\frac{t}{T}}t\in \left[0,T+b{T}_{CP}\right]& \left(17\right)\end{array}$

and

[00023]$q_{0,i}\left(t\right)={.Math.}_{m_1=\frac{-{\stackrel{\_}{M}}_i}{2}}^{\frac{\stackrel{\_}{M_i}}{2}-1}{q}_i\left(m_1\right)e^{j2\pi m\frac{t}{T}}$

is the baseband pulse shaping function used by the i.sup.th user. Now the transmitted signal may be rewritten as:

[00024]$\begin{array}{cc}{s}_i\left(t\right)=\frac{1}{N}\underset{l=0}{\overset{M_i-1}{.Math.}}{e}^{j{\theta }_i\left(l\right)}{a}_{i,t}\left(l\right)q_{0,i}\left(t-T_{CP}-\frac{lT}{M_i}+\frac{T}{2}\right)e^{j2\pi m_i\frac{\left(t-T_{CP}\frac{\mathrm{lT}}{M_i}+\frac{T}{2}\right)}{T}}& \left(18\right)\end{array}$

[0053] In an embodiment, the total number of subcarriers is N. However, only N.sub.u subcarriers out of N may be used by the transmitter 100. The remaining (N−N.sub.u) subcarriers do not carry the data. Furthermore, a number of users are frequency multiplexed over the N.sub.u subcarriers. The transmitted signal is given by

[00025]$s_i\left(t\right)=\frac{1}{Nu}\underset{m}{.Math.}{q}_i\left(m-m_i\right){\tilde{x}}_i\left(m\right)e^{\mathrm{j2\pi \Delta }f\left(t-T_{\mathrm{cp}}\right)}t\in \left[0,T+b{T}_{cp}\right]$

[0054] Here the transmitted signal spans over a group of subcarriers whose range is dictated by the subcarriers occupies by the signal of the i.sup.th user. Furthermore, the value of m.sub.i is a system design feature that can be used to control the amount of non-orthogonality introduced by the transmitter 100. The value of m.sub.i may be set to M.sub.i, M.sub.i or any other value. For example, setting the value of m.sub.i in the range [0 M.sub.i] increases the spectrum efficiency of the system. Another alternative is to choose the value of m.sub.i in the range. [M.sub.i M.sub.i] In certain cases, one may set the value of m.sub.i to be zero, if multiple users or signals of multiple antennas are allowed to transmit on the same time frequency resource.

[0055] Symbol Windowing: As the transmit signal is confined to a period of one OFDM symbol duration, effectively it imposes a rectangular window function that leads to high OBE. In order to reduce OBE, the proposed techniques employ alternative time domain window functions that offer smooth transitions at the OFDM symbol boundaries. The proposed method includes a cyclic prefix as well as cyclic postfix each of duration T.sub.CP. The analog signal can be rewritten as

[00026]$\begin{array}{cc}{s}_i\left(t\right)=\frac{1}{N}\underset{m=-\frac{N}{2}}{\overset{\frac{N}{2}-1}{.Math.}}w\left(t\right)q_i\left(m-m_i\right){\tilde{x}}_i\left(m\right)e^{\mathrm{j2\pi m\Delta }f\left(T-T_{CP}\right)},& \mathrm{ }\left(19\right)\\ t\in \left[0,T+b{T}_{CP}\right]& \\ =\frac{1}{N}\underset{l=0}{\overset{M_i-1}{.Math.}}{e}^{j{\theta }_i\left(l\right)}{a}_{i,t}\left(l\right)w\left(t\right)q_{i,p}\left(t-T_{CP}-\frac{lT}{M_i}+\frac{T}{2}\right),& \left(20\right)\\ t\in \left[0,T+b{T}_{CP}\right]& \end{array}$

Where, w(t) is the proposed window function defined over the interval tϵ[0, T+bT.sub.CP] (that is designed as the OFDM symbol block duration). The window w(t) is chosen such that it takes a constant value for the duration of the OFDM symbol that excludes cyclic prefix and suffix. The window takes a constant value during a portion of the cyclic prefix and/or suffix and it tapers to a zero value at the block boundaries. Standard time domain window functions such as SQRC, RC, Hamming, Hanning, Bartltt window can be used.
In an embodiment, the following RC window is used, where W and β are design parameters:

[00027]$W,.Math.t.Math.\le \frac{1-\beta }{2W}$$w\left(t\right)=\frac{W}{2}\left(1+\cos \left(\frac{\pi W}{\beta }\left(.Math.t.Math.-\frac{\left(1-\beta \right)}{2W}\right)\right)\right),\frac{1-\beta }{2W}<.Math.t.Math.\le \frac{1+\beta }{2W}$$0,\mathrm{otherwise}$

[0056] To avoid the dc subcarrier, the transmitted signal s.sub.i(t) is further multiplied with e.sup.jπaΔf(t−T.sup.CP.sup.) or e.sup.−jπaΔf(t−T.sup.CP.sup.) where a is real-valued number. In an embodiment a=1.

[0057] In an embodiment, the signal that is generated for multiple users over distinct (distributed) frequency resources is transmitted from the same user equipment. In this case, the low PAPR properties of the signal does not hold any more but the user will be able to transmit at a higher data rate using multiple distributed time-frequency resources.

[0058] The modulation data symbols transmitted by a user equipment is usually encoded by an error correction code such as block code, convolutional code, or a turbo code, followed by a scrambler, interleaver before mapped to the desired modulation format.

