Apparatus and method for single antenna interference cancellation (SAIC) enhancement

Abstract

An interference cancellation (IC) processor, a method, a method of manufacturing a semiconductor device, and a method of constructing an integrated circuit are provided. The IC processor includes a plurality of mono interference cancellation (MIC) filter estimation processors, each including a different equalizer offset k.sub.0 and an input for receiving a de-rotated signal, and providing an effective channel h.sub.res,i and an estimated filter p.sub.i; a plurality of filters, each including an input connected to the plurality of MIC filter estimation processors, and an output; a plurality of multipliers, each including a first input connected to the plurality of filters, a second input for receiving a weight, and an output; and a branch combiner including a plurality of inputs connected to the plurality of multipliers, a first output for providing a combined residual channel H.sub.res, and a second output for providing a projected output y of the de-rotated signal.

Claims

1. An interference cancelation (IC) processor, comprising: a plurality of mono interference cancellation (MIC) filter estimation processors, wherein each of the plurality of MIC filter estimation processors includes a different equalizer offset k.sub.0 and includes an input connected to a first input of the IC processor for receiving a de-rotated signal, and a first output that provides an effective channel h.sub.res,i and an estimated filter p.sub.i; a plurality of filters, wherein each of the plurality of filters includes an input connected to the output of one of the plurality of MIC filter estimation processors, and an output; a plurality of multipliers, wherein each of the plurality of multipliers includes a first input connected to the output of one of the plurality of filters, a second input for receiving a weight, and an output; and a branch combiner including a plurality of inputs connected to the outputs of the plurality of multipliers, a first output connected to a first output of the IC processor for providing a combined residual channel H.sub.res, and a second output connected to a second output of the IC processor for providing a projected output y of the de-rotated signal.

2. The IC processor of claim 1, further comprising a de-rotation processor configured to de-rotate a received signal, including an input for receiving a signal, and an output connected to the input of the IC processor.

3. The IC processor of claim 1, further comprising a phase-rotated maximum-likelihood sequence estimation (MLSE) processor, including a first input connected to the first output of the IC processor, a second input connected to the second output of the IC processor, a first output for providing a hard decision of the combined residual channel H.sub.res and the projected output y, and a second output for providing a soft decision of the combined residual channel H.sub.res and the projected output y.

4. The IC processor of claim 2, wherein the received signal is phase shift keying (PSK) modulated that includes interference that is Gaussian minimum shift keying (GMSK) modulated.

5. The IC processor of claim 2, wherein the de-rotation processor is further configured to phase de-rotate the received signal by $=\frac{}{2}$ as follows:
r[t]={tilde over (r)}[t]e.sup.jt=.sub.l=0.sup.L{tilde over (h)}[l]e.sup.jla[tl]e.sup.j(-)(t-l)+.sub.m=0.sup.L{tilde over (g)}[m]e.sup.jmb[tm]+{tilde over (w)}[t]e.sup.jt, wherein $r\left[t\right]=\underset{l=0}{\overset{L}{.Math.}}h\left[l\right]\tilde{a}\left[t-l\right]+\underset{\underset{n\left[t\right]}{}}{\underset{m=0}{\overset{L}{.Math.}}g\left[m\right]b\left[t-m\right]+w\left[t\right]},$ wherein [t]=a[t]e.sup.j(-)t, h[l]={tilde over (h)}[l]e.sup.jl, g[m]={tilde over (g)}[m]e.sup.jm and w[t]={tilde over (w)}[t]e.sup.jt, and wherein effective transmitted symbol [t] is $\frac{}{8}$ rotates, training symbol part a[t] is a binary phase shift keying (BPSK) (1) signal even for 8 phase shift keying (8PSK), [t] is a complex signal due to consecutive $\frac{}{8}$ rotations, {tilde over (r)}[t] is a received signal before phase de-rotation, L is a number of channel taps minus 1, {tilde over (h)}[l] is a channel of a user, {tilde over (g)}[m] is a channel of an interference user, {tilde over (w)}[t] is noise and other interference, r[t] is a received signal after de-rotation, [t] is an equivalent transmit signal after phase de-rotation, h[l] is an equivalent channel of a user after phase de-rotation, g[m] is an equivalent channel of an interference user after phase de-rotation, and w[t] is noise and other interference after phase de-rotation.

6. The IC processor of claim 1, wherein each of the plurality of MIC filter estimation processors is configured to perform temporal interference whitening by determining p.sub.i and h.sub.res,i as solutions to $\underset{p,h_{\mathrm{res}}}{\min }\underset{t\mathrm{TS}}{.Math.}{\left(p^T{r}_t-h_{\mathrm{res}}^T{a}_{t-k_0}\right)}^2,$ wherein k.sub.0 is an equalizer delay, h.sub.res is of length 2(Q.sub.d+1), and p is of length M(Q.sub.p+1) for temporal interference whitening, TS is a training sequence, t and T are integers, r[t] is a received signal after de-rotation, and training symbol part a[t] is a binary phase shift keying (BPSK) (1) signal even for 8 phase shift keying (8PSK).

7. The IC processor of claim 1, wherein each of the plurality of MIC filter estimation processors is configured to perform spatial interference whitening by selecting a BB interference whitening matrix P.sub.S=R.sub.ee.sup.1/2, wherein R.sub.ee is estimated by training symbols (TS) as follows: $R_{\mathrm{ee}}=E\left[e_T\left[t\right]{e_T\left[t\right]}^T\right]\frac{\underset{t\mathrm{TS}}{.Math.}\left(y_T\left[t\right]-H_{\mathrm{res},T}{a}_t\right){\left(y_T\left[t\right]-H_{\mathrm{res},T}{a}_t\right)}^T}{.Math.\mathrm{TS}.Math.},$ where $e_T\left[t\right]:=\left[\begin{array}{c}{e}_1\left[t\right]\\ e_2\left[t\right]\\ \mathrm{.Math.}\\ e_B\left[t\right]\end{array}\right],$ t and T are integers, y.sub.T[t]=H.sub.res,Ta.sub.t+e.sub.r[t], and a[t] is a binary phase shift keying (BPSK) (1) signal even for 8 phase shift keying (8PSK).

8. The IC processor of claim 3, wherein the phase-rotated MLSE processor is configured to process a burst in two parts by processing a left part of the burst from training symbols from a middle of the burst to a left of the burst, and process a right part of the burst from the training symbols from the middle of the burst to a right of the burst.

