A 1D double-zigzag framework, {[Zn(paps)(2)(H(2)O)(2)](ClO(4))(2)}(n) (1; paps = N,N'-bis(pyridylcarbonyl)-4,4'-diaminodiphenyl thioether), was synthesized by the reaction of Zn(ClO(4))(2) with paps. However, a similar reaction, except that dry solvents were used, led to the formation of a novel 2D polyrotaxane framework, [Zn(paps)(2)(ClO(4))(2)](n) (2). This difference relies on the fact that water coordinates to the Zn(II) ion in 1, but ClO(4)(-) ion coordination is found in 2. Notably, the structures can be interconverted by heating and grinding in the presence of moisture, and such a structural transformation can also be proven experimentally by powder and single-crystal X-ray diffraction studies. The related N,N'-bis- (pyridylcarbonyl)-4,4'-diaminodiphenyl ether (papo) and N,N'-(methylenedi-para-phenylene)bispyridine-4-carboxamide (papc) ligands were reacted with Zn(II) ions as well. When a similar reaction was performed with dry solvents, except that papo was used instead of paps, the product mixture contained mononuclear [Zn(papo)(CH(3)OH)(4)](ClO(4))(2) (5) and the polyrotaxane [Zn(papo)(2)(ClO(4))(2)](n) (4). From the powder XRD data, grinding this mixture in the presence of moisture resulted in total conversion to the pure double-zigzag {[Zn(papo)(2)(H(2)O)(2)](ClO(4))(2)}(n) (3) immediately. Upon heating 3, the polyrotaxane framework of 4 was recovered. The double-zigzag {[Zn(papc)(2)(H(2)O)(2)](ClO(4))(2)}(n) (6) and polyrotaxane [Zn(papc)(2)(ClO(4))(2)](n) (7) were synthesized in a similar reaction. Although upon heating the double-zigzag 6 undergoes structural transformation to give the polyrotaxane 7, grinding solid 7 in the presence of moisture does not lead to the formation of 6. Significantly, the bright emissions for double-zigzag frameworks of 1 and 3 and weak ones for polyrotaxane frameworks of 2 and 4 also show interesting mechanochromic luminescence.
We have synthesized a series of 1D double-zigzag ({[Cd(paps)(2)(H(2)O)(2)](ClO(4))(2)}(n) (1), {[Cd(papo)(2)(H(2)O)(2)](ClO(4))(2)}(n) (3), and {[Cd(papc)(2)(H(2)O)(2)](ClO(4))(2)}(n) (5)) and 2D polyrotaxane frameworks ([Cd(papc)(2)(ClO(4))(2)](n) (6)) by the reaction of Cd(ClO(4))(2) with dipyridylamide ligands N,N'-bis(pyridylcarbonyl)-4,4'-diaminodiphenyl thioether (paps), N,N'-bis(pyridylcarbonyl)-4,4'-diaminodiphenyl ether (papo), and N,N'-(methylenedi-p-phenylene)bispyridine-4-carboxamide (papc), respectively, where their molecular structures have been determined by X-ray diffraction studies. Based on the powder X-ray data (PXRD) of compound 3 and its Zn(II) analogue, heating the double-zigzag framework of compound 3 can give the polyrotaxane framework of [Cd(papo)(2)(ClO(4))(2)](n) (4) and grinding this powder sample in the presence of moisture resulted in its complete conversion back into the pure double-zigzag framework. In addition, heating the double-zigzag frameworks of compounds 1 and 5 can induce structural transformation into their respective polyrotaxanes, whereas grinding these solid samples in the presence of moisture did not lead to the formation of the double zigzags. Herein, we investigated the effect of the metal (from Zn(II) to Cd(II)) on the assembly process and luminescence properties, as well as on the particularly intriguing structural transformation of a series of papx-based frameworks. In fact, the assembly behavior and luminescence properties of the Cd(II)-papx and Zn(II)-papx frameworks were really similar. However, both Zn(II)-papx (x = s, o) frameworks can perform reversible structural transformation, but only the Cd(II)-papo framework can do it. Therefore, a delicate metal effect on such a new structural transformation can be observed.
II. RECEIVED SIGNAL MODELwhere a(¢n)~ [1, e-j¢n, ... ,e-j(L-l)¢n]T is the direcThese code-multiplexed physical channels are mutually orthogonal; more details of the signal structure are provided in [12], though they are not needed here to describe the DOA estimator. The received signals x(k) ~[xl(k), ... , xL(k)]T from N different base stations impinge on an L-element ULA, yielding(1) N x(k) == L a(¢n)s(n)(k) + n(k) n=l Although we consider the signal format of wideband CDMA (WCDMA) because pilot signals are available to train the beamformer, the reversed beamformer can be applied to other systems. Moreover, it is shown in [11] that the reversed array can also be used for blind direction finding, i.e., without a training signal.In the WCDMA downlink, let s(n) (k) denote the transmitted signal from the nth base station at time instant k. It consists of the common pilot channel (CPICH) s~n)(k) and M user traffic channels, which can be written in baseband form asThe DOA estimation technique presented here is also based on estimating a phase difference, but unlike the subarray approach, it exploits the phase difference between the output of a conventional beamformer and that of a reversed beamformer [8] with the same number of antenna signals. As a result, a more accurate DOA estimate is obtained while maintaining a complexity similar to that of the subarray approach. Although reversing the antenna signals has some similarity with forwardbackward averaging techniques and algorithms for centrosymmetric arrays [4], [9], [10], the approach here exploits phase differences rather than the properties of the received signal correlation matrix or subspaces. The phase estimate obtained using the reversed beamformer is an integer multiple of the unknown phase of the signal of interest, so that when dividing by this integer, the corresponding noise variance is reduced compared to the subarray approach.
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