[0059] Further, the FDPSF enables the low PAPR waveform design. The PAPR can be controlled using a suitable choice of constellation rotation factor θ(l), modulation size Q and the FDPSF q(m) given in equation (5). In an embodiment, let

[00028]$\theta \left(l\right)=\frac{\pi \left(l-1\right)}{2}$

for real constellations, and for Q-ary complex constellations such as QAM, let

[00029]$\theta \left(l\right)=\frac{\pi \left(l-1\right)}{Q}.$

For the special case of Q=2, the waveforms may be designed with nearly constant envelope by selecting

[00030]$\theta \left(l\right)=\frac{\pi \left(l-1\right)}{2},$

and by choosing the FDPSF based on the linearized Gaussian pulse that is obtained as the principal pulse in the PAM decomposition of a binary CPM signal with modulation index 0.5. The time domain samples of the FDPSF qt (n) can be chosen as:

[00031]${q_t\left(n\right)=p_0\left(t\right).Math.}_{t-{\tau }_0+\frac{\mathrm{nT}}{s}}$

where p0 (t) is the linearized Gaussian pulse, s is the over-sampling factor, and the factor BT controls the characteristics of the waveform, and τ.sub.0 is constant time offset, and n is an integer. Since the pulse is time limited, the values of n can be taken in the range

[00032]$\frac{-sM}{2}\le n\le \frac{sM}{2}-1.$

[0060] With an over-sampling rate of s, the Fourier transform of q.sub.t (n) is periodic with a period

[00033]$\frac{s}{T}.$

The FDPSF with a span of sMsubcarriers is obtained by taking a sMpoint DFT of q.sub.t(n) as defined in equation (11). Alternatively, the FDPSF can be obtained by taking an sM point DFT first as

[00034]$\tilde{q}\left(m\right)=\underset{n=0}{\overset{\mathrm{sM}-1}{.Math.}}{q}_t\left(n\right)e^{\frac{-j2\pi nm}{sM}}0\le m\le sM-1$

[0061] Further, the left and right halves of the DFT output can be swapped so that the zero frequency components are in the middle. Alternatively, the FDPSG can be obtained using a two sided DFT as

[00035]$q\left(m\right)=\underset{n=\frac{-\mathrm{sM}}{2}}{\overset{\frac{\mathrm{sM}}{2}-1}{.Math.}}{q}_t\left(n\right)e^{\frac{-j2\pi nm}{sM}}\frac{-sM}{2}\le m\le \frac{sM}{2}-1$

[0062] Since the sequence q.sub.t(n) is real-valued, in certain cases, it can be appropriately circularly shifted by certain amount before taking the DFT to make the DFT output real. Also, a FDPSF of length less than sM can be applied by truncating the FDPSF filter a.sub.t both ends.

[0063] Alternative to the proposed designed procedure, one can consider a M.sub.0point DFT of q.sub.t(n) where M.sub.0>sM and

[00036]${q_t\left(n\right)=p_0\left(t\right).Math.}_{t=\frac{nT}{s}}\mathrm{for}n=-\frac{-M_0}{2},\mathrm{.Math.},\frac{M_0}{2}-1,$

then collect sM points out of M.sub.0 points by decimating the DFT output to generate q(m). In yet another alternative implementation, the values of q(m) can be obtained by taking samples of p0(f) (that is the Fourier transform of p0 (t) taken at appropriate intervals).

[0064] For the special case of s=1, the technique can design PDPSF without excess BW. In this case, the waveform introduces ISI but has zero multi-user interference. To obtain the time domain samples for s=1, the technique can first generate the samples corresponding to s=2, then choose either the even or odd symbol spaced sample sequence to generate the required FDPSF.

[0065] Some examples of values of time domain samples of the q.sub.t(n) is given in the Tables 1 and 2, where the pulse response is forced to be causal i.e., the values of qt (n) is positive for n≥0 and takes a zero value for n<0. In the Table the values of qt (n) start with n=0. The method defines

[00037]$\tilde{q}\left(m\right)=\underset{n=0}{\overset{\mathrm{sM}-1}{.Math.}}{q}_t\left(n\right)e^{\frac{-j2\pi nm}{sM}}0\le m\le sM-1$

[0066] The FDPSF q(m) is obtained after the left and right halves of the DFT output {tilde over (q)}(m) is swapped so that the zero frequency components are at m=0. Alternatively, considering the range 0≤n≤sM−1, the causal response qt (n) can be circularly shifted to the left by certain amount so that the zero.sup.th time sample is located at n=0 and negative time samples are located in the left half. In this case, the pulse response is real and symmetric i.e., q.sub.t(n)=q.sub.t(sM−n). The DFT of this sequence is also real and symmetric i.e., {tilde over (q)}(m)={tilde over (q)}(sM−m) The FDPSF q(m) is obtained after the left and right halves of the DFT output {tilde over (q)}(m) is swapped so that the zero frequency components in located at m=0.

TABLE-US-00001 TABLE 1 MSK, s = 3 MSK, s = 1 MSK, s = 3 τ.sub.0 = 0 [00038]${\tau }_0=\frac{T}{2}$ MSK, s = 2 τ.sub.0 = 0 [00039]${\tau }_0=\frac{T}{2}$ 0.5   0.2588 0.7071 0.7071 0.866 0.7071 1     0.7071 1     0.9659 0.7071 0     0.866 0.9659 0     0     0.5   0.7071 0     0     0     0.2588 0     0     0     0     0     0    

TABLE-US-00002 TABLE 2 BT = 0.3, L = 6, s = 2 τ.sub.0 = 0 [00040]$\hspace{1em}\begin{array}{c}\mathrm{BT}=0.3,\\ L=6,\\ s=1\\ {\tau }_0=\frac{T}{2}\end{array}$ BT = 0.3, L = 6, s = 1 τ.sub.0 = 0 [00041]$\hspace{1em}\begin{array}{c}\mathrm{BT}=0.3,\\ L=6,\\ s=1\\ {\tau }_0=\frac{T}{2}\end{array}$ 0.0007 0.0315 0.0007 0.707 0.0315 0.7057 0.2605 0.7071 0.2605 0.7057 0.9268 0 0.7057 0.0315 0.2605 0 0.9268 0 0.0007 0 0.7057 0 0 0 0.2605 0 0 0 0.0315 0 0 0 0.0007 0 0 0

[0067] The proposed technique can be used to multiplex data of multiple users where each user transmits an approximated continuous phase modulation (CPM) signal. The approximated CPM signal can be obtained by representing CPM a superposition of multiple PAM signals and G-DFT-precoded-OFDM modulation is applied for each PAM component. Only the dominant PAM components can be used for transmission. A corresponding receiver needs to be developed in such cases.