9. The IC processor of claim 3, wherein the phase-rotated MLSE processor is configured to determine a maximum likelihood sequence estimation by solving $\underset{\tilde{a}}{\arg \min }\underset{t}{.Math.}{.Math.y\left[t\right]-\underset{l=0}{\overset{Q_d}{.Math.}}{H}_{\mathrm{res}}\left[l\right]\left[\begin{array}{c}{\tilde{a}}_I\left[t-l\right]\\ {\tilde{a}}_Q\left[t-l\right]\end{array}\right].Math.}^2,\mathrm{wherein}$ residue error e[t] is an independent identically distributed (i.i.d.) additive white Gaussian noise (AWGN) process, t and l are integers, y[t]:=h.sub.res.sup.Ta.sub.t+e[t], a[t] is a binary phase shift keying (BPSK) (1) signal even for 8 phase shift keying (8PSK), Q.sub.d is an integer for determining a length of a channel, and .sub.I[t1] and .sub.Q[tl] are equivalent transmit signals after phase de-rotation for a real part of a complex signal, and an imaginary part of a complex signal, respectively.

10. A method of combining channels of a de-rotated signal by an interference cancelation (IC) processor, comprising: generating an effective channel h.sub.res,i and an estimated filter p.sub.i by each of a plurality of mono interference cancellation (MIC) filter estimation processors, wherein each of the plurality of MIC filter estimation processors includes a different equalizer offset k.sub.0 and includes an input connected to a first input of the IC processor for receiving a de-rotated signal; filtering, by a plurality of filters, the generating effective channels h.sub.res,i of each of the plurality of MIC filter estimation processors; multiplying, by a plurality of multipliers, each of the filtered effective channels h.sub.res,i of the plurality of filters by one of a plurality of weights; and generating, by a branch combiner, a combined residual channel H.sub.res and a projected output y of the de-rotated signal.

11. The method of claim 10, further comprising de-rotating, by a de-rotation processor, a received signal, including an input for receiving a signal, and an output connected to the input of the IC processor.

12. The method of claim 10, further comprising generating, by a phase-rotated maximum-likelihood sequence estimation (MLSE) processor, a hard decision of the combined residual channel H.sub.res and the projected output y, and a soft decision of the combined residual channel H.sub.res and the projected output y.

13. The method of claim 11, wherein the received signal is phase shift keying (PSK) modulated that includes interference that is Gaussian minimum shift keying (GMSK) modulated.

14. The method of claim 11, wherein de-rotating, by the de-rotation processor, a received signal is comprised of phase de-rotating the received signal by $=\frac{}{2}$ as follows:
r[t]={tilde over (r)}[t]e.sup.jt=.sub.l=0.sup.L{tilde over (h)}[l]e.sup.jla[tl]e.sup.j(-)(t-l)+.sub.m=0.sup.L{tilde over (g)}[m]e.sup.jmb[tm]+{tilde over (w)}[t]e.sup.jt, wherein $r\left[t\right]=\underset{l=0}{\overset{L}{.Math.}}h\left[l\right]\tilde{a}\left[t-l\right]+\underset{\underset{n\left[t\right]}{}}{\underset{m=0}{\overset{L}{.Math.}}g\left[m\right]b\left[t-m\right]+w\left[t\right]},$ wherein [t]=a[t]e.sup.j(-)t, h[l]={tilde over (h)}[l]e.sup.jl, g[m]={tilde over (g)}[m]e.sup.jm and w[t]={tilde over (w)}[t]e.sup.jt, and wherein effective transmitted symbol [t] is $\frac{}{8}$ rotated, and training symbol part a[t] is a binary phase shift keying (BPSK) (1) signal even for 8 phase shift keying (8PSK), and [t] is a complex signal due to consecutive $\frac{}{8}$ rotations {tilde over (r)}[t] is a received signal before phase de-rotation, L is a number of channel taps minus 1, {tilde over (h)}[l] is a channel of a user, {tilde over (g)}[m] is a channel of an interference user, {tilde over (w)}[t] is noise and other interference, r[t] is a received signal after de-rotation, [t] is an equivalent transmit signal after phase de-rotation, h[l] is an equivalent channel of a user after phase de-rotation, g[m] is an equivalent channel of an interference user after phase de-rotation, and w[t] is noise and other interference after phase de-rotation.

15. The method of claim 10, further comprising performing, by each of the plurality of MIC filter estimation processors, temporal interference whitening by determining p.sub.i and h.sub.res,i as solutions to $\underset{p,h_{\mathrm{res}}}{\min }\underset{t\mathrm{TS}}{.Math.}{\left(p^T{r}_t-h_{\mathrm{res}}^T{a}_{t-k_0}\right)}^2,$ wherein k.sub.0 is an equalizer delay, h.sub.res is of length 2(Q.sub.d+1), and p is of length M(Q.sub.p+1) for temporal interference whitening, TS is a training sequence, t and T are integers, r[t] is a received signal after de-rotation, and training symbol part a[t] is a binary phase shift keying (BPSK) (1) signal even for 8 phase shift keying (8PSK).

16. The method of claim 10, further comprising performing, by each of the plurality of MIC filter estimation processors, spatial interference whitening by selecting a BB interference whitening matrix P.sub.S=R.sub.ee.sup.1/2, wherein R.sub.ee is estimated by training symbols (TS) as follows: $R_{\mathrm{ee}}=E\left[e_T\left[t\right]{e_T\left[t\right]}^T\right]\frac{\underset{t\mathrm{TS}}{.Math.}\left(y_T\left[t\right]-H_{\mathrm{res},T}{a}_t\right){\left(y_T\left[t\right]-H_{\mathrm{res},T}{a}_t\right)}^T}{.Math.\mathrm{TS}.Math.},$ where $e_T\left[t\right]:=\left[\begin{array}{c}{e}_1\left[t\right]\\ e_2\left[t\right]\\ \mathrm{.Math.}\\ e_B\left[t\right]\end{array}\right],$ t and T are integers, y.sub.T[t]=H.sub.res,Ta.sub.t+e.sub.T[t], and a[t] is a binary phase shift keying (BPSK) (1) signal even for 8 phase shift keying (8PSK).

17. The method of claim 12, further comprising processing, by the phase-rotated MLSE processor, a burst in two parts by processing a left part of the burst from training symbols from a middle of the burst to a left of the burst, and process a right part of the burst from the training symbols from the middle of the burst to a right of the burst.

18. The method of claim 12, further comprising determining, by the phase-rotated MLSE processor, a maximum likelihood sequence estimation by solving $\underset{\tilde{a}}{\arg \min }\underset{t}{.Math.}{.Math.y\left[t\right]-\underset{l=0}{\overset{Q_d}{.Math.}}{H}_{\mathrm{res}}\left[l\right]\left[\begin{array}{c}{\tilde{a}}_I\left[t-l\right]\\ {\tilde{a}}_Q\left[t-l\right]\end{array}\right].Math.}^2,$ wherein residue error e[t] is an independent identically distributed (i.i.d.) additive white Gaussian noise (AWGN) process, t and l are integers, y[t]: =h.sub.res.sup.Ta.sub.t+e[t], a[t] is a binary phase shift keying (BPSK) (1) signal even for 8 phase shift keying (8PSK), Q.sub.d is an integer for determining a length of a channel, and .sub.I[tl] and .sub.Q[tl] are equivalent transmit signals after phase de-rotation for a real part of a complex signal, and an imaginary part of a complex signal, respectively.

