K指數型濾波器的關鍵點是這種濾波器可以保持在相同頻寬下，頻率響應會隨著一個名為k值的參數不同而改變且沒有符元間干擾。當頻寬的滾落率固定時，不同的k值會增加衰減的深度。對於匹配濾波器而言，能有效減少訊號的反射和多重路徑所引的失真與傳統所用的升餘弦濾波器相比。模擬結果顯示，在正交分頻多工系統中且不同多重路徑環境下，使用K指數型濾波器可得到較好的傳輸表現。特別是在調變一個符號內包含的位元數越多時，效果就越顯著，就算通道估測錯誤或是在都卜勒效應影響下，都可以有較好的傳輸品質。

The key point of the K-exponential filter is that the frequency responses of the filter can vary with different specified parameter k without inter symbol interference (ISI) while keeping the same bandwidth. When the rolling factor αof the bandwidth is fixed, different value k will increase the depth of attenuation. For the application to the pulse shaping, it can reduce the signal reflection and multipath distortion that is compared with the traditional Raised cosine filter. Simulation results show that the K index filter obtains the better performance in OFDM systems with different multi-path environments. In particular, the effect is more significant if the modulation symbol contains more bits. Besides, it can provide a better transmission quality even if the channel estimation error or the influence of the Doppler effect is considered.

[1] IEEE Standard 802.11a-1999: Wireless LAN MAC and PHY
Specifications—High-Speed Physical Layer in the 5GHz Band, New York, IEEE, 2000.
[2] M. S. Alouini and A. J. Goldsmith, “A Unified Approach for
Calculating Error Rates of Linearly Modulated Signals over
Generalised Fading Channel,” IEEE Transaction on Communications, vol.47, no.9, pp.1324-1333, SeptE. 1999.
[3] J. Zhang, L. L. Yang, X. Liu and L. Hanzo, “Inter-Carrier
Interference Analysis of OFDM System Communicating over
Rapidly-Fading Nakagami-m Channels,” IEEE 9th International Symposium on Spread Spctram Techniques and
Applications, 2006.
[4] P. Banelli and S. Cacopardi, “Theoretical Analysis and
Performance of OFDM Signals in Nonlinear AWGN
Channels,” IEEE Transaction on Communications, vol.48,
no.3, pp.430-438, March 2000.
[5] B. B. Barrow, “Diversity combination of fading signals with
unequal mean strengths,” IEEE Transaction Communications
System, vol.11, pp.73-78, March 1963.
[6] B. R. Davis, “FM noise with fading channels and diversity,”
IEEE Transaction Communication Technology, vol.COM-19,
pp.1189-1200, December 1971.
[7] H. Kang, W. Hwang and K. Kim, “Performance Analysis of
the OFDM System with one tap Equalizer against the two-ray
Multipath Channel,” IEEE TENCON, pp.45-48, 1999.
[8] M. Nazarathy, “Accurate evaluation of bit-error rates of
optical communication systems using the Gram-Charlier
series,” IEEE Transactions on Communications, vol.54, no.2,
pp.295-301, February 2006.
[9] P. K. Vitthaladevuni, M. S. Alouini and J. C. Kieffer, “Exact
BER computation for cross QAM constellations,” IEEE
Transactions on Wireless Communications, vol.4, no.6,
pp.3039-3050, November 2005.
[10] P. Kylemark, J. Ren, Y. Myslivets, N. Alic, S. Radic, Peter A.
Andrekson and M. Karlsson, “Impact of pump phase-
modulation on the bit-error rate in fiber-optical parametric-
amplifier-based systems,” IEEE Photonics Technology
Letters, vol.19, no.2, pp.79-81, January 2007.
[11] H. Nyquist, “Certain topics in telegraph transmission theory,” AIEE
transactions, vol. 47, pp. 617-644, 1928
[12] Norman C. Beaulieu, Fellow, IEEE, and Mohamed Oussama Damen,
Member, IEEE, “Parametric construction of Nyquist-I pulses,” IEEE
Trans. Commun., vol. 52, No. 12, pp. 2134–2142, Dec. 2004.
[13] Bernard Sklar ,” Digital Communications: Fundamentals and Applications (2nd Edition)”, anuary 21, 2001
[14] Yi-De WEI, Yung-Fang CHEN,” Peak-to-average power ratio (PAPR) reduction by pulse shaping using the K-exponential filter”, IEICE TRANSACTIONS on Communications Vol.E93-B No.11 pp.3180-3183, November 2010
[15] Ramjee Prasad,”OFDM for Wireless Communications Systems”,2004
[16] 3rd Generation Partnership Project Technical Specification Group,’’ 3GPP TS 26.430 V1.0.0 (2009-12) Technical Specification 3rd Generation Partnership Project; Technical Specification Group Services and System Aspects”.
[17] Tardeval, J;Lever, K.V.,” Digital implementation of baseband pulse-shaping filters and modulators for high-capacity QAM digital radio system”, Multi-Level Modulation Techniques and Point-to-Point and Mobile Radio, IEE Colloquium on, 8/1 - 8/5, Mar 1990
[18] Hyunsoo Cheon, Daesik Hong,”Effect of Channel Estimation Error in OFDM-Based WLAN”,IEEE COMMUNICATIONS LETTERS, VOL. 6, NO. 5,p. 190-192,may 2002