[0068] The principal pulse p.sub.0 (t) is the main pulse in Laurent's decomposition [9] is given by

[00042]$p_0\left(t\right)=\{\begin{array}{c}{.Math.}_{k=1}^{k=L_1}c\left(t-\mathrm{kT}\right)t\in \left[0,\left(L_1+1\right)T\right]\\ 0\mathrm{otherwise}\end{array}\mathrm{where}c\left(t\right)=\{\begin{array}{c}\cos \left(-\frac{\pi }{2}q\left(t\right)\right)t\in \left[0,L_{1}T\right)\\ c\left(-t\right)t\in \left(-L_{1}T,0\right]\\ 0.Math.t.Math.\ge L_{1}T\end{array}$

[0069] The pulse q(t) is a Gaussian filtered rectangular pulse response defined as

[00043]$q\left(t\right)=\frac{1}{T}\left[Q\left(\gamma \left(\frac{t}{T}-\frac{1}{2}\right)\right)-Q\left(\gamma \left(\frac{t}{T}+\frac{1}{2}\right)\right)\right]$

where

[00044]$\gamma \cong \frac{2\pi BT}{\sqrt{\left(\ln \left(2\right)\right)}},$

BT is a parameter that controls the pulse shape, and

[00045]$Q\left(x\right)\cong \frac{1}{\sqrt{2\pi }}{\int }_x^{\infty }{e}^{-\frac{u^2}{2}}du.$

The value of L.sub.1 determines the pulse duration. Typically this value is chosen to be in the range 4-6.

[0070] FIG. 2 is a flow diagram illustrating a method 200 for designing a waveform for data communication, according to the embodiments as disclosed herein. At the step 202, the method involves applying the constellation specific phase rotation between consecutive data symbols in the data stream to obtain the constellation rotated data stream. In an embodiment, the method 200 allows the phase rotation applying unit 102 to apply the constellation specific phase rotation between consecutive data symbols in the data stream to obtain the constellation rotated data stream.

[0071] At the step 204, the method 200 involves introducing the ISI between modulated data symbols of the constellation rotated data stream. In an embodiment, the method 200 allows the frequency domain pulse shaping filter 104 to introduce the ISI between modulated data symbols of the constellation rotated data stream.

[0072] The various actions, acts, blocks, steps, and the like in method 200 may be performed in the order presented, in a different order or simultaneously. Further, in some embodiments, some actions, acts, blocks, steps, and the like may be omitted, added, modified, skipped, and the like without departing from the scope of the invention.

[0073] FIG. 3a shows the sequence of steps followed in generating a BPSK modulated G-DFT-precoded-OFDM signal with linearized Gaussian pulse shaping. At the step 302a, the method 300a involves sending/transmitting BPSK modulation data by the transmitter 100. At the step 304a, the method 300a includes performing constellation rotation by pi/2 on the BPSK modulation data using the transmitter 100. At the step 306a, the method 300a includes performing, by the transmitter 100, Mi-point DFT after performing constellation rotation. At the step 308a, the method 300a includes performing, by the transmitter 100, DFT spreading process after performing Mi-point DFT. At the step 310a, the method 300a includes obtaining, by the transmitter 100, the user specific pulse shaping filter after performing the DFT spreading process. At the step 312a, the method 300a includes performing, by the transmitter 100, an orthogonal/Non-orthogonal subcarrier mapping after obtaining the user specific pulse shaping filter. At the step 314a, the method 300a includes introducing, by the transmitter 100, a half sub-carrier shift after performing the orthogonal/Non-orthogonal subcarrier mapping.

[0074] The various actions, acts, blocks, steps, and the like in method 300a may be performed in the order presented, in a different order or simultaneously. Further, in some embodiments, some actions, acts, blocks, steps, and the like may be omitted, added, modified, skipped, and the like without departing from the scope of the invention.

[0075] FIG. 3b shows the steps involved for designing the waveform for QAM systems with arbitrary pulse shaping filter. At the step 302b, the method 300b involves providing PAM or QAM modulation data by the transmitter 100. At the step 304b, the method 300b includes performing constellation rotation by pi/2 on the modulation data using the transmitter 100. At the step 306b, the method 300b includes performing, by the transmitter 100, Mi-point DFT after performing the constellation rotation. At the step 308b, the method 300b includes performing, by the transmitter 100, DFT spreading process after performing the Mi-point DFT.

[0076] At the step 310b, the method 300b includes obtaining, by the transmitter 100, the user specific pulse shaping filter after performing the DFT spreading process. At the step 312b, the method 300b includes performing, by the transmitter 100, an orthogonal/Non-orthogonal subcarrier mapping after obtaining the user specific pulse shaping filter. At the step 314b, the method 300b includes introducing, by the transmitter 100, a half sub-carrier shift after performing the orthogonal/Non-orthogonal subcarrier mapping.

[0077] The various actions, acts, blocks, steps, and the like in method 300b may be performed in the order presented, in a different order or simultaneously. Further, in some embodiments, some actions, acts, blocks, steps, and the like may be omitted, added, modified, skipped, and the like without departing from the scope of the invention.

[0078] FIG. 4a shows the sequence of steps involved in the design of a frequency domain pulse shaping filter using linearized Gaussian pulse.