19. A method of manufacturing a semiconductor device, comprising: forming the semiconductor device as part of a wafer or package that includes a plurality of mono interference cancellation (MIC) filter estimation processors, wherein each of the plurality of MIC filter estimation processors includes a different equalizer offset k.sub.0 and includes an input connected to a first input of the IC processor for receiving a de-rotated signal, and a first output that provides an effective channel h.sub.res,i and an estimated filter p.sub.i; a plurality of filters, wherein each of the plurality of filters includes an input connected to the output of one of the plurality of MIC filter estimation processors, and an output; a plurality of multipliers, wherein each of the plurality of multipliers includes a first input connected to the output of one of the plurality of filters, a second input for receiving a weight, and an output; and a branch combiner including a plurality of inputs connected to the outputs of the plurality of multipliers, a first output connected to a first output of the IC processor for providing a combined residual channel H.sub.res, and a second output connected to a second output of the IC processor for providing a projected output y of the de-rotated signal; and testing the semiconductor device, wherein testing of the semiconductor device is performed using at least one electrical to optical converter, at least one optical splitter that splits an optical signal into at least two optical signals, and at least one optical to electrical converter.

20. A method of constructing an integrated circuit, comprising: generating a mask layout for a set of features for a layer of the integrated circuit, the mask layout having standard cell library macros for: a plurality of mono interference cancellation (MIC) filter estimation processors, wherein each of the plurality of MIC filter estimation processors includes a different equalizer offset k.sub.0 and includes an input connected to a first input of the IC processor for receiving a de-rotated signal, and a first output that provides an effective channel h.sub.res,i and an estimated filter p.sub.i; a plurality of filters, wherein each of the plurality of filters includes an input connected to the output of one of the plurality of MIC filter estimation processors, and an output; a plurality of multipliers, wherein each of the plurality of multipliers includes a first input connected to the output of one of the plurality of filters, a second input for receiving a weight, and an output; and a branch combiner including a plurality of inputs connected to the outputs of the plurality of multipliers, a first output connected to a first output of the IC processor for providing a combined residual channel H.sub.res, and a second output connected to a second output of the IC processor for providing a projected output y of the de-rotated signal; disregarding relative positions of the macros for layout design rule compliance during generation of the mask layout; monitoring the relative positions of the macros for layout design rule compliance after disregarding the relative positions; upon detection of layout design rule noncompliance of the macros, generating an adapted mask layout by adapting the noncompliance macros for layout design rule compliance; generating a mask according to the adapted layout with the set of features for the layer of the integrated circuit; and manufacturing the integrated circuit layer according to the mask.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above and other aspects, features, and advantages of certain embodiments of the present disclosure will be more apparent from the following detailed description, taken in conjunction with the accompanying drawings, in which:

(2) FIG. 1 is a block diagram of a GSM receiver, according to an embodiment of the present disclosure;

(3) FIG. 2 is a block diagram of a multiple input multiple output (MIMO) MIC (MMIC) processor of FIG. 1, according to an embodiment of the present disclosure;

(4) FIG. 3 is a flowchart of a method of SAIC enhancement in a GSM user equipment (UE) receiver, according to an embodiment of the present disclosure;

(5) FIG. 4 is a flowchart of a method of the MMIC processor of FIG. 2, according to an embodiment of the present disclosure;

(6) FIG. 5 is a flowchart of a method of manufacturing an IC processor, according to an embodiment of the present disclosure; and

(7) FIG. 6 is a flowchart of constructing an integrated circuit, according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE PRESENT DISCLOSURE

(8) Hereinafter, embodiments of the present disclosure are described in detail with reference to the accompanying drawings. It should be noted that the same elements will be designated by the same reference numerals although they are shown in different drawings. In the following description, specific details such as detailed configurations and components are merely provided to assist with the overall understanding of the embodiments of the present disclosure. Therefore, it should be apparent to those skilled in the art that various changes and modifications of the embodiments described herein may be made without departing from the scope and spirit of the present disclosure. In addition, descriptions of well-known functions and constructions are omitted for clarity and conciseness. The terms described below are terms defined in consideration of the functions in the present disclosure, and may be different according to users, intentions of the users, or customs. Therefore, the definitions of the terms should be determined based on the contents throughout this specification.

(9) The present disclosure may have various modifications and various embodiments, among which embodiments are described below in detail with reference to the accompanying drawings. However, it should be understood that the present disclosure is not limited to the embodiments, but includes all modifications, equivalents, and alternatives within the spirit and the scope of the present disclosure.

(10) Although the terms including an ordinal number such as first, second, etc. may be used for describing various elements, the structural elements are not restricted by the terms. The terms are only used to distinguish one element from another element. For example, without departing from the scope of the present disclosure, a first structural element may be referred to as a second structural element. Similarly, the second structural element may also be referred to as the first structural element. As used herein, the term and/or includes any and all combinations of one or more associated items.

(11) The terms used herein are merely used to describe various embodiments of the present disclosure but are not intended to limit the present disclosure. Singular forms are intended to include plural forms unless the context clearly indicates otherwise. In the present disclosure, it should be understood that the terms include or have indicate existence of a feature, a number, a step, an operation, a structural element, parts, or a combination thereof, and do not exclude the existence or probability of the addition of one or more other features, numerals, steps, operations, structural elements, parts, or combinations thereof.

(12) Unless defined differently, all terms used herein have the same meanings as those understood by a person skilled in the art to which the present disclosure belongs. Such terms as those defined in a generally used dictionary are to be interpreted to have the same meanings as the contextual meanings in the relevant field of art, and are not to be interpreted to have ideal or excessively formal meanings unless clearly defined in the present disclosure.

(13) According to one embodiment, the present system and method provides SAIC to improve the performance of enhanced data rates for GSM evolution (EDGE), if the desired signal is 8PSK modulated and the interferences are GMSK modulated. The present system and method decomposes the spatial and temporal interference whitening issue into multiple least square issues, where each multiple least square issue (referred to as a branch) is formulated with different equalizer delays and different constraints on the residue channel.

(14) According to one embodiment, the branches are weight combined based on a mean squared error (MSE) of least square solutions before the branches are provided for maximum likelihood sequence estimation (MLSE) processing. By choosing a different main tap in left/right burst processing, the need to calculate a minimum/maximum phase filter prior to MLSE processing is eliminated.