[0079] At the step 402a, the method includes 400a obtaining, by the transmitter 100, the linearized Gaussian pulse using Laurent's decomposition of GMSK. At the step 404a, the method includes 400a oversampling, by the transmitter 100, linearized Gaussian pulse by a factor “S” after obtaining the linearized Gaussian pulse. At the step 406a, the method includes 400a truncating, by the transmitter 100, the sequence to “sM” points and optionally circularly shifting the sequence by certain amount. At the step 408a, the method includes 400a computing “sM” point DFT. At the step 410a, the method includes 400a swapping, by the transmitter 100, the left and right halves of the sequence with zero frequency in the middle after computing “sM” point DFT.

[0080] The various actions, acts, blocks, steps, and the like in method 400a may be performed in the order presented, in a different order or simultaneously. Further, in some embodiments, some actions, acts, blocks, steps, and the like may be omitted, added, modified, skipped, and the like without departing from the scope of the invention.

[0081] FIG. 4b shows the sequence of steps involved in the design of a frequency domain pulse shaping filter for any time domain pulse. At the step 402b, the method includes 400b providing, by the transmitter 100, a time domain pulse shaping function. At the step 404b, the method includes 400b oversampling, by the transmitter 100, the pulse by a factor “s” after obtaining time domain pulse shaping function. At the step 406b, the method includes 400b truncating, by the transmitter 100, the sequence to “sM” points and optionally circularly shifting the sequence by certain amount. At the step 408b, the method includes 400b computing “sM” point DFT. At the step 410b, the method includes 400b swapping, by the transmitter 100, the left and right halves of the sequence with zero frequency in the middle after computing “sM” point DFT.

[0082] The various actions, acts, blocks, steps, and the like in method 400b may be performed in the order presented, in a different order or simultaneously. Further, in some embodiments, some actions, acts, blocks, steps, and the like may be omitted, added, modified, skipped, and the like without departing from the scope of the invention.

[0083] In an embodiment, the base station may schedule the users such that the users located a.sub.t the cell boundaries or users with low signal-to-noise ratio use the frequency domain pulse shaping filter together with transmit power boosting. The base station signals to the user a.sub.t least one of: the type of frequency domain pulse shaping filter to be used, the number of allocated subcarriers, the location of subcarriers in the time-frequency plane, the constellation rotation, and the modulation type. The frequency domain pulse shaping filter may use zero or non-zero excess bandwidth. The base station may schedule users such that the users with low signal-to-noise ratio user narrowband width, frequency domain pulse shaping with or without excess band width while the users scheduled in adjacent bands have high signal-to-noise ratio and possibly wider bandwidth allocation. Furthermore, the users may use overlapping set of subcarriers due to excess bandwidth employed a.sub.t one or more users. At the base station receiver, the inter-user-interference caused by the non-orthogonal transmission may not give rise to significant interference because of the higher received power associated with the high signal-to-noise ratio users.

[0084] FIG. 5 is a block diagram of various units present in a receiver 500, according to the embodiments as disclosed herein. The receiver 500 receives the data stream. The data stream is received in the form of waveform designed by the frequency domain pulse shaping filter 104. The receiver 500 includes receiving unit 502, a vector/matrix-valued filter 504, a converting unit 506, and an eliminating unit 508. A receiver front end operations such as sampling, synchronization, frequency offset removal, I/Q imbalance correction, DC offset correction, clock recovery, and CP (including cyclic prefix and/or suffix) removal and channel estimation operations are similar to a conventional receiver system. Further, the memory introduced by the propagation channel of any given user is assumed to be less than that of the CP duration. Furthermore, receiver obtains the overall channel impulse response using pilots and the knowledge of FDPSF.

[0085] The receiving unit 502 is configured to receive the data stream. After receiving the data stream, the vector/matrix-valued filter 504 is configured to suppress the ISI between the modulated data symbols in the data stream. Based on suppressing the ISI between the modulated data symbols in the data stream, the converting unit 506 is configured to convert the received data stream to time domain for detection of the signal.

[0086] In an embodiment, the eliminating unit 508 is configured to eliminate constellation rotation in the received data stream by de-rotating the received data stream in the frequency domain.

[0087] In an embodiment, the eliminating unit 508 is configured to eliminate constellation rotation in the received data stream by de-rotating the received data stream in the time domain. In an embodiment, the eliminating unit 508 is configured to eliminate the cyclic prefix and the cyclic suffix from the received data stream after de-rotating the received data stream.

[0088] The time domain sampled received signal after removing CP is given by

[00046]$y_t\left(n\right)=\underset{i=1}{\overset{u}{.Math.}}{s}_{i,t}\left(n\right).Math.h_{i,t}\left(n\right)+n_t\left(n\right)n=\frac{-N}{2},\mathrm{.Math.},\frac{N}{2}-1$

[0089] Here s.sub.i,n(n) corresponds to the sampled version of the analog signal for the i.sup.th user. The symbol .Math. denotes linear convolution operation. The noise vector n.sub.t(n) is an i.i.d complex-Gaussian random variable each with zero-mean and variance

[00047]$\frac{{\sigma }_n^2}{2}$

per dimension. Note that h.sub.i,t(n) is assumed to be a time limited channel of the i.sup.th user. Taking the N-point two-sided DFT of yt (n), the proposed technique get

[00048]$\begin{array}{cc}\stackrel{\_}{y}\left(m\right)=\underset{n=-\frac{N}{2}}{\overset{\frac{N}{2}}{.Math.}}{y}_t\left(n\right)e^{-j2\pi \mathrm{nm}/M},m=\frac{-N}{2},\mathrm{.Math.},\frac{N}{2}-1& 22\end{array}$