(15) According to one embodiment, a desired signal may be 8PSK modulated and interference may be GMSK modulated. It is understood that the desired signal and interference may be extended to other types, without deviating from the scope of the present disclosure. It is assumed that the channel length is L+1 in chipx1 (i.e., oversampling rate of 1). For single GMSK interference, the received signal may be expressed as in Equation (1) as follows:

(16) $\begin{array}{cc}\tilde{r}\left[t\right]=\underset{l=0}{\overset{L}{.Math.}}\tilde{h}\left[l\right]a\left[t-l\right]e^{j\left(t-1\right)}+\underset{\underset{\tilde{n}\left[t\right]}{}}{\underset{m=0}{\overset{L}{.Math.}}\tilde{g}\left[m\right]b\left[t-m\right]e^{j\left(t-m\right)}+\tilde{w}\left[t\right]}& \left(1\right)\end{array}$
where a[t] is 8PSK modulated and its phase rotation

(17) $=\frac{3}{8},b\left[t\right]$
is GMSK modulated and its phase rotation

(18) $=\frac{}{2},\tilde{r}\left[t\right]$
is a received signal before phase de-rotation, L is a number of channel taps minus 1, {tilde over (h)}[1] is a channel of a user, {tilde over (g)}[m] is a channel of an interference user, and {tilde over (w)}[t] is noise and other interference.

(19) For SAIC processing, because the interference is assumed to be GMSK modulated, phase de-rotation of

(20) $=\frac{}{2}$
must be performed, i.e., as in Equation (2) as follows:
r[t]={tilde over (r)}[t]e.sup.jt=.sub.l=0.sup.L{tilde over (h)}[l]e.sup.jla[tl]e.sup.j(-)(t-l)+.sub.m=0.sup.L{tilde over (g)}[m]e.sup.jmb[tm]+{tilde over (w)}[t]e.sup.jt(2)
where r[t] is a received signal after de-rotation.

(21) Thus, Equation (3) is as follows:

(22) $\begin{array}{cc}\tilde{r}\left[t\right]=\underset{l=0}{\overset{L}{.Math.}}h\left[l\right]\tilde{a}\left[t-l\right]+\underset{\underset{n\left[t\right]}{}}{\underset{m=0}{\overset{L}{.Math.}}g\left[m\right]b\left[t-m\right]+w\left[t\right]}& \left(3\right)\end{array}$
where [t]=a[t]e.sup.j(-)t, [t] is an equivalent transmit signal after phase de-rotation, h[l]={tilde over (h)}[l]e.sup.jl, h[l] is an equivalent channel of a user after phase de-rotation, g[m]={tilde over (g)}[m]e.sup.jm, g[m] is an equivalent channel of an interference user after phase de-rotation, w[t]={tilde over (w)}[t]e.sup.jt, and w[t] is noise and other interference after phase de-rotation.

(23) The effective transmitted symbol [t] is

(24) $\frac{}{8}$
rotated, and the training symbol part a[t] is still a BPSK (1) signal even for 8PSK. However, [t] is a complex signal due to the consecutive

(25) $\frac{}{8}$
rotation.

(26) The above complex signal model can be rewritten as an intersymbol interference (ISI) MIMO model with all real components as in Equation (4) as follows:

(27) $\begin{array}{cc}\left[\begin{array}{c}{r}_I\left[t\right]\\ r_Q\left[t\right]\end{array}\right]=\underset{l=0}{\overset{L}{.Math.}}\left[\begin{array}{cc}{h}_I\left[l\right]& -h_Q\left[l\right]\\ h_Q\left[l\right]& h_I\left[l\right]\end{array}\right]\left[\begin{array}{c}{\tilde{a}}_I\left[t-l\right]\\ {\tilde{a}}_Q\left[t-l\right]\end{array}\right]+\left[\begin{array}{c}{n}_I\left[t\right]\\ n_Q\left[t\right]\end{array}\right]& \left(4\right)\end{array}$
where r.sub.I[t] and h.sub.I[l] are real parts of an imaginary signal, and r.sub.Q[t] and g.sub.Q[l] are imaginary parts of a complex signal.

(28) More generally, multiple receive antennas may be taken into account by oversampling (e.g., 2 samples per symbol time). Thus, Equation (5) may be defined as follows:

(29) $\begin{array}{cc}r\left[t\right]=\underset{l=0}{\overset{L}{.Math.}}H\left[l\right]\left[\begin{array}{c}{\tilde{a}}_I\left[t-l\right]\\ {\tilde{a}}_Q\left[t-l\right]\end{array}\right]+n\left[t\right]& \left(5\right)\end{array}$
where H[l] is M2 matrix. r[t] and n[t] are M1 vector, M=2number of Rxoversampling rate. For a single antenna with oversample rate 2, M=4.

(30) In matrix form, by concatenating Q.sub.p chipx1 consecutive time samples, Equation (6) may be defined as follows:
r.sub.t=Ha.sub.t+n.sub.t(6)

(31) The channel matrix of M(1+Q.sub.p)2(1+Q.sub.p+L) is as expressed in Equation (7) as follows:

(32) 0$\begin{array}{cc}H:=\left[\begin{array}{cccccc}H\left[0\right]& \mathrm{.Math.}& H\left[L\right]& 0& \mathrm{.Math.}& 0\\ 0& H\left[0\right]& \mathrm{.Math.}& H\left[L\right]& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & & \mathrm{.Math.}& & \mathrm{.Math.}\\ 0& \mathrm{.Math.}& 0& H\left[0\right]& \mathrm{.Math.}& H\left[L\right]\end{array}\right]& \left(7\right)\end{array}$

(33) A received vector of M(1+Q.sub.p)1: r.sub.t:=[r[t].sup.T r[t1].sup.T . . . r[tQ.sub.p].sup.T].sup.T

(34) A transmitted vector of 2(1+Q.sub.p+L)1: a.sub.t:=[.sub.I[t] .sub.Q[t] . . . .sub.I[tLQ.sub.p] .sub.Q[tLQ.sub.p]].sup.T

(35) An interference vector of M(1+Q.sub.p)1: n.sub.t:=[n[t].sup.T n[t1].sup.T . . . n[tQ.sub.p].sup.T].sup.T

(36) According to one embodiment, MMIC may be referred to as a temporal interference whitening (IW) operation followed by a spatial IW operation.

(37) The present system may perform temporal IW to decompose the issue into multiple least square (LS) issues, where each issue corresponds to a branch, and where each branch is formulated by solving Equation (8) as follows:

(38) $\begin{array}{cc}\underset{p,h_{\mathrm{res}}}{\min }\underset{t\mathrm{TS}}{.Math.}{\left(p^T{r}_t-h_{\mathrm{res}}^T{a}_{t-k_0}\right)}^2& \left(8\right)\end{array}$
where k.sub.0 is some given equalizer delay. h.sub.res is of length 2(Q.sub.d+1), and p is of length M(Q.sub.p+1). To avoid an all zero trivial solution, a constraint must be imposed on either h.sub.res or p. Imposing constraints on h.sub.res generally results in better performance than imposing constraints on p.

(39) For example, when constructing 8 branches, k.sub.0=1, 2, 3 and 4 may be selected. In a GMSK case, the length of h.sub.res may be (Q.sub.d+1). In this case, for 8PSK formulation, the length of h.sub.res may be 2(1+Q.sub.d). Thus, for each , h.sub.res[0]=1 (corresponding to a real part of a complex channel) or h.sub.res[1]=1 (corresponding to an imaginary part of of a complex channel) may be constrained.

(40) Eight branches may be formulated, where each branch corresponds to the solution of the LS issue in Equation (9) as follows:

(41) $\begin{array}{cc}\underset{p,h_{\mathrm{res}}:h_{\mathrm{res}}\left[n\right]=1,}{\min }\underset{t\mathrm{TS}}{.Math.}{\left(p^T{r}_t-h_{\mathrm{res}}^T{a}_{t-k_0}\right)}^2& \left(9\right)\end{array}$
where =1, 2, 3 or 4, and n=0 or 1.

(42) More generally, by choosing different k.sub.0 and a different constraint on h.sub.res, a B number of branches may be formulated as in Equations (10)-(12) as follows:
p.sub.1.sup.Tr.sub.t=h.sub.res,1.sup.Ta.sub.tk.sub.0,1+e.sub.1[tk.sub.0,1](10)
p.sub.2.sup.Tr.sub.t=h.sub.res,2.sup.Ta.sub.tk.sub.0,2+e.sub.2[tk.sub.0,2](11)
. . .
p.sub.B.sup.Tr.sub.t=h.sub.res,B.sup.Ta.sub.tk.sub.0,B+e.sub.B[tk.sub.0,B](12)

(43) By properly shifting with k.sub.0,1, . . . , k.sub.0,B, the following in Equations (13)-(15) is obtained:
y.sub.1[t]: =p.sub.1.sup.Tr.sub.t+k.sub.0,1=h.sub.res,1.sup.Ta.sub.t+e.sub.1[t](13)
y.sub.2[t]:=p.sub.2.sup.Tr.sub.t+k.sub.0,2=h.sub.res,2.sup.Ta.sub.t+e.sub.2[t](14)
y.sub.B[t]:=p.sub.B.sup.Tr.sub.t+k.sub.0,B=h.sub.res,B.sup.Ta.sub.t+e.sub.2[t](15)

(44) By defining

(45) $H_{\mathrm{res},T}:=\left[\begin{array}{c}{h}_{\mathrm{res},1}^T\\ h_{\mathrm{res},2}^T\\ \mathrm{.Math.}\\ h_{\mathrm{res},B}^T\end{array}\right],P_T:=\left[\begin{array}{c}{p}_1^T\\ p_2^T\\ \mathrm{.Math.}\\ p_B^T\end{array}\right],e_T\left[t\right]:=\left[\begin{array}{c}{e}_1\left[t\right]\\ e_2\left[t\right]\\ \mathrm{.Math.}\\ e_B\left[t\right]\end{array}\right],$
and

(46) $y_T\left[t\right]:=\left[\begin{array}{c}{y}_1\left[t\right]\\ y_2\left[t\right]\\ \mathrm{.Math.}\\ y_B\left[t\right]\end{array}\right],$
Equation (16) as follows may be compactly written:
y.sub.T[t]=H.sub.res,Ta.sub.t+e.sub.r[t](16)

(47) After performing temporal IW, the present system may further perform a spatial IW based on a spatial covariance of a residue error. More specifically, BB IW matrix P.sub.S=R.sub.ee.sup.1/2 is selected, where R.sub.ee may be estimated by training symbols as in Equation (17) as follows:

(48) $\begin{array}{cc}{R}_{\mathrm{ee}}=E\left[e_T\left[t\right]{e_T\left[t\right]}^T\right]\frac{\underset{t\mathrm{TS}}{.Math.}\left(y_T\left[t\right]-H_{\mathrm{res},T}{a}_t\right){\left(y_T\left[t\right]-H_{\mathrm{res},T}{a}_t\right)}^T}{.Math.\mathrm{TS}.Math.}& \left(17\right)\end{array}$

(49) After spatial IW, Equation (18) is expressed as follows:
y[t]:=P.sub.Sy.sub.T[t]=P.sub.SH.sub.res,Ta.sub.t+P.sub.Se.sub.T[t]=H.sub.resa.sub.t+e[t](18)
where H.sub.res:=P.sub.SH.sub.res,T and e[t]=P.sub.Se.sub.T[t].

(50) The dimension of H.sub.res is B2(1+Q.sub.d). H.sub.res may be rewritten as H.sub.res=[H.sub.res [0] H.sub.res [1] . . . H.sub.res [Q.sub.d]], where H.sub.res [l] is a B2 real matrix. Then, Equation (18) above may be rewritten as Equation (19) as follows:

(51) $\begin{array}{cc}y\left[t\right]=\underset{l=0}{\overset{Q_d}{.Math.}}{H}_{\mathrm{res}}\left[l\right]\left[\begin{array}{c}{\tilde{a}}_I\left[t-l\right]\\ {\tilde{a}}_Q\left[t-l\right]\end{array}\right]+e\left[t\right]& \left(19\right)\end{array}$

(52) According to one embodiment, the present system approximates R.sub.ee as a diagonal matrix by ignoring off-diagonal elements, i.e., as in Equation (20) as follows:

(53) $\begin{array}{cc}{R}_{\mathrm{ee}}\left[\begin{array}{ccc}{\hat{}}_1^2& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & \mathrm{.Math.}\\ 0& \mathrm{.Math.}& {\hat{}}_B^2\end{array}\right]& \left(20\right)\end{array}$
where

(54) ${\hat{}}_i^2=\frac{\underset{t\mathrm{TS}}{.Math.}{\left(p_i^T{r}_t-h_{\mathrm{res},i}^T{a}_{t-k_{0,i}}\right)}^2}{.Math.\mathrm{TS}.Math.}.$
Then, Equation (21) may be expressed as follows:

(55) $\begin{array}{cc}{P}_S=R_{\mathrm{ee}}^{-1/2}=\left[\begin{array}{ccc}{w}_1& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & \mathrm{.Math.}\\ 0& \mathrm{.Math.}& w_B\end{array}\right]& \left(21\right)\end{array}$
where w.sub.i=1/{circumflex over ()}.sub.i.