[0090] the proposed technique can write y.sup.−(m) as

[00049]$\begin{array}{cc}\stackrel{\_}{y}\left(m\right)=\underset{i=1}{\overset{u}{.Math.}}{q}_i\left(m-m_i\right)h_i\left(m\right){\tilde{x}}_i\left(m\right)+n\left(m\right),m=\frac{-N}{2},\mathrm{.Math.},\frac{N}{2}-1& 23\end{array}$

Multi-User System Model:

[0091] For the purpose of developing a multi-user generalized MMSE receiver, the proposed techniques assume that a) all the users employ equal number of subcarriers i.e., Mi=M and b) the proposed techniques apply zero excess BW for the users located a.sub.t the band edges i.e., M.sub.1=M.sub.2=M. The remaining users M.sub.i=M for i=2, 3, . . . , L−1. The proposed techniques have a total of u=L users where L takes a minimum value of 1. For this case

[00050]$m_i=\left(i-1\right)M-\frac{N-\stackrel{\_}{M}}{2}$

for i=2, 3, . . . , L−1 and

[00051]$m_i=\frac{N-\stackrel{\_}{M}}{2},m_L=\left(L-1\right)M-\frac{N-M}{2}$

since the proposed method employ zero excess BW at the band edges. As an illustrative example, the proposed techniques restrict to the case where M≤3M i.e, the frequency domain pulse causes interference to a maximum of one user located on either side. The receiver 500 can easily generalized to the case where users apply arbitrary values of M.sub.i. Furthermore, here the proposed techniques assume that all N subcarriers are utilized for data transmission. In practice, the actual number of subcarriers is equal to Nu<N.

[0092] In (23), letting

[00052]$m=k+\left(i-1\right)M-\frac{N}{2}$

for k=0, 1, . . . , M−1 and i=1, 2, . . . , L, let's have

[00053]$y\left(k+\left(i-1\right)M\right)=y\left(k+\left(i-1\right)M-\frac{N}{2}\right),k=0,1,\mathrm{.Math.},M-1,i=1,\mathrm{.Math.},L\mathrm{and}$$p_i\left(k+\left(i-1\right)M\right)=q_i\left(k-\frac{{\stackrel{\_}{M}}_i}{2}\right)h_i\left(k+\left(i-1\right)M-\frac{N}{2}\right),k=0,1,\mathrm{.Math.},M-1,i=1,\mathrm{.Math.},L$

where h.sub.i(k) is the frequency domain channel for the i.sup.th user and {tilde over (x)}.sub.i

[00054]$\left(k+\left(i-1\right)M-\frac{N}{2}\right)=x_i\left(k\right)\mathrm{for}i=1,\mathrm{.Math.},L.$

[0093] The proposed detector jointly detects all the L users simultaneously using the generalized MMSE-DFE receiver. The receiver 500 exploits the redundancy (excess BW) contained in the signal. Let us collect multiple copies of the received signals as

[00055]$\begin{array}{cc}\stackrel{\_}{y}\left(k\right)=\stackrel{\_}{H}\left(k\right)x\left(k\right)+\stackrel{\_}{n}\left(k\right)\mathrm{for}k=0,\mathrm{.Math.},M-1\stackrel{\_}{y}\left(k\right)=\left[\begin{array}{c}y\left(k\right)\\ y\left(k+M\right)\\ y\left(k+2M\right)\\ y\left(k+3M\right)\\ \mathrm{.Math.}\\ y\left(k+\left(L-1\right)M\right)\end{array}\right]\stackrel{\_}{n}\left(k\right)=\left[\begin{array}{c}n\left(k\right)\\ n\left(k+M\right)\\ n\left(k+2M\right)\\ n\left(k+3M\right)\\ \mathrm{.Math.}\\ n\left(k+\left(L-1\right)M\right)\end{array}\right]x\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ x_3\left(k\right)\\ \mathrm{.Math.}\\ x_L\left(k\right)\end{array}\right]& 24\end{array}$

[0094] and H(k) is given by

[00056]$\begin{array}{cc}\left[\begin{array}{cccccccc}p\text{?}\left(k\right)& p\text{?}\left(k\right)& 0& 0\mathrm{.Math.}& 0& 0& 0& 0\\ 0& p\text{?}\left(k+M\right)& p\text{?}\left(k+M\right)& 0\mathrm{.Math.}& 0& 0& 0& 0\\ 0& p\text{?}\left(k+2M\right)& p\text{?}\left(k+2M\right)& p\text{?}\left(k+2M\right)& 0& 0& \mathrm{.Math.}& \mathrm{.Math.}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ 0& 0& 0& 0& 0& p\text{?}\left(k+\left(L-2\right)M\right)& p\text{?}\left(k+\left(L-2\right)M\right)& 0\\ 0& 0& 0& 0& 0& 0& p\text{?}\left(k+\left(L-1\right)M\right)& p\text{?}\left(k+\left(L-1\right)M\right)\end{array}\right]\text{?}\text{indicates text missing or illegible when filed}& \end{array}$

where the proposed techniques illustrate the channel matrix for the case where a maximum of two users interfere with any given user. This scenario corresponds to the case where the excess BW employed by any user is less than 200%.