(56) With this simplification, the spatial IW is reduced to simple component-wise scaling as in Equation (22) as follows:

(57) 0$\begin{array}{cc}{H}_{\mathrm{res}}=\left[\begin{array}{c}{w}_1{h}_{\mathrm{res},1}^T\\ w_2{h}_{\mathrm{res},2}^T\\ \mathrm{.Math.}\\ w_B{h}_{\mathrm{res},B}^T\end{array}\right],=\left[\begin{array}{c}{w}_1{p}_1^T\\ w_2{p}_2^T\\ \mathrm{.Math.}\\ w_B{p}_B^T\end{array}\right],e\left[t\right]=\left[\begin{array}{c}{w}_1{e}_1\left[t\right]\\ w_2{e}_2\left[t\right]\\ \mathrm{.Math.}\\ w_B{e}_B\left[t\right]\end{array}\right],\mathrm{and}y\left[t\right]=\left[\begin{array}{c}{w}_1{y}_1\left[t\right]\\ w_2{y}_2\left[t\right]\\ \mathrm{.Math.}\\ w_B{y}_B\left[t\right]\end{array}\right]& \left(22\right)\end{array}$

(58) This scaling operation may be viewed as a simplified post-MIC IW process where only the power scaling is performed. In particular, it is assumed that the residual error across different branch outputs are uncorrelated, which may not be necessarily true in practice. However, it is found that the performance gap between using simple scaling and using full spatial IW is quite small.

(59) In a case where a suboptimal MLSE algorithm (e.g. decision feedback sequence estimation (DFSE), reduced state sequence estimation (RSSE)) is used instead of a full MLSE, it may be better to process a burst in two parts: process the left part of the burst from training symbols from the middle to the left, and process the right part of the burst from the training symbols from the middle to the right.

(60) For non-SAIC processing, a minimum phase filter is applied to right burst processing to concentrate channel tap energy to the earliest tap, which may provide better confidence in the sequence estimation algorithm. Likewise, a maximum phase filter may be applied to left burst processing to concentrate tap channel tap energy to a latest tap due to the reversed order in MLSE processing.

(61) For SAIC processing with MMIC, a similar purpose may be achieved without having to find the minimum/maximum phase filters. It may be done by choosing a main-tap differently for a left/right burst. For a right burst, the present system may use the 0-th tap as the main-tap. For 8PSK, the 0-th tap corresponds to the first two components (real and imaginary) of h.sub.res. That is, the present system constrains either h.sub.res[0]=1 or h.sub.res[1]=1 in Equation (8) above. For the left burst, the Q.sub.d-th tap is used as the main-tap. That is, the present system constrains either h.sub.res[2Q.sub.p]=1 or h.sub.res[2Q.sub.p+1]=1 in Equation (8) above.

(62) Assuming the residue error e[t] is an independent identically distributed (i.i.d.) AWGN process, then by adopting Forney's MLSE approach, maximum likelihood sequence estimation may be formulated as in Equation (23) as follows:

(63) $\begin{array}{cc}\underset{\tilde{a}}{\arg \min }\underset{t}{.Math.}{.Math.y\left[t\right]-\underset{l=0}{\overset{Q_d}{.Math.}}{H}_{\mathrm{res}}\left[l\right]\left[\begin{array}{c}{\tilde{a}}_I\left[t-l\right]\\ {\tilde{a}}_Q\left[t-l\right]\end{array}\right].Math.}^2& \left(23\right)\end{array}$

(64) Since [t]=.sub.I[t]+j.sub.Q[t]=a[t]e.sup.j(-)t may be

(65) $\frac{}{8}$
phase-rotated 8PSK signal, the constellation may be time-varying with a period of 16 chipx1 samples. If Equation 24 below is implemented in its nave form, it would require implementing the Viterbi algorithm with a time-varying trellis state, which would require significant complexity. To avoid this, the following equation may be expressed as in Equation (24) as follows:

(66) $\begin{array}{cc}\left[\begin{array}{c}{\tilde{a}}_I\left[t\right]\\ {\tilde{a}}_Q\left[t\right]\end{array}\right]=U\left[t\right]\left[\begin{array}{c}{a}_I\left[t\right]\\ a_Q\left[t\right]\end{array}\right]& \left(24\right)\end{array}$
where U[t] is a 22 rotation matrix, defined by Equation (25) as follows:

(67) $\begin{array}{cc}U\left[t\right]=\left[\begin{array}{cc}\cos \left(-\right)t& -\sin \left(-\right)t\\ \sin \left(-\right)t& \cos \left(-\right)t\end{array}\right]& \left(25\right)\end{array}$

(68) For a rotation matrix, the property in Equation (26) as follows applies:
U[a+b]=U[a]U[b](26)

(69) Thus, Equation (27) is as follows:

(70) $\begin{array}{cc}\underset{l=0}{\overset{Q_d}{.Math.}}{H}_{\mathrm{res}}\left[l\right]\left[\begin{array}{c}{\tilde{a}}_I\left[t-l\right]\\ {\tilde{a}}_Q\left[t-l\right]\end{array}\right]=\underset{l=0}{\overset{Q_d}{.Math.}}{H}_{\mathrm{res}}\left[l\right]U\left[t-l\right]\left[\begin{array}{c}{a}_I\left[t-l\right]\\ a_Q\left[t-l\right]\end{array}\right]=\underset{l=0}{\overset{Q_d}{.Math.}}{H}_{\mathrm{res}}\left[l\right]U\left[-l\right]U\left[t\right]\left[\begin{array}{c}{a}_I\left[t-l\right]\\ a_Q\left[t-l\right]\end{array}\right]=\underset{l=0}{\overset{Q_d}{.Math.}}{\tilde{H}}_{\mathrm{res}}\left[l\right]U\left[t\right]\left[\begin{array}{c}{a}_I\left[t-l\right]\\ a_Q\left[t-l\right]\end{array}\right]& \left(27\right)\end{array}$
where {tilde over (H)}.sub.res[l]=H.sub.res[l]U[l].

(71) To handle U[t], Equation (28) is as follows:

(72) $\begin{array}{cc}U\left[t\right]\left[\begin{array}{c}{a}_I\left[t-l\right]\\ a_Q\left[t-l\right]\end{array}\right]=\left[\begin{array}{cc}{a}_I\left[t-l\right]& -a_Q\left[t-l\right]\\ a_Q\left[t-l\right]& a_I\left[t-l\right]\end{array}\right]\left[\begin{array}{c}\cos \left(-\right)t\\ \sin \left(-\right)t\end{array}\right]& \left(28\right)\end{array}$

(73) A[t] is defined in Equation (29) as follows:

(74) $\begin{array}{cc}A\left[t\right]=\left[\begin{array}{cc}{a}_I\left[t\right]& -a_Q\left[t\right]\\ a_Q\left[t\right]& a_I\left[t\right]\end{array}\right]& \left(29\right)\end{array}$

(75) Thus, Equation (30) is as follows:

(76) $\begin{array}{cc}\underset{l=0}{\overset{Q_d}{.Math.}}{H}_{\mathrm{res}}\left[l\right]\left[\begin{array}{c}{\tilde{a}}_I\left[t-l\right]\\ {\tilde{a}}_Q\left[t-l\right]\end{array}\right]=\left(\underset{l=0}{\overset{Q_d}{.Math.}}{\tilde{H}}_{\mathrm{res}}\left[l\right]A\left[t-l\right]\right)\left[\begin{array}{c}\cos \left(-\right)t\\ \sin \left(-\right)t\end{array}\right]& \left(30\right)\end{array}$

(77) Equation (23) above is equivalent to Equation (31) as follows:

(78) $\begin{array}{cc}\underset{a}{\min }\underset{t}{.Math.}{.Math.y\left[t\right]-\left(\underset{l=0}{\overset{Q_d}{.Math.}}{\tilde{H}}_{\mathrm{res}}\left[l\right]A\left[t-l\right]\right)\left[\begin{array}{c}\cos \left(-\right)t\\ \sin \left(-\right)t\end{array}\right].Math.}^2& \left(31\right)\end{array}$
which does not involve a time-varying constellation. Instead there is a time varying multiplication term

(79) 0$\left[\begin{array}{c}\cos \left(-\right)t\\ \sin \left(-\right)t\end{array}\right].$
This may result in a simplification of an implementation and much less modification to existing code of a non-SAIC MLSE equalizer. Equation (31) above may be referred to as a phase-rotated MLSE. Equation (31) above may be represented by using complex signal notation.

(80) h.sub.c[l] may be a complex channel vector whose real part is the first column of H.sub.res[l] and whose imaginary part is the negative of the second column of H.sub.res[l]. Similarly, {tilde over (h)}.sub.c[l] may be the complex channel vector whose real part is the first column of {tilde over (H)}.sub.res[l] and whose imaginary part is the negative of the second column of {tilde over (H)}.sub.res[l], then Equation (32) is as follows
{tilde over (H)}.sub.res[l]=H.sub.res[l]U[l](32)
and is equivalent to Equation (33) as follows:
{tilde over (h)}.sub.c[l]=e.sup.j(-)lh.sub.c[l](33)

(81) Thus, Equation (34) is as follows:

(82) $\begin{array}{cc}\underset{l=0}{\overset{Q_d}{.Math.}}{H}_{\mathrm{res}}\left[l\right]\left[\begin{array}{c}{\tilde{a}}_I\left[t-l\right]\\ {\tilde{a}}_Q\left[t-l\right]\end{array}\right]=\mathrm{Re}\left\{\underset{l=0}{\overset{Q_d}{.Math.}}{h}_c\left[l\right]\stackrel{~}{}\left[t-l\right]\right\}=\mathrm{Re}\left\{\underset{l=0}{\overset{Q_d}{.Math.}}{h}_c\left[l\right]a\left[t-l\right]e^{j\left(-\right)\left(t-l\right)}\right\}=\mathrm{Re}\left\{e^{j\left(-\right)t}\underset{l=0}{\overset{Q_d}{.Math.}}{\tilde{h}}_c\left[l\right]a\left[t-l\right]\right\}& \left(34\right)\end{array}$

(83) Equation (31) above is equivalent to Equation (35) as follows:

(84) $\begin{array}{cc}\underset{a}{\min }\underset{t}{.Math.}{.Math.y\left[t\right]-\mathrm{Re}\left\{e^{j\left(-\right)t}\underset{l=0}{\overset{Q_d}{.Math.}}{\tilde{h}}_c\left[l\right]a\left[t-l\right]\right\}.Math.}^2& \left(35\right)\end{array}$
where both {tilde over (h)}.sub.c[l] and a[t] are complex valued. Since

(85) $-=-\frac{}{8}$
and a[t] is a 8PSK constellation in the form of

(86) $e^{j\frac{}{4}k}$
(k=0, . . . , 7), actual time-varying complex multiplication does not have to be performed.

(87) In practice, .sub.l=0.sup.Q.sup.d{tilde over (h)}.sub.c[l]a[t1] is implemented in the form of a lookup table (LUT); the present system may generate two LUTs, LUT.sub.0={.sub.l=0.sup.Q.sup.d{tilde over (h)}.sub.c[l]a[tl]} and

(88) ${\mathrm{LUT}}_1=\left\{e^{j\frac{}{8}}\underset{l=0}{\overset{Q_d}{.Math.}}{\tilde{h}}_c\left[l\right]a\left[t-l\right]\right\}.$
For even time samples (t=0, 2, 4, . . . ), the present system may use LUT.sub.0 with a time-varying state index mapping. For odd time samples (t=1, 3, 5, . . . ), the present system may use LUT.sub.1 with a time-varying state index mapping. FIG. 12 described below illustrates a block diagram of the present MMIC system, according to one embodiment. The present system and method improves the 8PSK performance in case of CCI being GMSK modulated.

(89) FIG. 1 is a block diagram of a GSM receiver 100, according to an embodiment of the present disclosure.

(90) Referring to FIG. 1, the GSM receiver 100 includes a phase shift keying (PSK) signal de-rotation processor 101, an MMIC processor 103, and a phase-rotated MLSE processor 105. In an embodiment of the present disclosure, the PSK signal de-rotation processor 101, the MMIC processor 103, and the phase-rotated MLSE processor 105 may be included in one processor (e.g., a digital signal processor (DSP)) or may each be realized in more than one processor.

(91) The PSK signal de-rotation processor 101 includes an input for receiving a PSK signal, and an output. The PSK signal de-rotation processor 101 approximates the received signal as a BPSK signal with consecutive 90 degree phase rotations.

(92) The MMIC processor 103 includes an input connected to the output of the PSK signal de-rotation processor 101, a first output, and a second output. The input of the MMIC processor 103 receives a BPSK approximation of the received signal from the PSK signal de-rotation processor 101. The first output of the MMIC processor 103 provides a combination of residual channels associated with the received signal approximated as a BPSK signal. The second output of the MMIC processor 103 provides a projected output of the received PSK signal approximated as a BPSK signal.

(93) The phase-rotated MLSE processor 105 includes a first input connected to the first output of the MMIC processor 103, a second input connected to the second output of the MMIC processor 103, a first output, and a second output. The first input of the phase-rotated MLSE processor 105 receives the combination of the residual channels from the MMIC processor 103. The second input of the phase-rotated MLSE processor 105 receives the filtered BPSK approximation of the received signal from the MMIC processor 103. The first output of the phase-rotated MLSE processor provides a hard decision associated with an ISI-removed filtered output of the MMIC processor 103. The second output of the phase-rotated MLSE processor 105 provides a soft decision associated with the ISI-removed filtered output of the MMIC processor 103.

(94) FIG. 2 is a block diagram of the MMIC processor 103 of FIG. 1, according to an embodiment of the present disclosure.