Multi-User Widely Linear Generalized MMSE Equalizer

[0095] In order to exploit the real-valued nature of modulation symbols, the receiver first removes the constellation rotation using frequency domain operations. The first step in the WL receiver is to de-shift the received signal by

[00057]$\frac{M}{4}$

samples to render the modulation data to be a real-valued signal. Note that if M is not an integer multiple of 4, constellation de-rotation step need to be performed in time domain and then transform the signal to frequency domain. After shifting y.sup.−(k) by

[00058]$\frac{M}{4}$

samples, the proposed techniques get:

[00059]$\begin{array}{cc}\hat{y}\left(k\right)=\hat{H}\left(k\right)a\left(k\right)=\hat{n}\left(k\right)\mathrm{Where}\hat{y}\left(k\right)=y\left(k.Math.\frac{M}{4}\right),\hat{H}\left(k\right)=\stackrel{\_}{H}\left(k\oplus \frac{M}{4}\right),\hat{n}\left(k\right)=\stackrel{\_}{n}\left(k\oplus \frac{M}{4}\right)& \left(25\right)\end{array}$

and the proposed techniques use the fact that

[00060]$x_i\left(k\oplus \frac{M}{4}\right)=a_i\left(k\right).$

Next, the receiver 500 applies complex conjugation and frequency reversal operations on ŷ(k) to obtain:

ŷ*(M−k)=Ĥ*(M−k)a(k)+{circumflex over (n)}*(M−k)  (26)

Here a*(M−k)=a(k). Stacking (25) and (26) in column vector format

[00061]$\begin{array}{cc}\left(\begin{array}{c}\hat{y}\left(k\right)\\ {\hat{y}}^{*}\left(k\right)\end{array}\right)=\left(\begin{array}{c}\\ {\hat{H}}^{*}\left(M-k\right)\end{array}\right)a\left(k\right)+\left(\begin{array}{c}\hat{n}\left(k\right)\\ {\hat{n}}^{*}\left(M-k\right)\end{array}\right)& \left(27\right)\end{array}$

[0096] In compact matrix form

y(k)=H(k)a(k)+n(k)  (28)

[0097] In the proposed WL GMMSE receiver, the received signal is filtered using a matrix-valued feed-forward filter W(k) to obtain: z(k)=W(k)y(k). Following the approach presented in [13],[14], the proposed techniques define error signal

e(k)={right arrow over (z)}(k)−a(k)  (29)

This is written in time domain as

e.sub.t(l)=z.sub.t(l)−a.sub.t(l)  (30)

Applying orthogonality principle [14]

E(e(k)y.sup.†(k))=0, for k=0,1, . . . ,M−1  (31)

Substituting (29) in (31) and evaluating the expectation, the FFF can be expressed as

W(k)=R.sub.ay(k)R.sub.yy.sup.−1(k)  (32)

Where R.sub.ay(k)=E(a(k)y.sup.†(k))=R.sub.aa(k)H†(k)

and R.sub.yy(k)=E(y(k)y.sup.†(k))=[H(k)R.sub.aa(k)H†(k)+R.sub.nn(k)]

Here,

R.sub.aa(k)=E(a(k)a.sup.†(k))=Mσ.sub.a.sup.2I and

R.sub.nn(k)=E(n(k)n.sup.†(k))=Mσ.sub.n.sup.2I.

The FFF can be, expressed in alternative form as

[00062]$\begin{array}{cc}W\left(k\right)=R_{\mathrm{aa}}\left(k\right){H^{†}\left(k\right)\left[H\left(k\right)R_{\mathrm{aa}}\left(k\right)H^{†}\left(k\right)+R_{\mathrm{nn}}\left(k\right)\right]}^{-1}& \left(33\right)\\ ={\left[R_{\mathrm{aa}}^{-1}\left(k\right)+H^{†}\left(k\right)R_{\mathrm{nn}}^{-1}\left(k\right)H\left(k\right)\right]}^{-1}{H}^{†}\left(k\right)R_{\mathrm{nn}}^{-1}\left(k\right)& \left(34\right)\end{array}$

[0098] Note that (36) follows from applying matrix inversion lemm. Let, R.sub.ee(k)=E(e(k)e.sup.†(k)). Using the optimum FFF, the minimum MSE can be shown to be [13],[14]

[00063]$\begin{array}{cc}{R}_{ee}=\frac{1}{M^2}\underset{k=0}{\overset{M-1}{.Math.}}{R}_{ee}\left(k\right)=\frac{1}{M}\underset{k=0}{\overset{M-1}{.Math.}}Q\left(k\right)& \left(35\right)\end{array}$

where Q(k)=[R.sub.aa.sup.−1(k)+H.sup.†(k)R.sub.aa.sup.−1H(k)].sup.−1. The symbols of individual users are detected using z.sub.t(l) using standard slicing methods.

Conventional GMMSE Receiver

[0099] The WL GMMSE receiver design is designed by performing following steps: [0100] Step1: Removal of constellation as a first step is done for the special case of real constellations only. For complex-valued constellations, the system works with y (k) directly. [0101] Step2: Remarking here that for the special case of s=1, since there is no multi-user interference among the users, the proposed conventional or WL GMMSE receiver can be decoupled into multiple single user conventional or WL MMSE equalizers.

[0102] Using Conventional GMMSE receiver, the received signal (25) is filtered using a matrix-valued feed-forward filter W{circumflex over ( )} (k) to obtain: {circumflex over (z)}(k)=Ŵ(k)ŷ(k). The expressions for the FFF is given by

Ŵ(k)=[R.sub.aa.sup.−1(k)+Ĥ.sup.†(k)R.sub.{circumflex over (n)}.sup.−1(k)ĥ(k)].sup.−1Ĥ.sup.†(k)R.sub.{circumflex over (n)}.sup.−1(k)  (36)

and the MMSE becomes

[00064]$\begin{array}{cc}{R}_{conv}=\frac{1}{M}\underset{k=0}{\overset{M-1}{.Math.}}{\left[R_{aa}^{-1}\left(k\right)+{\hat{H}}^{†}\left(k\right)R_{\hat{n}}^{-1}\left(k\right)\hat{H}\left(k\right)\right]}^{-1}& \left(37\right)\end{array}$

[0103] The noise covariance term R.sub.{circumflex over (n)}(k)=Mσ.sub.n.sup.2I.

[0104] For complex constellations, the conventional GMMSE receiver can be applied directly on y (k) followed by a time domain constellation removal step after frequency domain equalization.