(95) Referring to FIG. 2, the MMIC processor 103 includes a plurality of MIC filter estimation processors 201, 203, and 205, a plurality of filters 207, 209, and 211 corresponding to the plurality of MIC filter estimation processors 201, 203, and 205, a plurality of multipliers 213, 215, and 217 corresponding to the plurality of filters 207, 209, and 211, and a branch combiner 219. FIG. 2 illustrates three of each of the plurality of MIC filter estimation processors 201, 203, and 205, the plurality of filters 207, 209, and 211, and the plurality of multipliers 213, 215, and 217. However, the present disclosure is not limited to using three each of these components, but may use any number of each of these components.

(96) Each MIC filter estimation processor 201, 203, and 205, or virtual channel, is referred to as a branch, and is formulated by choosing a different equalizer delay k.sub.0 for each branch. Each MIC filter estimation processor 201, 203, and 205, or virtual channel, includes an input connected to the output of the de-rotation processor 101, an output for outputting a residual channel h.sub.i and an estimated filter p.sub.i for the corresponding branch.

(97) Each input of the plurality of filters 207, 209, and 211, includes an input connected to the output of one of the plurality of MIC filter estimation processors 201, 203, and 205, and an output.

(98) Each of the plurality of multipliers 213, 215, and 217 includes a first input connected to the output of one of the plurality of filters 207, 209, and 211, a second input for receiving a weight w.sub.1, w.sub.2, . . . , w.sub.n corresponding to one of the plurality of MIC filter estimation processors 201, 203, and 205 to which each of the plurality of multipliers 213, 215, and 217 are connected to via the plurality of filters 207, 209, and 211, and an output.

(99) The branch combiner 219 includes a plurality of inputs connected to the outputs of the plurality of multipliers 213, 215, and 217, a first output for providing a combined combined residual channel H.sub.res, and a second output for providing a projected output y.

(100) FIG. 3 is a flowchart of a method of SAIC enhancement in a GSM UE receiver, according to an embodiment of the present disclosure.

(101) Referring to FIG. 3, a PSK signal is received at 301.

(102) At 303, the received PSK signal is de-rotated by a de-rotation processor.

(103) At 305, the de-rotated PSK signal is processed by an MMIC processor to produce a combined residual channel and a projected output of the de-rotated PSK signal.

(104) At 307, the combined residual channel and the filtered output are processed by a phase-rotated MLSE processor to produce a hard decision output and a soft decision output.

(105) FIG. 4 is a flowchart of a method of the MMIC processor 103 of FIG. 1, according to an embodiment of the present disclosure.

(106) Referring to FIG. 4, the MMIC processor 103 receives a de-rotated signal at 401.

(107) At 403, the de-rotated signal is processed by a plurality of MIC filter estimation processors (e.g., MIC filter estimation processors 201, 203, and 205 of FIG. 2), or branches, where each branch is formulated by choosing a different equalizer delay k.sub.0 for each branch, outputs an effective channel h.sub.res,i for the corresponding branch, and outputs an estimated filter p.sub.i for the corresponding branch. For example, three branches may be formulated as expressed in Equations (10)-(12) above.

(108) At 405, the effective channel h.sub.res,i of each of the branches is filtered by a filter.

(109) At 407, each filtered effective channel is multiplied by a weight by a multiplier.

(110) At 409, the weighted and filtered effective channels are combined to produce a residual channel and a projected output of the received signal.

(111) FIG. 5 is a flowchart of a method of manufacturing a semiconductor device, according to an embodiment of the present disclosure.

(112) Referring to FIG. 5, the semiconductor device is formed on a wafer or a package with at least one semiconductor device, where the semiconductor device includes a plurality of MIC filter estimation processors, wherein each of the plurality of MIC filter estimation processors includes a different equalizer offset k.sub.0 and includes an input connected to a first input of the IC processor for receiving a de-rotated signal, and a first output that provides an effective channel h.sub.res,i and an estimated filter p.sub.i; a plurality of filters, wherein each of the plurality of filters includes an input connected to the output of one of the plurality of MIC filter estimation processors, and an output; a plurality of multipliers, wherein each of the plurality of multipliers includes a first input connected to the output of one of the plurality of filters, a second input for receiving a weight, and an output; and a branch combiner including a plurality of inputs connected to the outputs of the plurality of multipliers, a first output connected to a first output of the IC processor for providing a combined residual channel H.sub.res, and a second output connected to a second output of the IC processor for providing a projected output y of the de-rotated signal at 501.

(113) At 503, the functionality of the semiconductor device is tested. Testing the semiconductor device includes testing the semiconductor device using one or more electrical to optical converters, one or more optical splitters that split an optical signal into two or more optical signals, and one or more optical to electrical converters.

(114) FIG. 6 is a flowchart of constructing an integrated circuit, according to an embodiment of the present disclosure.

(115) Referring to FIG. 6, initial layout data is constructed in 601. For example, a mask layout is generated for a set of features for a layer of the integrated circuit, wherein the mask layout includes standard cell library macros for one or more circuit features that include a plurality of MIC filter estimation processors, wherein each of the plurality of MIC filter estimation processors includes a different equalizer offset k.sub.0 and includes an input connected to a first input of the IC processor for receiving a de-rotated signal, and a first output that provides an effective channel h.sub.res,i and an estimated filter p.sub.i; a plurality of filters, wherein each of the plurality of filters includes an input connected to the output of one of the plurality of MIC filter estimation processors, and an output; a plurality of multipliers, wherein each of the plurality of multipliers includes a first input connected to the output of one of the plurality of filters, a second input for receiving a weight, and an output; and a branch combiner including a plurality of inputs connected to the outputs of the plurality of multipliers, a first output connected to a first output of the IC processor for providing a combined residual channel H.sub.res, and a second output connected to a second output of the IC processor for providing a projected output y of the de-rotated signal, and disregarding relative positions of the macros for compliance to layout design rules during the generation of the mask layout.

(116) At 603, a design rule check is performed. For example, the method may check the relative positions of the macros for compliance to layout design rules after generating the mask layout.

(117) At 605, the layout is adjusted. For example, the method, upon detection of noncompliance with the layout design rules by any of the macros, may modify the mask layout by modifying each of the noncompliant macros to comply with the layout design rules.

(118) At 607, new layout data is generated. For example, the method may generate a mask according to the modified mask layout with the set of features for the layer of the integrated circuit. Then, the integrated circuit layer according to the mask may be manufactured.

(119) Although certain embodiments of the present disclosure have been described in the detailed description of the present disclosure, the present disclosure may be modified in various forms without departing from the scope of the present disclosure. Thus, the scope of the present disclosure shall not be determined merely based on the described embodiments, but rather determined based on the accompanying claims and equivalents thereto.