Conventional Single User Equalizer

[0105] The multi-user equalizer involves inversion of a channel matrix of size L×L. Furthermore, the multi-user user equalizer is applicable only to the case where M.sub.i=M. The following method can be used to detect both real and complex constellations. In this case, the equalizer modifies the signal model yl(k) where the elements of y.sub.i(k)

.sup.1(A+BCD).sup.−1=A.sup.−1+A.sup.−1BC.sup.−1+DA.sup.−1B.sup.−1DA.sup.−1

are formed by appropriately collecting the subcarriers of interest. Assuming Mi be the allocated for the user, the received signal model y.sub.i(k) can be modified as

[00065]$\stackrel{\_}{y}\left(k\right)=\left[\begin{array}{c}\mathrm{.Math.}\\ y\left(k+\left(i-2\right)M_i\right)\\ y\left(k+\left(i-1\right)M_i\right)\\ y\left(k+\left({\mathrm{iM}}_i\right)\right)\\ \mathrm{.Math.}\end{array}\right]$${\stackrel{\_}{h}}_i\left(k\right)=\left[\begin{array}{c}\mathrm{.Math.}\\ p_i\left(k+\left(i-2\right)M_i\right)\\ p_i\left(k+\left(i-1\right)M_i\right)\\ p_i\left(k+\left({\mathrm{iM}}_i\right)\right)\\ \mathrm{.Math.}\end{array}\right]$${\stackrel{\_}{n}}_i\left(k\right)=\left[\begin{array}{c}\mathrm{.Math.}\\ n_i\left(k+\left(i-2\right)M_i\right)\\ n_i\left(k+\left(i-1\right)M_i\right)\\ n_i\left(k+\left({\mathrm{iM}}_i\right)\right)\\ \mathrm{.Math.}\end{array}\right]$

can be used to develop the single user equalizer. Using this, for the case of conventional signal model, the proposed techniques can rewrite y.sub.i(k) as

[00066]$\begin{array}{cc}{\stackrel{\_}{y}}_i\left(k\right)={\stackrel{\_}{h}}_i\left(k\right)a_i\left(k\right)+\underset{i\ne j}{.Math.}{\stackrel{\_}{h}}_j\left(k\right)a_j\left(k\right)+\stackrel{\_}{n}\left(k\right),i=1,2,\mathrm{.Math.},L& \left(38\right)\end{array}$

where h.sub.i(k) is the i.sup.th column of H(k) with certain rows containing zeros in h.sup.− i(k) are eliminated. The received signal (38) is filtered using a vector valued feed-forward filter w.sub.i(k) to obtain: z(k)=W(k)y.sub.i(k) where z.sub.i(k) is a scalar-valued frequency domain equalized signal for the i.sup.th user. Following the MMSE approach, the expression for FFF is given by:

[00067]$\begin{array}{cc}{\stackrel{\_}{w}}_i\left(k\right)={\left[{\sigma }_{a_i}^2+{\stackrel{\_}{h}}_i^{†}{R}_{i,\stackrel{\_}{n}}^{-1}\left(k\right){\stackrel{\_}{h}}_i\left(k\right)\right]}^{-1}{h}_i^{†}\left(k\right)R_{i,\stackrel{\_}{n}}^{-1}\left(n\right)& \left(39\right)\\ \mathrm{Where},R_{i,\stackrel{\_}{n}}\left(k\right)=\underset{i\ne j}{.Math.}{\stackrel{\_}{h}}_j\left(k\right){\stackrel{\_}{h}}_j^{†}\left(k\right){\sigma }_{a_j}^2+{\sigma }_n^2& \left(40\right)\end{array}$

where σ.sub.ai.sup.2 is the variance of the i.sup.th user data. The MSE for the i.sup.th user is given by

[00068]$\begin{array}{cc}{\hat{r}}_{i,\mathrm{ee}}=\frac{1}{M}\underset{k=0}{\overset{M-1}{.Math.}}{\left[{\sigma }_{a_i}^2+{\stackrel{\_}{h}}_i^{†}{R}_{i,\hat{n}}^{-1}\left(k\right){\stackrel{\_}{h}}_i\left(k\right)\right]}^{-1}& \left(41\right)\end{array}$

Taking the IDFT of zi(k) gives the time domain decision variable for detecting i.sup.th user. The constellation de-rotation can be performed on z.sub.i(k).

Single User WL Equalizer

[0106] The single user WL equalizer is designed by collecting the signal (38) and its complex-conjugate and reversed copy in a column format.

[00069]$\left(\begin{array}{c}\stackrel{\_}{y}\left(k\right)\\ {\stackrel{\_}{y}}^{*}\left(M_i-k\right)\end{array}\right)=\left(\begin{array}{c}{\stackrel{\_}{h}}_i\left(k\right)\\ {\stackrel{\_}{h}}_j^{*}\left(M_i-k\right)\end{array}\right)a_i\left(k\right)+\underset{j\ne i}{.Math.}\left(\begin{array}{c}{\stackrel{\_}{h}}_j\left(k\right)\\ {\stackrel{\_}{h}}_j^{*}\left(M_i-k\right)\end{array}\right)a_j\left(k\right)+\left(\begin{array}{c}\stackrel{\_}{n}\left(k\right)\\ {\stackrel{\_}{n}}^{*}\left(M_i-k\right)\end{array}\right)$

[0107] In compact matrix form:

[00070]$\begin{array}{cc}\tilde{y}\left(k\right)={\tilde{h}}_i\left(k\right)a_i\left(k\right)+\underset{i\ne j}{.Math.}{\tilde{h}}_j\left(k\right)a_j\left(k\right)+\tilde{n}\left(k\right)& \left(43\right)\end{array}$

[0108] The received signal (43) is filtered using vector-valued feed-forward filter {tilde over (w)}.sub.i(k) to obtain {tilde over (z)}.sub.i(k)={tilde over (w)}.sub.i(k){tilde over (y)}.sub.i(k): where {tilde over (z)}.sub.i(k) is a scalar valued frequency domain equalized signal for the i.sup.th user. Following the MMSE approach, the expression for FFF is given by:

[00071]$\begin{array}{cc}{\tilde{w}}_i\left(k\right)={\left[{\sigma }_{a_i}^2+{\tilde{h}}_i^{†}\left(k\right)R_{i,\tilde{n}}^{-1}\left(k\right)h_i\right]}^{-1}{\tilde{h}}_i^{†}\left(k\right)R_{i,,\tilde{n}}^{-1}\left(k\right)& \left(44\right)\\ \mathrm{where},R_{i,,\tilde{n}}\left(k\right)=\underset{i\ne j}{.Math.}{\tilde{h}}_j\left(k\right){\tilde{h}}_j^{†}\left(k\right){\sigma }_{a_i}^2+{\sigma }_n^2& \left(45\right)\end{array}$

where σ.sub.ai.sup.2 is the variance of the i.sup.th user data. The MSE for the i.sup.th user is given by

[00072]$\begin{array}{cc}{\tilde{r}}_{i,\mathrm{ee}}=\frac{1}{M}\underset{k=0}{\overset{M-1}{.Math.}}{\left[{\sigma }_{a_i}^2+{\tilde{h}}_i^{†}\left(k\right)R_{i,,\tilde{n}}^{-1}\left(k\right){\tilde{h}}_i\left(k\right)\right]}^{-1}& \left(46\right)\end{array}$

[0109] Taking the IDFT of {tilde over (z)}.sub.i(k) gives the time domain decision variable for detecting i.sup.th user. The constellation de-rotation can be performed on z.sub.i(k).

[0110] FIG. 6 a flow diagram illustrating a method 600 for processing the received data stream, according to the embodiments as disclosed herein. At the step 602, the method 600 includes receiving the data stream. In an embodiment, the method 600 allows the receiving unit 502 to receive the data stream. In an embodiment, the data stream comprises the ISI between modulated data symbols of the data stream.

[0111] At the step 604, the method 600 includes suppressing the ISI between the modulated data symbols in the data stream. In an embodiment, the method 600 allows the vector/matrix-valued filter 504 to suppress the ISI between the modulated data symbols in the data stream.

[0112] At the step 606, the method 600 includes converting the received data stream to time domain for detection of a signal. In an embodiment, the method 600 allows the converting unit 506 to convert the received data stream to the time domain for detection of the signal after suppressing the ISI.

[0113] At the step 608, the method 600 includes eliminating the constellation rotation in the received data stream. At the step 610, the method 600 includes eliminating the cyclic prefix or cyclic suffix from the received data stream.

[0114] The various actions, acts, blocks, steps, and the like in method 600 may be performed in the order presented, in a different order or simultaneously. Further, in some embodiments, some actions, acts, blocks, steps, and the like may be omitted, added, modified, skipped, and the like without departing from the scope of the invention.

[0115] FIG. 7 shows the sequence of steps involved during signal reception in the GMMSE receiver design. At the step 702, the method 700 includes providing a vector-matrix representation of multi-user signals in the frequency domain using the M-subcarrier for each user. At the step 704, the method 700 includes performing frequency domain filtering of signals using the multi-user GMMSE receiver after providing the vector-matrix representation of multi-user signals in the frequency domain. At the step 706, the method 700 includes converting, by the receiver, each user data to time domain for signal detection after performing frequency domain filtering of signals.

[0116] The various actions, acts, blocks, steps, and the like in method 700 may be performed in the order presented, in a different order or simultaneously. Further, in some embodiments, some actions, acts, blocks, steps, and the like may be omitted, added, modified, skipped, and the like without departing from the scope of the invention.

[0117] FIG. 8 shows the sequence of steps involved in during signal reception the single user MMSE receiver design. At the step 802, the method 800 includes providing the vector-matrix representation of the single-user signals with the interference in the frequency domain using the M-subcarrier for each user. At the step 804, the method 800 includes performing the frequency MMSE filtering of signals using the single user MMSE receiver after providing the vector-matrix representation of the single-user signals with the interference in the frequency domain. At the step 806, the method 800 includes converting each user data to time domain for the signal detection after performing the frequency MMSE filtering of signals.

[0118] The various actions, acts, blocks, steps, and the like in method 800 may be performed in the order presented, in a different order or simultaneously. Further, in some embodiments, some actions, acts, blocks, steps, and the like may be omitted, added, modified, skipped, and the like without departing from the scope of the invention.

[0119] FIG. 9 shows the sequence of steps during signal reception in the single user WL MMSE receiver design. At the step 902, the method 900 includes providing the vector-matrix representation of single-user signal with interference in the frequency domain using the M-subcarrier for each user. At the step 904, the method 900 includes performing constellation de-rotation frequency/time domain after providing the vector-matrix representation of single-user signal with interference in the frequency domain. At the step 906, the method 900 includes performing frequency WL MMSE filtering of signals and it's conjugated and frequency reversed copy using single user WL MMSE receiver. At the step 908, the method 900 includes converting each user data to the time domain for the signal detection.

[0120] The various actions, acts, blocks, steps, and the like in method 900 may be performed in the order presented, in a different order or simultaneously. Further, in some embodiments, some actions, acts, blocks, steps, and the like may be omitted, added, modified, skipped, and the like without departing from the scope of the invention.

[0121] The foregoing description of the specific embodiments will so fully reveal the general nature of the embodiments herein that others can, by applying current knowledge, readily modify and/or adapt for various applications such specific embodiments without departing from the generic concept, and, therefore, such adaptations and modifications should and are intended to be comprehended within the meaning and range of equivalents of the disclosed embodiments. It is to be understood that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Therefore, while the embodiments herein have been described in terms of preferred embodiments, those skilled in the art will recognize that the embodiments herein can be practiced with modification within the spirit and scope of the embodiments as described herein.